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Its +unchanged predecessor bytes, notices, provenance and cumulative source credit +are retained in vendor/g20. Native BIT source word and helper/controller work +retain DreamingOfClouds/eumemic and each original contributor's attribution. +Completed ordinary composition: rohanarun PR185/199/204; PR4760/4814 application +for ai-nanachi with OpenAI Codex assistance. See SOURCES.json and vendor notices. + +Independent checks included here are separate internal AI implementations; +they do not constitute external human acceptance. diff --git a/research/bit-g20-nine-owned-relations/ORDINARY-RESULT.json b/research/bit-g20-nine-owned-relations/ORDINARY-RESULT.json new file mode 100644 index 0000000000..9925183e33 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/ORDINARY-RESULT.json @@ -0,0 +1,169 @@ +{ + "status": "PASS_CONDITIONAL_G20_NINE_RELATIONS_ORDINARY_THREE_FINITE_LEVELS", + "invoice": { + "paid": { + "1": 25227, + "2": 24156, + "3": 1386, + "4": 720, + "5": 1836, + "6": 180, + "7": 162, + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + }, + "targets": { + "4": 72, + "8": 7614, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "127": 222 + }, + "originals": 11238, + "owned_allocated": 11, + "owned_output_credit": 0, + "QUERYs": 56997, + "rank_surplus": 753 + }, + "params": { + "tested": "174199/50000000", + "uniform": "348397/100000000", + "cover_gap": "95367431706161/6553600000000000000000000", + "rho": "1/100", + "v": 1024, + "alpha_gap": "1/549755813888", + "cutoff": 17, + "floor": 18, + "u": "1/5" + }, + "raw_crossing_independent_exact": { + "lower": { + "saving": "4354981663/1250000000000", + "margin": [ + "11340555348878123036008909592367/1250000000000000000000000000000000000000", + "22681110697756246072017819395877/2500000000000000000000000000000000000000" + ] + }, + "upper": { + "saving": "6967970661/2000000000000", + "margin": [ + "-30952647388748809910337337099857/2500000000000000000000000000000000000000", + "-61905294777497619820674673780791/5000000000000000000000000000000000000000" + ] + }, + "tested": { + "saving": "174199/50000000", + "margin": [ + "571783310909751218729713260508338489/500000000000000000000000000000000000000", + "285891655454875609364856630254190381/250000000000000000000000000000000000000" + ] + } + }, + "tail": { + "alpha": [ + "6277101701678533736911774263191374800116154347949458842651/6277101735386680763835789423207666416102355444464034512896", + "3138550850839266868455887131595687400058077173974729527965/3138550867693340381917894711603833208051177722232017256448" + ], + "gamma": [ + "6020186953171155655635684230817080731997608336956948012963/6277101735386680763835789423207666416102355444464034512896", + "188130842286598614238615132213033772874925260529904636669/196159429230833773869868419475239575503198607639501078528" + ], + "delta": [ + "1476005891108099102340667660880386867002669457723736243139/1569275433846670190958947355801916604025588861116008628224", + "738002945554049551170333830440193433501334728861868146855/784637716923335095479473677900958302012794430558004314112" + ], + "normalized_surplus": "536870911/576460753377165312", + "H0": 378121592832, + "H1": 263473235277373441 + }, + "C1": "22832545696632568293839/6553600000000000000000000", + "finite_backend_levels": [ + { + "level": 1, + "completed_backend": "1737729/500000000", + "ordinary_exact": "2283198785515424261090061/655360000000000000000000000", + "admitted": "696776973/200000000000" + }, + { + "level": 2, + "completed_backend": "696776973/200000000000", + "ordinary_exact": "2283254011817888261090061/655360000000000000000000000", + "admitted": "1741984567/500000000000" + }, + { + "level": 3, + "completed_backend": "1741984567/500000000000", + "ordinary_exact": "2283254564083206661090061/655360000000000000000000000", + "admitted": "435496247/125000000000" + } + ], + "admitted": "435496247/125000000000", + "comparator": "1737729/500000000", + "relative_gain": "1063997/434432250", + "relative_gain_percent": "2127994/8688645", + "qualifies_0_1_percent": true, + "uniform_signed_invoice_improvement": "Pnew-Pold=-162H1-162H7; Tnew-Told=-162H8, gain162*(1+7^t-8^t)>0 for0max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice." + }, + "all_in_fixed_primitive_fee": { + "F": "(q+2)^(32*(N+1)^2)*(A(N)+2)^8", + "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.", + "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=11*A(N); F dominates their products.", + "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument." + }, + "stock": { + "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend", + "D": "floor(log_N ceil(e/w))+1", + "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)", + "ownership": "All11whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed." + }, + "eventual_threshold": { + "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.", + "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0", + "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).", + "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized." + } + }, + "whole_kappa": null, + "assumptions": "Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed." +} diff --git a/research/bit-g20-nine-owned-relations/PRIVATE-EPISODES.json b/research/bit-g20-nine-owned-relations/PRIVATE-EPISODES.json new file mode 100644 index 0000000000..23f6d8d383 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/PRIVATE-EPISODES.json @@ -0,0 +1,12737 @@ +[ + { + "owner": 11239, + "stage": 0, + "begin": 21715, + "end": 25785 + }, + { + "owner": 11240, + "stage": 0, + "begin": 6563, + "end": 29084 + }, + { + "owner": 11241, + "stage": 0, + "begin": 6620, + "end": 29085 + }, + { + "owner": 11242, + "stage": 0, + "begin": 6681, + "end": 29086 + }, + { + "owner": 11243, + "stage": 0, + "begin": 6740, + "end": 29087 + }, + { + "owner": 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a/research/bit-g20-nine-owned-relations/PROOF.md b/research/bit-g20-nine-owned-relations/PROOF.md new file mode 100644 index 0000000000..951ce90c64 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/PROOF.md @@ -0,0 +1,278 @@ +# G20 partial helpers with nine owned relations + +The admitted conditional ordinary BIT saving is + + 435496247 / 125000000000 = 0.003483969976. + +The comparator is the completed PR4814 supplier +1737729/500000000 = 0.003475458. The relative increase is exactly +1063997/434432250, or 2127994/8688645 percent (about 0.24491667%). +This is a BIT component result. No complete multiplication coefficient or +selected result is changed. All native, arbitrary-function/all-column, +ROW/spectator, mixed-target finite compiler, ordinary fallback, precision +and fixed-tape hypotheses retained by PR4760/PR4814 remain hypotheses. + +## Sources, ownership and credit + +The two-transport source word is due to DreamingOfClouds (PR589), following +eumemic's 111-port construction (PR555) and their credited predecessors. +Cinna Davis / 1337isnot1337 supplies the query-thinned controller, physical +port/ROW interface and delayed-cover bridge. The productive helper +restriction and finite ordinary bootstrap follow our PR4760 and PR4814. +The finite bootstrap is prior work of rohanarun (PR185/199/204), not a new +general compiler theorem. The unchanged exact interval engine credits zxv +and Jacob Alan Sussman's mixed-target recursion; its source notices remain. + +Ali Romman's PR5421, head +295b00764305694b3c510d3b0bebc2ab024a7809, supplies the nine-owned-relation +method. We rederive it on a different actual word: the previously private +G20 partial436/capture-shadow producer. Its complete frozen source and +proof are included unchanged under vendor/g20, together with its public +predecessor source pins. It was not a previously published or externally +approved mathematical result. The nine pivots here are 469 through 477, +not the pivots in PR5421. Public5421 has 661 original fields; our source +has 658 and retains its four partial-rank4 helper jobs. These contracts +are not substituted for one another. Substantial OpenAI Codex assistance +was used. New work is Apache-2.0; vendor notices remain unchanged. + +VENDOR-PINS.json records the exact immutable closure. Old absolute paths +inside historical provenance are descriptive; no executable in the new +scientific package reads a workspace path or network service. + +## 1. The actual G20 word and changed premise + +The source has 111 X fields, 111 Y fields, 436 arbitrary helper fields, +one owned rank7 capture centre (658), and one owned shadow (659). Its +productive helper targets are 432 rank8 and four rank4 jobs. Its complete +local paid profile is + + P0={1:1318,2:1342,3:77,4:40,5:102,6:10,7:18}. + +G20's positive-fee shadow window replaces [1,3,3] by [3,4] at the actual +helper464/SOURCE0 interaction. The frozen proof describes both directions, +the fresh rank4 matcher and the paid shadow's exact lifetime. The new +verifier does not merely trust the profile: it checks every instruction +of the emitted inverse, every current FRAME, proper nested residual and +common-FRAME XOR. The exact frame induction proves arbitrary-function +correctness; finite q101 and q101^2 sparse controls exercise every one of +the 660 distinct entry symbols. The integer majorant bounds cancellation +free growth; it is not an integer-valued endpoint identity. + +This construction changes the initial-data contract by retiring nine +independent helper targets and owning those fields. It does not reopen +the closed unchanged-word QUERY-fusion or wrong-FRAME cache censuses. +No surviving arbitrary original is cleared or presumed zero. + +## 2. Nine paid owned relations + +Replay the actual G20 inverse in scalar F2 symbols and record the current +SOURCE row at every one of its nine COPY entries. Gaussian elimination +using helper columns gives nine independent rows. Each reduced row has +exactly its own pivot among {469,...,477}; its other terms are X fields +0,...,110. Every term has the actual full8 entrance FRAME1, and each pivot +has a complete full8 target (birth FRAME0, exit FRAME1). None is one of +the four partial helpers 462,463,466,468. + +Own the nine pivots. At entry, erase each entire owned payload and XOR +the other terms of its relation into it at FRAME1. These 523 pointwise +XORs are paid. They set all nine recorded COPY forms to zero while +preserving the 649 independent retained fields. The capture centre and +shadow also receive paid whole-payload entry erasures; arbitrary DIRTY +entry values in all eleven owned fields therefore have no output effect. + +Chronological exact replay shows nine rank1 QUERYs occur on whole zero +fields and all nine rank7 COPY values are zero. Only these eighteen +charged jobs disappear. A free zero FRAME change requires the entire +symbolic function to be zero, not only its scalar bitmap. The centre is +kept zero with paid erasure/header operations; no immutable old SOURCE +ticket remains. The original shadow operations remain. At exit each +pivot receives a paid whole-payload erasure, and all eleven owned fields +return to their declared zero/end headers. + +The actual resulting profile and complete local operations are + + P1={1:1309,2:1342,3:77,4:40,5:102,6:10,7:9}, + 19595 XORs, 39 whole ERASEs, 1 zero INIT, 9 zero FRAME changes. + +All 660 independent RAW/DIRTY entry columns are checked: the retained +649-field map is (X,Y)->(X,Y+X), identity on the 427 retained helpers, +and every owned output is zero. Native controls include the complete +paired HEAD/TAIL function, not just the scalar rows. Missing initial +DIRTY erasure is rejected. Independent checks also reject a changed +relation and an unearned zero transition. + +## 3. Why the reverse body serves every thick caller + +Let P be an actual port rank1 projector, K=I-P and let D denote the +paired ADDRESS interchange, including the source's fixed bank reversal. +Exact rational checks give D_P^2=D_K^2=D_I^2=I and +D_I D_P=D_P D_I=D_K. These are ADDRESS compositions. Their induced data +permutations commute and have the same involution laws. + +With the two-field shear M over F2, both the original forward and inverse +physical endpoints are + + diag(D_I,D_K) M diag(D_P,I) + = diag(D_P,I) M diag(D_I,D_K) + = [[D_K,0],[D_I,D_K]]. + +The bottom-left term in its square is zero by characteristic two and +commutation. Each retained helper has physical endpoint D_U for its +actual full8 or partial4 projector U; D_U is also an involution. Owning +and restoring the nine retired helpers does not change any surviving +physical output. Thus the new inverse implementation realizes exactly +the previous physical thick-call operator in either direction. + +Every new thick core explicitly starts at base.final and ends at +base.start. These are its internal decomposition coframes. We do not +claim that they equal the old forward internal headers. The outer paid +rho15 entry/return is unchanged and conjugates the same physical operator, +so no additional unimplemented physical map is hidden in a header +relabeling. All 111 exact rho matrices and P/K complements are checked. +For multiplicity f tensor every projector/route with I_f and retain the +whole ROW and spectator coordinates. The identities remain exact under +the inherited streaming/native interface; different ports receive no +common free physical chart. + +## 4. Literal global word and full target debit + +The p16/a7 controller has eighteen thick calls and fifteen thin stages. +We instantiate the new body on its actual source/target banks, reuse +nine separately owned pivot arrays between calls, and keep the centre +and shadow separate. No erased helper remains an independent input. +The global domain has 11238 independent retained fields and eleven +owned arrays, with paid initialization, clear and teardown. Distinct +owned banks are reserved again for every compiled unit instance, +including suspended instances; they are never credited as DATA targets. + +The literal tape has 456232 events, canonical SHA256 +30f5f0cc16bb700465d05cafa04b6d15b86289721c84671a17cf41ecb2b86c4e. +It checks all 11249 independent RAW/DIRTY entry columns, all eighteen +exact mapped cores and owned returns. There are 1845 nonzero owned +payload episodes. Exact controller group-ring evaluation gives the +prescribed diagonal monomial on all 32 main bank inputs, including the +real scalar boundaries. Independent orthogonal stage factors and the +local arbitrary-function statement lift it to the complete function +operator. Source descriptors bind every actual prefix, owner, version, +epoch and geometric job; a RAW bitmap is only additional control data. + +The entire target inventory is + + T={4:72,8:7614,15:444,22:444,29:444,36:444, + 43:444,50:444,57:444,64:222,127:222}. + +The entire paid inventory is + + P={1:25227,2:24156,3:1386,4:720,5:1836,6:180,7:162, + 14:444,21:444,28:444,35:444,42:444,49:444,56:444,63:222}. + +There are 56997 paid QUERYs and rank surplus753. Relative to G20 this is +-162 H1 -162 H7 in paid jobs and -162 H8 in targets. All four partial +helpers per call remain credited exactly once. For any 00, by strict subadditivity. +No lost target, CLEAR, normalizer or consumer cost is treated as free. + +Every retained target descriptor has exactly its old matcher, port, +physical job, ROW routes and domain, with only a compact owner renaming. +MAIN projectors are the exact central P or I8 plus disjoint coordinate +stage projectors. All helper projectors are checked over Q. For each +actual projector U, U^2=U=U^T and the paired D_U is a symmetric ADDRESS +involution. Its induced FUNCTION permutation therefore satisfies +A^-1=A=A^T=A^-T. The whole target operator is their direct sum. The SAME +complete literal program, with eleven newly paid owned banks, supplies +forward, inverse, transpose and inverse-transpose under the identical +external domain. We never reverse or transpose a destructive erasure. +This is an operator statement, not a scalar-bit-transpose inference. + +## 5. Complete finite fees and compiler + +The new literal invoice counts 389118 XOR passes, 2389 whole owned CLEARs, +18 zero header acquisitions, 162 zero FRAME changes, and 7548 internal +paid port routes. Separate canonical whole-job routing is still 7248 +routes, including 144 partial-helper routes. Even the known zero-centre +header/clear steps and extra conservative initialization/teardown scans +are charged. Before each child, charge + + 4*(11238+11)*56997 = 2564637012 FIELD passes + +for parent parking, input/output, restore and head return. No ancestor +region is swept. Every fixed route and actual current SOURCE normalizer +also carries its positive retained primitive constant. A 1e9 raw-record +cap is not reused as an all-in machine coefficient. + +The new cancellation-free global envelope is 517 bits. The actual +rational base geometry has at most three-bit entries, and the retained +fixed base height bound1024 covers both. All old numerical rank/prime, +precision and tape thresholds are regenerated rather than reused. + +Use tested saving0.00348398, uniform saving0.00348397, tensor power1024, +cutoff17, floor18, and second-moment parameter1/5. Two unchanged rational +interval engines independently check the new complete P/T, including a +strict raw crossing in (0.0034839853304,0.0034839853305). With t=1-tested, + + alpha=P_t/T_t < 1-2^-39, + gamma=P_(t+1/5)/(17^(1/5)*T_t) <31/32, + delta=11238*18/(17^tested*T_t) <19/20. + +Complete every small target on the SAME owner at18^1024, and split every +paid job at17^1024 with all pieces charged. Both decay blocks raised to128 +are below1/16. The normalized contraction surplus is the positive +536870911/576460753377165312. Separation follows from17^64<18^63; +the minimum4 and maximum paid63 are not falsely compared directly. + +The fresh exact finite integer-compiler thresholds are + + H0=378121592832, H1=263473235277373441, N=2^H1. + +The source inequalities for h=1/64, z0 halfway between t and1-uniform +are checked exactly. They are rank-compiler thresholds, not old machine +thresholds. With K=2^262144, use + + J(n)=(n+1)^4*K^(4*n+4), A(1)=K^4, + A(n)=(J(n)+2)^4*(A(n-1)+2)^(4*n+8). + +These oversized finite integers bound productive roles, leaves, compiled +instances and primitive descriptions, including the denominator-clearer +product of smaller widths. Reserve C_N<=11*A(N) whole owned banks. +Let T_arith=(2N+2)^4*(A(N)+2)^2 and H=1026*4^(T_arith+1). +Choose an odd prime q>max(2^45*N^5,2^(2H)) avoiding all finitely compiled +denominators and rank witnesses. These choices precede the input width. +The positive multiplier + + F=(q+2)^(32*(N+1)^2)*(A(N)+2)^8 + +dominates the charged fixed scans, parking, low-type/carry normalizers and +routes in retained primitive invocations, multiplied by the positive +maximum retained primitive/backend constant. It is not a universal unit +machine cost. The inherited bad-class ordinary calls are charged in the +moment/cover argument. ORDINARY-RESULT.json records the corresponding +reserve, borrowed digits and explicit finite eventual-threshold schema. + +## 6. Three finite ordinary backends + +Use cover gap2^-36+10^-20 and atom fraction rho=1/100. The cover prime +inequality 2^45*gap>256 is checked. Begin with the already completed +PR4814 ordinary backend b0=1737729/500000000. At each j=1,2,3 freeze +the completed preceding algorithm, then compile + + a_j=(1-rho)*(uniform-cover_gap)+rho*b_(j-1), + b_j=floor(10^12*a_j)/10^12. + +No algorithm calls itself as its own atom backend. The adapter, stock, +rounding and improvement gaps are all positive. Newly fixed finite +constants and each completed all-width fallback determine a fresh +eventual threshold; the retained proof absorbs every positive coefficient +before taking the input-size limit. The result is b3=0.003483969976. +The astronomical winning uniform program, prime and decimal eventual +threshold are not expanded. This remains a conditional construction, +not a formal or complete multiplication-theorem verification. + +## Open next questions + +An independent universal audit of the retained native/ROW, precision, +fixed-tape and analytic recovery premises is still valuable. A feasible +first step is one caller-bound quantified interface, with explicit all-f +and spectator scope. The present finite checks do not close those +framework assumptions. Further scalar savings alone do not justify a +new exponent: any changed paid mechanism needs a fresh complete target, +ownership, whole-program and ordinary invoice. diff --git a/research/bit-g20-nine-owned-relations/README.md b/research/bit-g20-nine-owned-relations/README.md new file mode 100644 index 0000000000..349a8ea93f --- /dev/null +++ b/research/bit-g20-nine-owned-relations/README.md @@ -0,0 +1,65 @@ +# Ordinary BIT saving 0.003483969976 + +This conditional ordinary BIT supplier admits **435496247/125000000000 = +0.003483969976**, a **0.24491667%** gain over the completed PR4814 endpoint +1737729/500000000. The native program changes: private G20 shadow retiming +is combined with Ali Romman's nine owned capture-relation method from PR5421. +The actual G20 generators and source closure are published here for the first +time. The raw moment crossing is a separate quantity. + +The local word retains649 arbitrary original functions and allocates11 owned +arrays. Its complete18-call caller retains11238 original outputs, debits162 +rank8 helper targets, and pays56997 recursive jobs. Every partial rank4 helper +remains credited exactly once. All11 owned arrays return zero and receive no +productive credit. The literal global prefix envelope is517bits. New finite +fees include parking, scans, routes, precision, distinct owned reserves for +each compiled/suspended instance, and fresh compiler/cover/backend thresholds. + +The written argument and exact rational certificates retain the existing +native/all-column, owned erasure, mixed-target finite compiler, precision/tape +and analytic framework assumptions. The winning enormous uniform program is +algorithm-defined. This package claims an ordinary BIT component improvement; +the selected whole multiplication result remains unchanged. See PROOF.md and +RECORD.json for precise scope and the three finite backend levels. + +## Reproduce + +From a committed repository checkout, using Python3.12 and the standard library: + +```sh +python3 -B scripts/research_package.py --package research/bit-g20-nine-owned-relations --check-only +python3 -B scripts/research_package.py --package research/bit-g20-nine-owned-relations +``` + +The registered wrapper checks immutable inputs and regenerates the scientific +receipts in a fresh private copy. The separate reviewer reconstructs native +FRAME/ownership identities, the literal caller and exact ordinary arithmetic. +Cold normal and optimized checks compare canonical proof-relevant payloads; +timing and compression headers are not mathematical equality tests. +Every runtime input is package-local. VERIFY.json lists no external dependency; +package-local changes trigger its registered replay. A standalone committed +export can run the same verify.py without a live Git checkout. + +## Open next questions + +TASK.json records two scoped requests: independent complete whole-ROW/tape +admission, and a new physical producer/caller mechanism beyond the consumed +nine capture relations. Start with one partial rank4 helper and one owned +relation. A source-sensitive native replay and a full implementation proof are +different checks. No universal barrier or further saving is claimed. + +## Credit and evidence status + +Ali Romman (PR5421) supplied the nine-owned-relation method. The unchanged +source word/controller and cumulative geometry lineage retain DreamingOfClouds, +eumemic and all source-specific authors in vendor notices. PR4760/4814 supplied +the compact productive controller and completed ordinary baseline; finite +acyclic backend composition follows rohanarun's PR185/199/204 lineage. +G20 shadow retiming and this application were prepared for ai-nanachi with +substantial OpenAI Codex assistance. New work is Apache-2.0; retained source +licenses and notices remain in the vendor closure. + +Separate internal AI audits, hosted CI, archival merge and mathematical +acceptance are distinct evidence. No external-human audit, formal verification +of integer multiplication, unconditional theorem, or selected-frontier change +is claimed. diff --git a/research/bit-g20-nine-owned-relations/RECORD.json b/research/bit-g20-nine-owned-relations/RECORD.json new file mode 100644 index 0000000000..501cdde1cc --- /dev/null +++ b/research/bit-g20-nine-owned-relations/RECORD.json @@ -0,0 +1,20 @@ +{ + "schema_version": 1, + "status": "PROPOSED_CONDITIONAL_ORDINARY_BIT_003483969976", + "scientific_base": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "axis": "ordinary_BIT_saving", + "admitted": "435496247/125000000000", + "comparator_PR": 4814, + "comparator_head": "f56ae4533a7d97d782a2c596a33fe844cd051747", + "comparator": "1737729/500000000", + "relative_gain": "1063997/434432250", + "relative_gain_percent": "2127994/8688645", + "raw_paid_profile_changed": true, + "owned_productive_credit": 0, + "whole_kappa_changed": false, + "selected_global_kappa": "605457647/200000000000", + "maintainer_mathematical_review": "Pending", + "external_independent_reproduction": "Not claimed; separate internal AI audits.", + "hosted_CI": "Not yet observed for this proposed package.", + "publication": "Actual PR identity/head/time is recorded only after creation." +} diff --git a/research/bit-g20-nine-owned-relations/REPLAY.json b/research/bit-g20-nine-owned-relations/REPLAY.json new file mode 100644 index 0000000000..1a0bdf73a4 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/REPLAY.json @@ -0,0 +1,83 @@ +{ + "schema_version": 1, + "evidence_kind": "Separate internal AI cold validation; not external or maintainer acceptance.", + "python": "3.12.14 (main, Aug 25 2026, 14:01:42) [MSC v.1944 64 bit (AMD64)]", + "source_manifest_sha256_at_cold_run": "b3a62011ed854709c04976a214d041be5339cc02cac4549532462de632008ca8", + "source_change_after_run": "Only package-local .gitattributes, this receipt and the README rounded gain label are changed after the four cold runs; all mathematical sources, wrappers, immutable inputs and proof payloads are byte-identical. Registered replay and Git-free committed export cold replay passed on ancestor62b41a07894bf1b0042b9dd3f0c0e8060391fb22.", + "canonical_comparison": "Every proof-relevant JSON value and decompressed complete stream; only CPU_seconds/at_utc are excluded. Every unchanged vendor byte is authenticated before and after replay.", + "runs": [ + { + "command": [ + "python", + "-B", + "verify.py" + ], + "returncode": 0, + "wall_seconds": 18.391000000000076, + "result": { + "status": "PASS_G20_NINE_OWNED_RELATIONS_COLD_PRIMARY", + "proof_payloads": 11, + "admitted": "435496247/125000000000", + "python_optimize": 0, + "scope": "Conditional ordinary BIT component; no whole multiplication or external acceptance claim." + } + }, + { + "command": [ + "python", + "-B", + "independent.py" + ], + "returncode": 0, + "wall_seconds": 5.514999999999873, + "result": { + "status": "PASS_G20_NINE_OWNED_RELATIONS_COLD_SEPARATE_AUDIT", + "proof_payloads": 4, + "admitted": "435496247/125000000000", + "python_optimize": 0, + "scope": "Separate internal AI audits, not external or complete theorem verification." + } + }, + { + "command": [ + "python", + "-O", + "-B", + "verify.py" + ], + "returncode": 0, + "wall_seconds": 16.188000000000102, + "result": { + "status": "PASS_G20_NINE_OWNED_RELATIONS_COLD_PRIMARY", + "proof_payloads": 11, + "admitted": "435496247/125000000000", + "python_optimize": 1, + "scope": "Conditional ordinary BIT component; no whole multiplication or external acceptance claim." + } + }, + { + "command": [ + "python", + "-O", + "-B", + "independent.py" + ], + "returncode": 0, + "wall_seconds": 6.342999999999847, + "result": { + "status": "PASS_G20_NINE_OWNED_RELATIONS_COLD_SEPARATE_AUDIT", + "proof_payloads": 4, + "admitted": "435496247/125000000000", + "python_optimize": 1, + "scope": "Separate internal AI audits, not external or complete theorem verification." + } + } + ], + "git_free_committed_export": { + "commit": "62b41a07894bf1b0042b9dd3f0c0e8060391fb22", + "primary": "PASS_G20_NINE_OWNED_RELATIONS_COLD_PRIMARY", + "separate_audit": "PASS_G20_NINE_OWNED_RELATIONS_COLD_SEPARATE_AUDIT", + "export_integrity": "PASS_RESEARCH_EXPORT", + "external_runtime_dependencies": false + } +} diff --git a/research/bit-g20-nine-owned-relations/SOURCE-DESCRIPTORS.json.gz b/research/bit-g20-nine-owned-relations/SOURCE-DESCRIPTORS.json.gz new file mode 100644 index 0000000000..e9474fd6b3 Binary files /dev/null and b/research/bit-g20-nine-owned-relations/SOURCE-DESCRIPTORS.json.gz differ diff --git a/research/bit-g20-nine-owned-relations/SOURCES.json b/research/bit-g20-nine-owned-relations/SOURCES.json new file mode 100644 index 0000000000..44e289e339 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/SOURCES.json @@ -0,0 +1,44 @@ +{ + "schema_version": 1, + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903" + } + ], + "historical_attribution": [ + { + "PR": 5421, + "head": "295b00764305694b3c510d3b0bebc2ab024a7809", + "author": "Ali Romman", + "role": "Nine owned capture-relation method; independently rederived on the distinct G20 partial436 source." + }, + { + "PR": 4814, + "head": "f56ae4533a7d97d782a2c596a33fe844cd051747", + "author": "ai-nanachi with substantial OpenAI Codex assistance", + "role": "Completed ordinary baseline and three finite acyclic backend composition." + }, + { + "PR": 4760, + "head": "ecdfcabd56dfa663ae020733f9f1a88c6644743c", + "role": "Compact productive BIT controller and partial-helper output credit; retained in vendor source closure." + }, + { + "PR": 185, + "head": "561d6ecbbeb94a11b67862ccedd32bfcbad2cae0", + "author": "rohanarun", + "role": "Finite completed ordinary-leaf composition; PR199/204 successors retained in4814 credit." + } + ], + "private_predecessor_disclosure": "G20 shadow-rank4 source was private and unpublished before this PR. Its actual generators, proof and immutable runtime closure are shipped in vendor/g20; it is not represented as a prior public acceptance. Package-local bytes are authenticated by MANIFEST.json and committed export; no workspace or cached foreign Git object is a runtime dependency." +} diff --git a/research/bit-g20-nine-owned-relations/TARGET-INVOLUTIONS.json b/research/bit-g20-nine-owned-relations/TARGET-INVOLUTIONS.json new file mode 100644 index 0000000000..0dc472c591 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/TARGET-INVOLUTIONS.json @@ -0,0 +1,1599 @@ +{ + "status": "PASS_ALL11238_TARGET_PHYSICAL_SYMMETRIC_INVOLUTIONS_AND_SAME_DOMAINS", + "main_templates": { + "MAIN_BANK_0": { + "rank": 15, + "fresh_axes": [ + 8, + 9, + 10, + 11, + 12, + 13, + 14 + ], + "central": "I8", + "P_squared": "P", + "P_transpose": "P", + "D_P_squared": "I", + "D_P_transpose": "D_P" + }, + "MAIN_BANK_1": { + "rank": 15, + "fresh_axes": [ + 8, + 9, + 10, + 11, + 12, + 13, + 14 + ], + "central": "I8", + "P_squared": "P", + "P_transpose": "P", + "D_P_squared": "I", + "D_P_transpose": "D_P" + }, + "MAIN_BANK_2": { + "rank": 22, + 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"retained_helper_frames": { + "1": { + "rank": 8, + "D_P_squared": "I", + "D_P_transpose": "D_P" + }, + "506": { + "rank": 4, + "D_P_squared": "I", + "D_P_transpose": "D_P" + }, + "508": { + "rank": 4, + "D_P_squared": "I", + "D_P_transpose": "D_P" + }, + "509": { + "rank": 4, + "D_P_squared": "I", + "D_P_transpose": "D_P" + } + }, + "target_count": 11238, + "domain_binding": "Retained old owner IDs compactly renamed; all proof-relevant rank/matcher/port/operator/routing fields exactly identical at entry and output. External role permutation is a fixed physical layout choice.", + "physical_function_rule": "For every f tensor P with I_f and retain all spectator axes. D_P is an involutive permutation; therefore its FUNCTION permutation M satisfies M^-1=M=M^T=M^-T on arbitrary DATA. The whole target operator is their direct sum. Run the SAME literal complete GLOBAL programme with11 freshly paid owned banks for each direction; never reverse or transpose a destructive CLEAR.", + "header_rule": "Each new thick body explicitly uses inverse internal birth=base.final, exit=base.start. Exact physical equality to the previous forward body holds for [[D_K,0],[D_I,D_K]] and for every helperD_P. The unchanged paid outer rho15 route therefore conjugates the same physical operator. Internal header labels do not add an unimplemented physical map." +} diff --git a/research/bit-g20-nine-owned-relations/TARGET-OWNERS.json b/research/bit-g20-nine-owned-relations/TARGET-OWNERS.json new file mode 100644 index 0000000000..9016fdcde5 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/TARGET-OWNERS.json @@ -0,0 +1,82220 @@ +[ + { + "original_owner": 0, + "rank": 15, + "matcher": "MAIN_BANK_0", + "port": 0, + "operator": "D_(P_line+selectedorthogonalstageblocks)", + "route_pair_required_in_generic_job_matching": true + }, + { + "original_owner": 1, + "rank": 15, + "matcher": "MAIN_BANK_0", + "port": 1, + "operator": "D_(P_line+selectedorthogonalstageblocks)", + "route_pair_required_in_generic_job_matching": true + }, + { + "original_owner": 2, + "rank": 15, + "matcher": "MAIN_BANK_0", + "port": 2, + "operator": "D_(P_line+selectedorthogonalstageblocks)", + "route_pair_required_in_generic_job_matching": true + }, + { + "original_owner": 3, + "rank": 15, + "matcher": 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paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/staged-fourth-mixture-ceiling/README.md", + "research/r437-two-window-carrier/README.md" + ], + "methods": [ + "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.", + "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls." + ], + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.", + "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.", + "allowed_variations": [ + "Reconstruct either a source ledger or a numeric enclosure with a different method." + ], + "scope_change_triggers": [ + "Importing the primary function and calling its output independent verification.", + "Calling an aggregate histogram or source archive an independently accepted physical supplier." + ], + "overlap_terms": [ + "independent moment", + "rank histogram", + "exact enclosure", + "2979", + "rank7 joint endframes", + "paired extraction", + "joint lowering", + "4088", + "4091", + "4067", + "staged544-mixed-fourth-entry", + "staged-fourth-mixture-ceiling", + "r437-two-window-carrier" + ], + "existing_checks": [ + { + "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.", + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.", + "status": "author-checked", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.", + "evidence": "research/r437-two-window-carrier/README.md", + "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.", + "status": "author-checked", + "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Publish a complete conditional ordinary BIT supplier combining the private G20 shadow-rank4 producer with nine owned capture relations and three finite completed backend levels.", + "scope_change_reason": "Explicit donor assignment targets a genuinely improved fully priced BIT record. The package changes the actual native paid program and target census, including complete ownership/ROW/fee accounting; this is broader than independent moment screening.", + "bottleneck_link": "Remove nine rank1/rank7 pairs per full call while debiting nine rank8 helper targets, and compose the resulting changed invoice into a completed ordinary endpoint.", + "budget_minutes": 120, + "stop_rule": "Require all retained arbitrary columns, owned lifecycle, exact native endpoint and charts, complete paid/target profile, positive fees, three tails, compiler/cover/stock/bootstrap and separate normal/optimized cold checks; refresh public same-axis strict-best comparison before posting.", + "outcome": "completed", + "evidence": "PROOF.md; LOCAL/GLOBAL/TARGET/ORDINARY receipts; separate independent reviews; MANIFEST.json and bounded registered verification.", + "author": "ai-nanachi", + "ai_assistance": "Substantial OpenAI Codex assistance, including separate scientific construction and independent native/ledger/interval audits. These internal AI checks are not external or human acceptance.", + "open_questions": [ + { + "question": "Can the changed native supplier be independently admitted through the complete whole-ROW compiler and fixed-tape implementation?", + "why_it_matters": "Finite exact certificates and inherited uniform implementation contracts have distinct coverage.", + "first_step": "Reproduce the self-contained cold package and inspect one partial rank4 helper plus one owned relation through all-column whole-fibre routing.", + "blocked_by": "The five retained framework/implementation assumptions are not discharged by the finite certificate." + }, + { + "question": "Can a different producer or caller remove further paid native work after the nine independent capture relations are consumed?", + "why_it_matters": "A changed paid profile may raise the ordinary BIT endpoint again.", + "first_step": "Name a new physical boundary mechanism and first derive its complete paid/target relaxation, including every lost helper output and owned scan.", + "blocked_by": "No further legal paid-profile improvement is supplied; fixed-relation ceiling claims do not cover changed words." + } + ] +} diff --git a/research/bit-g20-nine-owned-relations/VENDOR-PINS.json b/research/bit-g20-nine-owned-relations/VENDOR-PINS.json new file mode 100644 index 0000000000..c75576903a --- /dev/null +++ b/research/bit-g20-nine-owned-relations/VENDOR-PINS.json @@ -0,0 +1,586 @@ +{ + "status": "IMMUTABLE_VENDOR_CLOSURE_PINNED", + "source_roles": { + "G20": "Previously private actual partial436/capture-shadow producer included in full; source proof and public predecessor attribution are retained byte-for-byte. Not a prior public mathematical approval.", + "PR5421": "Ali Romman nine-owned-relation method at head295b00764305694b3c510d3b0bebc2ab024a7809, rederived on actual differentG20word.", + "PR4814": "Own merged finite acyclic ordinary bootstrap at f56ae4533a7d97d782a2c596a33fe844cd051747; conservative comparator1737729/500000000.", + "interval_engines": "Unchanged credited zxv rational interval engine plus prior independent series engine. 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"833f3b451506e0f59ee5c00b19f5e34fbe3575a030cbf7f473d220c2afb56fca" + } + ] +} diff --git a/research/bit-g20-nine-owned-relations/VERIFY.json b/research/bit-g20-nine-owned-relations/VERIFY.json new file mode 100644 index 0000000000..2e3231883e --- /dev/null +++ b/research/bit-g20-nine-owned-relations/VERIFY.json @@ -0,0 +1,27 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 240, + "checks": "Package-local input integrity; fresh local native and full literal caller; target symmetric-involution native adapter; two exact moment engines, positive complete finite fees and ordinary three-level compiler." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/independent.py" + ], + "timeout_seconds": 240, + "checks": "Separate no-primary-import 660local/11249global columns, QQ native/owned/frame/ledger/source descriptors and independent positive-series ordinary arithmetic with semantic failure controls." + } + ] +} diff --git a/research/bit-g20-nine-owned-relations/WORD.json.gz b/research/bit-g20-nine-owned-relations/WORD.json.gz new file mode 100644 index 0000000000..6ffe744d17 Binary files /dev/null and b/research/bit-g20-nine-owned-relations/WORD.json.gz differ diff --git a/research/bit-g20-nine-owned-relations/global_relations.py b/research/bit-g20-nine-owned-relations/global_relations.py new file mode 100644 index 0000000000..aed289de8b --- /dev/null +++ b/research/bit-g20-nine-owned-relations/global_relations.py @@ -0,0 +1,104 @@ +"""Literal p16/a7 caller with nine retired helper targets and shared owned work. + +Retains G20 native controller/geometry; uses the independently checked reverse +physical involution at each full call. No old helper target is given to owned work. +""" +from pathlib import Path +from collections import Counter +from hashlib import sha256 +from time import process_time +import gzip,json,importlib.util,sys +import local_relations as L +R=L.R;S=L.S +def need(c,m): + if not c:raise ValueError(m) +def read(p):return L.read(p) +def put(n,x):L.put(n,x) +def run(): + clock=process_time();controller=read(S/'inputs/CONTROLLER.json');base,frames,_=L.source();local=read(R/'WORD.json.gz');owned=local['owned'];pivots=owned[:-2];need(pivots==list(range(469,478)),'Exact retired helper owners') + oldcalls=read(S/'provider/data/CALLS.json');retired={c['helper_owner_begin']+p-222 for c in oldcalls for p in pivots};retained=[i for i in range(11400)if i not in retired];compact={x:i for i,x in enumerate(retained)};N=len(retained);W=list(range(N,N+11));center,shadow=W[:2];pivotwork=dict(zip(pivots,W[2:]));need(N==11238,'New retained original count') + values=[1<0,'Positive rank');source.append({'event':len(events),'prefix_sha256':prefix.hexdigest(),'owner':d,'version':versions[d],'epoch':epochs[d],'rank':k,'detail':detail,'RAW_hex':hex(values[d]),'function_identity':'Exact literal program prefix plus current owner/epoch/version and actual geometric source job; RAW bitmap is extra evidence, not a claim of purity.'});paid[k]+=1;versions[d]+=1;emit(['QUERY',d,k,detail]) + def swap(d,s,why):add(d,s,why);add(s,d,why);add(d,s,why) + def boundary(program,why): + for op,d,s in program: + for p in range(111): + if op=='ADD':add(compact[d*111+p],compact[s*111+p],why) + else:need(op=='SWAP','Controller opcode');swap(compact[d*111+p],compact[s*111+p],why) + boundary(controller['boundaries']['right_program'],'RIGHT_BOUNDARY') + thick=controller['invoice']['thick_stages'];stage_index={s:i for i,s in enumerate(thick)} + for event in controller['physical_events']: + op=event[0] + if op=='LOCAL': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + helper=3552+436*stage_index[stage] + def owner(r): + if r==658:return center + if r==659:return shadow + if r in pivotwork:return pivotwork[r] + return compact[(x if r<111 else y)*111+r%111]if r<222 else compact[helper+r-222] + sx=[values[owner(i)]for i in range(111)];sy=[values[owner(111+i)]for i in range(111)];helpers=[r for r in range(222,658)if r not in pivotwork];before={r:values[owner(r)]for r in helpers} + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'ENTRY']) + start=len(events);lp=Counter();st=local['start'][:];livebegin={} + for ix,e in enumerate(local['records']): + typ,d=e[:2];gd=owner(d) + if typ=='ERASE': + erase(gd,['LOCAL',stage,ix],e[2]);st[d]=e[2] + if gd in livebegin:episodes.append({'owner':gd,'stage':stage,'begin':livebegin.pop(gd),'end':len(events)-1}) + elif typ=='INIT':need(values[gd]==0,'Whole zero INIT');st[d]=e[2];emit(['OWNED_ZERO_HEADER',gd,e[2],stage]) + elif typ=='ADD': + s,f=e[2:];need(st[d]==st[s]==f,'Actual instantiated coframe') + if gd in W and gd not in livebegin:livebegin[gd]=len(events) + add(gd,owner(s),['LOCAL',stage,f,ix]) + elif typ in('Q','ZERO_Q'): + a,b,k=e[2:];need(st[d]==a,'Current instantiated query frame');st[d]=b + if typ=='Q':query(gd,k,['LOCAL_INVERSE',stage,a,b,ix]);lp[k]+=1 + else:need(values[gd]==0,'Zero only free query');emit(['WHOLE_ZERO_FRAME',gd,a,b,k,stage]) + else:raise ValueError('Local opcode '+typ) + need(not livebegin and st==local['final'],'No live local owned state at return') + need(all(values[owner(i)]==sx[i]and values[owner(111+i)]==sy[i]^sx[i]for i in range(111)),'All retained main RAW inputs') + need(all(values[owner(r)]==before[r]for r in helpers)and all(values[w]==0 for w in W),'All427 independent retained helper inputs and11owned returns') + need(lp==Counter(read(R/'LOCAL-RESULT.json')['stats']['paid'])or lp==Counter({int(k):v for k,v in read(R/'LOCAL-RESULT.json')['stats']['paid'].items()}),'Actual local query count') + calls.append({'stage':stage,'pair':pair,'source_bank':x,'target_bank':y,'old_direction_inverse':rev,'new_direction_inverse':True,'helper_old_owner_begin':helper,'core_begin':start,'core_end':len(events),'owned_global_indices':W,'retained_helper_count':427,'paid':dict(lp)}) + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'RETURN']) + elif op=='QUERY_SHEAR': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + for p in range(111): + src,dst=compact[x*111+p],compact[y*111+p];need(values[center]==0,'Clean thin scratch');v=versions[src];begin=len(events);add(center,src,['THIN_COPY',stage,p]);query(center,1,['THIN',stage,p]);add(dst,center,['THIN_DELIVER',stage,p]);need(versions[src]==v,'Thin immutable SOURCE');erase(center,['THIN',stage,p]);episodes.append({'owner':center,'stage':stage,'kind':'THIN','begin':begin,'end':len(events)-1}) + elif op=='IDLE': + _,pair,stages=event;k=7*len(stages) + for bank in(2*pair,2*pair+1): + for p in range(111):query(compact[bank*111+p],k,['WHOLE_IDLE',stages,p]) + elif op=='ADD': + for p in range(111):add(compact[event[1]*111+p],compact[event[2]*111+p],'BRIDGE') + else: + need(op=='SWAP','Known controller event') + for p in range(111):swap(compact[event[1]*111+p],compact[event[2]*111+p],'FINAL_SWAP') + boundary(controller['boundaries']['left_program'],'LEFT_BOUNDARY') + for d in W:erase(d,'GLOBAL_EXIT_TEARDOWN') + need(values==[1<0,'Paid query rank');paid[e[2]]+=1;queries.append((ix,d,versions[d],epochs[d],e[2],rows[d],prefix.hexdigest()));versions[d]+=1 + elif op in('OWNED_ZERO_HEADER','WHOLE_ZERO_FRAME'):need(d in owned and rows[d]==0,'Zero-only frame/header') + else:need(op=='PAID_PORT_ROUTE','Unknown event') + prefix.update(lines[ix]) + need(rows==[1<0,'Full normalized completion surplus') + need(17**64<18**63 and max(tgt)<256,'Proper postcompletion separation') + z=1-uniform;z0=(t+z)/2;d=z0-t;h=F(1,64) + h0=ceil((d*(5+8*h)*v+1+8*v*(1-z0))/(h*d));h1=(h0*(1-z0)/(z-z0)).__floor__()+1 + need(h0==378121592832 and h1==263473235277373441,'Fresh exact rank compiler thresholds') + need(h0>=8*v and h0*h*d>=d*(5+8*h)*v+1+8*v*(1-z0)and h1*(z-z0)>h0*(1-z0),'Both strict compiler gaps') + cover=F(1,2**36)+F(1,10**20);need(2**45*cover>256,'Charged prime/cover surcharge') + c1=uniform-cover;backend=F(1737729,500000000);old=backend;levels=[] + for j in range(3): + a=F(99,100)*c1+F(1,100)*backend;b=F((a*10**12).__floor__(),10**12) + need(backendF(1,1000),'Same-axis publication gain >=0.1 percent') + # Independently recount every finite positive base charge from literal proof data. + ops=g['operation_counts'];scans=sum(ops[k]for k in('ADD','OWNED_CLEAR','OWNED_ZERO_HEADER','WHOLE_ZERO_FRAME'))+22 + park=4*(11238+11)*56997;routes=7548+7248;base=scans+park+routes+g['expanded_event_count']+56997*(32*127**2+8*127**3) + need(scans==391709 and park==2564637012 and base==965996734173 and base<2**64,'All positive scalar/park/route/dimension fees') + need(g['majorant_bits']==517 and 517<1024,'Fresh precision majorant') + fee=r['fee_bounds'];need(fee['base_counts']['all_owned_allocated']==11 and fee['base_counts']['owned_productive_credit']==0,'No owned productive credit') + need(fee['finite_compiler']['N']=='2^'+str(h1),'Fresh finite uniform dimension') + # Semantic failure controls use the mathematical predicates, not echoed outputs. + failures={'unfunded_alpha':not(alpha[1]<1-F(1,1000)),'old_tiny_H0':not(F(171012)*h*d>=d*(5+8*h)*v+1+8*v*(1-z0)), 'insufficient_prime':not(2**20*cover>256),'raw_as_ordinary':not(F('.0034839853304')>(a['stage']+1)&1];fresh=[v for j in selected if j for v in axes[j]['axes']] + need(len(set(fresh))==len(fresh)and all(8<=v<127 for v in fresh),'Fresh orthogonal direct-sum stage axes') + rk=(8 if 0 in selected else 1)+len(fresh);need(rk==1+7*len(selected),'Actual main target rank') + templates[f'MAIN_BANK_{bank}']=rk + helper=set() + for d in targets: + if d['matcher'].startswith('MAIN_BANK_'):need(d['rank']==templates[d['matcher']]and 0<=d['port']<111,'Exact main descriptor') + else: + f=d['native_frame'];helper.add(f);need(d['rank']==frames[str(f)]['dim'],'Actual partial/full target dimension') + need(len(targets)==11238 and helper=={1,506,508,509},'All target classes retained') + out={'status':'PASS_INDEPENDENT_TARGET_DOMAINS_ROUTES_SYMMETRIC_FUNCTION_INVOLUTIONS','at_utc':datetime.datetime.now(datetime.timezone.utc).isoformat(),'ports':111,'rational_rho15':111,'main_templates':32,'helper_frames':sorted(helper),'target_count':11238,'proof':'Exact QQ orthogonal projectors give paired address involutions on every main/helper field. Tensor I_f and spectator identity preserve this. Any involutive permutation has a symmetric FUNCTION permutation matrix, so inverse=transpose=inverse-transpose. Direct sum and identical domain/role layouts preserve this equality; the same complete paid program serves all four requested directions with11 newly allocated owned banks. No destructive ERASE is reversed or transposed. The separate global audit binds every target descriptor to its exact retained old physical operator/matcher/port/routes.'} + (HERE/'TARGET-REVIEW.json').write_text(json.dumps(out,indent=2)+'\n',encoding='utf8');print(json.dumps(out)) +if __name__=='__main__':main() diff --git a/research/bit-g20-nine-owned-relations/local_relations.py b/research/bit-g20-nine-owned-relations/local_relations.py new file mode 100644 index 0000000000..38e547280c --- /dev/null +++ b/research/bit-g20-nine-owned-relations/local_relations.py @@ -0,0 +1,118 @@ +"""Own nine G20 capture relations; retain 649 independent original fields. + +The nine-owned-relation method is Ali Romman's PR5421. The present program +rederives it on the distinct G20 partial436 producer, including its shadow. +Prepared with substantial OpenAI Codex assistance; Apache-2.0. +""" +from pathlib import Path +from collections import Counter +from time import process_time +import gzip,json,hashlib,sys +R=Path(__file__).resolve().parent +S=R/'vendor/g20' +sys.path.insert(0,str(S/'provider')) +from local_ir import Geometry +N=658 +def need(c,m): + if not c:raise ValueError(m) +def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +def put(name,obj): + p=R/name;b=(json.dumps(obj,indent=2)+'\n').encode();p.write_bytes(gzip.compress(b,mtime=0)if p.suffix=='.gz'else b) +def bitids(row):return [i for i in range(N+2)if row>>i&1] +def source():return read(S/'inputs/BASELINE-LOCAL.json.gz'),read(S/'inputs/FRAMES.json')['frames'],read(S/'provider/data/INVERSE.json.gz')['records'] +def relations(program): + rows=[1<>p&1:row^=v + h=row>>222;need(h,'New helper pivot');p=222+(h&-h).bit_length()-1 + for k in basis: + if basis[k]>>p&1:basis[k]^=row + basis[p]=row + need(len(basis)==9,'Nine independent relations') + pm=sum(1<

=4*v*64,'Explicit tensor count envelope') + return{'status':'PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA','base_counts':{'raw_records':raw,'all_XOR_CLEAR_INIT_zeroheader_passes':scans,'parent_parking_FIELD_passes':park,'internal_and_wholejob_routes':routes,'coarse_primitive_count_with_dimension_work':base,'strict_upper':2**64,'all_owned_allocated':11,'owned_productive_credit':0}, + 'fixed_tensor_unit':{'v':v,'K':'2^262144','meaning':'Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting.'}, + 'finite_compiler':{'N':'2^'+str(H1),'J(n)':'(n+1)^4*K^(4*n+4)','A(1)':'K^4','A(n)':'(J(n)+2)^4*(A(n-1)+2)^(4*n+8)','counts':'Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets11distinct owned banks; C_N<=11*A(N). Denominator replication product <=A(n-1)^(n-1).'}, + 'height_prime':{'base_height_bits':1024,'T':'(2*N+2)^4*(A(N)+2)^2','H':'1026*4^(T+1)','q':'Choose odd prime q>max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice.'}, + 'all_in_fixed_primitive_fee':{'F':'(q+2)^(32*(N+1)^2)*(A(N)+2)^8','actual_cost':'F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.','parking':'4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=11*A(N); F dominates their products.','bad_classes':'<=32*N^2 ordinary calls charged separately by the retained moment/cover argument.'}, + 'stock':{'reserve':'[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend','D':'floor(log_N ceil(e/w))+1','borrowed_digits':'D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)','ownership':'All11whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed.'}, + 'eventual_threshold':{'K_j':'At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.','eta_j':'min(rho-a_j,1-rho-a_j,a_j-b_j)>0','e_j':'Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).','scope':'Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized.'}} +def run(): + invoice=L.read(R/'INVOICE.json');glob=L.read(R/'GLOBAL-RESULT.json');P={int(k):v for k,v in invoice['paid'].items()};T={int(k):v for k,v in invoice['targets'].items()} + need(sum(T.values())==11238 and sum(P.values())==56997 and T[4]==72 and T[8]==7614 and P[7]==162,'Actual complete new target/paid bill') + E=load('nine_credited_interval',S/'ordinary-certificate/inputs/credited_intervals.py');I=load('nine_independent_series',S/'ordinary-certificate/inputs/separate_series.py') + tested=F('.00348398');uniform=F('.00348397');cover_gap=F(1,2**36)+F(1,10**20);rho=F(1,100);reserve=F(1,2**39);v=1024;t=1-tested;u=F(1,5) + target=E.moment(T,t);paid=E.moment(P,t);alpha=E.divide(paid,target);gamma=E.divide(E.moment(P,t+u),E.mul(E.power(17,u),target));delta=E.divide((F(11238*18),)*2,E.mul(E.power(17,tested),target)) + need(alpha[1]<1-reserve and gamma[1]0 if sign>0 else margin[1]<0,'Independent root sign '+label);cross[label]={'saving':c,'margin':margin} + need(F(31,32)**1280 and 17**64<18**63 and max(T)<256,'Charged completion, separation and ambient') + z=1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64);H0=ceil((gap*(5+8*h)*v+1+8*v*(1-z0))/(h*gap));H1=(H0*(1-z0)/(z-z0)).__floor__()+1 + need(H0>=8*v and H0*h*gap>=gap*(5+8*h)*v+1+8*v*(1-z0)and H1*(z-z0)>H0*(1-z0),'Fresh finite integer compiler thresholds') + C1=uniform-cover_gap;need(F(2**45)*cover_gap>256,'Cover/bad-prime gap') + backend=F(1737729,500000000);old=backend;levels=[] + for j in range(1,4): + a=(1-rho)*C1+rho*backend;b=F((a*10**12).__floor__(),10**12);need(backendF(1,1000),'New actual ordinary gain clears .1percent publication guard') + result={'status':'PASS_CONDITIONAL_G20_NINE_RELATIONS_ORDINARY_THREE_FINITE_LEVELS','invoice':invoice,'params':{'tested':tested,'uniform':uniform,'cover_gap':cover_gap,'rho':rho,'v':v,'alpha_gap':reserve,'cutoff':17,'floor':18,'u':u},'raw_crossing_independent_exact':cross,'tail':{'alpha':alpha,'gamma':gamma,'delta':delta,'normalized_surplus':surplus,'H0':H0,'H1':H1},'C1':C1,'finite_backend_levels':levels,'admitted':backend,'comparator':old,'relative_gain':backend/old-1,'relative_gain_percent':100*(backend/old-1),'qualifies_0_1_percent':True,'uniform_signed_invoice_improvement':'Pnew-Pold=-162H1-162H7; Tnew-Told=-162H8, gain162*(1+7^t-8^t)>0 for01 else'-O') + for script in scripts: + p=subprocess.run([sys.executable,*flags,str(scratch/script)],cwd=scratch,env=env,stdout=subprocess.PIPE,stderr=subprocess.STDOUT,timeout=180) + need(p.returncode==0,script+' replay failed: '+p.stdout.decode(errors='replace')[-3000:]) + checks=[] + for name in outputs: + expected=HERE/name;actual=scratch/name + need(actual.is_file(),'Missing output '+name) + if name.endswith('.jsonl.gz'):need(gzip.decompress(expected.read_bytes())==gzip.decompress(actual.read_bytes()),'Canonical complete stream '+name) + else:need(canonical(read(expected))==canonical(read(actual)),'Deterministic proof payload '+name) + checks.append(name) + # The input vendor is immutable even inside the scratch replay. + for r in manifest['files']: + if r['path'].startswith('vendor/'): + need(hashlib.sha256((scratch/r['path']).read_bytes()).hexdigest()==r['sha256'],'Vendor changed during replay '+r['path']) + return checks diff --git a/research/bit-g20-nine-owned-relations/target_involutions.py b/research/bit-g20-nine-owned-relations/target_involutions.py new file mode 100644 index 0000000000..097609e78e --- /dev/null +++ b/research/bit-g20-nine-owned-relations/target_involutions.py @@ -0,0 +1,46 @@ +"""Bind every retained target descriptor to the same self-dual physical job.""" +from fractions import Fraction as F +from collections import Counter +import importlib.util,sys,json +import local_relations as L +R=L.R;S=L.S +def need(c,m): + if not c:raise ValueError(m) +def mm(a,b):return[[sum(x*y for x,y in zip(row,col))for col in zip(*b)]for row in a] +def eye(n):return[[F(i==j)for j in range(n)]for i in range(n)] +def swap(p): + n=len(p);return[[(F(i==j)-p[i%n][j%n])if(i>(a['stage']+1)&1];fresh=[a for j in selected if j for a in axes[j]['axes']];need(len(set(fresh))==len(fresh)and all(8<=a<127 for a in fresh),'Disjoint fresh actual stage axes');centralrank=8 if 0 in selected else 1;rank=centralrank+len(fresh);need(rank==1+7*len(selected),'Every actual MAIN target rank') + templates[f'MAIN_BANK_{bank}']={'rank':rank,'fresh_axes':fresh,'central':'I8'if 0 in selected else'P_port','P_squared':'P','P_transpose':'P','D_P_squared':'I','D_P_transpose':'D_P'} + helperframes=sorted({t['native_frame']for t in targets if'native_frame'in t});helperchecked={} + for f in helperframes: + p=B.project(frames[str(f)]);rank=frames[str(f)]['dim'];certP(p,rank);helperchecked[str(f)]={'rank':rank,'D_P_squared':'I','D_P_transpose':'D_P'} + retained=glob['retained_old_ids'];need(len(retained)==11238 and len(set(retained))==11238,'Retained domain independent roles') + for new,t in enumerate(targets): + previous=next(x for x in old if x['original_owner']==retained[new]);need(t['original_owner']==new,'Same retained physical role domain') + need({k:v for k,v in t.items()if k!='original_owner'}=={k:v for k,v in previous.items()if k!='original_owner'},'Exact same rank, matcher, port, physical operator and routes on entry/output') + if t['matcher'].startswith('MAIN_BANK_'):need(t['rank']==templates[t['matcher']]['rank']and 0<=t['port']<111,'Actual complete MAIN field target binding') + else:need(t['native_frame']in helperframes and t['rank']==helperchecked[str(t['native_frame'])]['rank'],'Actual retained partial/full helper binding') + invoice=L.read(R/'INVOICE.json');need(Counter(t['rank']for t in targets)==Counter({int(k):v for k,v in invoice['targets'].items()}),'Full retained target invoice') + result={'status':'PASS_ALL11238_TARGET_PHYSICAL_SYMMETRIC_INVOLUTIONS_AND_SAME_DOMAINS','main_templates':templates,'port_projectors_checked':111,'paid_rho15_checked':111,'retained_helper_frames':helperchecked,'target_count':len(targets),'domain_binding':'Retained old owner IDs compactly renamed; all proof-relevant rank/matcher/port/operator/routing fields exactly identical at entry and output. External role permutation is a fixed physical layout choice.','physical_function_rule':'For every f tensor P with I_f and retain all spectator axes. D_P is an involutive permutation; therefore its FUNCTION permutation M satisfies M^-1=M=M^T=M^-T on arbitrary DATA. The whole target operator is their direct sum. Run the SAME literal complete GLOBAL programme with11 freshly paid owned banks for each direction; never reverse or transpose a destructive CLEAR.','header_rule':'Each new thick body explicitly uses inverse internal birth=base.final, exit=base.start. Exact physical equality to the previous forward body holds for [[D_K,0],[D_I,D_K]] and for every helperD_P. The unchanged paid outer rho15 route therefore conjugates the same physical operator. Internal header labels do not add an unimplemented physical map.'} + L.put('TARGET-INVOLUTIONS.json',result);return {k:result[k]for k in('status','target_count','port_projectors_checked','paid_rho15_checked','retained_helper_frames')} +if __name__=='__main__':print(json.dumps(run(),indent=2)) diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/INPUT-PINS.json b/research/bit-g20-nine-owned-relations/vendor/g20/INPUT-PINS.json new file mode 100644 index 0000000000..2fe34e776a --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/INPUT-PINS.json @@ -0,0 +1,139 @@ +{ + "schema": "g20-private-candidate-inputs/1", + "at_utc": "2026-10-23T00:56:10.848823+00:00", + "files": [ + { + "relative_path": "inputs/BASELINE-LOCAL.json.gz", + "sha256": "4535dde53162b426e597aea9d0106fb1405358f775d9370bd36bfb5686ed21df", + "bytes": 62568, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\native-small\\gate0003\\local-partial\\WORD.json.gz" + }, + { + "relative_path": "inputs/FORWARD.json.gz", + "sha256": "34166a521475f1868293fbd8dbbbac0a9a90d489d7cea9c8ff8d1e7801781f74", + "bytes": 60673, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\center-bit-extension\\gate0020-shadow-assisted-query-fusion\\WORD.json.gz" + }, + { + "relative_path": "inputs/INVERSE.json.gz", + "sha256": "29fb50d17a58e18988df2bdb1f7c65f7a12328ac75c676d34dd31a036aeaf483", + "bytes": 59078, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\center-bit-extension\\gate0022-shadow-fusion-inverse-and-requests\\INVERSE-WORD.json.gz" + }, + { + "relative_path": "inputs/FRAMES.json", + "sha256": 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"9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443", + "bytes": 16874, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\source4359\\current-main-repository\\research\\kappa-rebuild\\bit\\DELAYED-COVER-BRIDGE.md" + }, + { + "relative_path": "inputs/FINITE-PRECOMPILATION.md", + "sha256": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8", + "bytes": 15898, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\source4359\\current-main-repository\\research\\kappa-rebuild\\architecture\\FINITE-PRECOMPILATION.md" + }, + { + "relative_path": "inputs/three-stage-cover-bit.tex", + "sha256": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511", + "bytes": 13061, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\source4359\\current-main-repository\\notes\\three-stage-cover-bit.tex" + }, + { + "relative_path": "inputs/three-stage-cover-rows.tex", + "sha256": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8", + "bytes": 4815, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\source4359\\current-main-repository\\notes\\three-stage-cover-rows.tex" + }, + { + "relative_path": "inputs/02-streams.tex", + "sha256": "606c80db61cad13aa0c3b6060dc4b88dbbe7ac60cdd831aa93f28d908fd09dab", + "bytes": 11311, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261020\\framework\\openai109\\02-streams.tex" + }, + { + "relative_path": "inputs/4814-local_word.py.txt", + "sha256": "bfca7ff22066863086ebdb1cd67d26682fb167b8b11ff9be585f43ad36de06f3", + "bytes": 12478, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\bootstrap-publication\\gitfree-0003\\research\\bit-compact-productive-controller\\local_word.py" + }, + { + "relative_path": "inputs/4814-global_word.py.txt", + "sha256": "601ecd78439e65b46f357e9b2275f6f86c234506687939da1df9259e8422872e", + "bytes": 20395, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\bootstrap-publication\\gitfree-0003\\research\\bit-compact-productive-controller\\global_word.py" + }, + { + "relative_path": "inputs/4814-audit_stream.py.txt", + "sha256": "a0a4ca5c58bf299b1c75ba93caa3cb902b179ca78dfe99e4defb42dd58dfa5dc", + "bytes": 8422, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\bootstrap-publication\\gitfree-0003\\research\\bit-compact-productive-controller\\audit_stream.py" + }, + { + "relative_path": "inputs/4814-independent_native.py.txt", + "sha256": "2bd775c92ae5c79f82606909078c73ccf08eebc369faae2d111f74cb4e73ee87", + "bytes": 6726, + "read_only_origin": "C:\\Users\\AI\\Documents\\\u6570\u5b66\\session-research\\continuous-bit-goal\\resumed\\20261023-reset-to50\\bootstrap-publication\\gitfree-0003\\research\\bit-compact-productive-controller\\independent_native.py" + } + ], + "scope": "Historical4760/4814 and research proof bytes are copied read-only. Runtime provider uses these relative local paths only. No publication/ordinary claim." +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/LATEST-ORDINARY.json b/research/bit-g20-nine-owned-relations/vendor/g20/LATEST-ORDINARY.json new file mode 100644 index 0000000000..212c7f60bf --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/LATEST-ORDINARY.json @@ -0,0 +1,37 @@ +{ + "status": "PRIVATE_CONDITIONAL_ORDINARY_G20_SUCCESSOR_COMPLETE", + "at_utc": "2026-10-23T01:55:19.468032+00:00", + "read_first": "ordinary-certificate/REPORT.txt", + "certificate": { + "path": "ordinary-certificate/RESULT.json", + "bytes": 10418, + "sha256": "1bc9fc591924be76eabb02190ead2a95f162491cbe101f19c76fe34d29b3920e" + }, + "independent": { + "path": "ordinary-certificate/INDEPENDENT.json", + "bytes": 875, + "sha256": "613569326ce0894e85b4834982e0da24934af0ff993fcc21cfa41970a73ec509" + }, + "runtime_manifest": { + "path": "ordinary-certificate/MANIFEST.json", + "bytes": 5309, + "sha256": "77cc1b9a69aba096466df23a180256303ee4f91d9a451d9ab42cb0a80ab427f4" + }, + "normal": { + "path": "ordinary-certificate/cold-normal-0001/RESULT.json", + "bytes": 1101, + "sha256": "3f286af97c97d0001b24503cb6836af6426602f290b1a9170da8eb0c537ff8cb" + }, + "optimized": { + "path": "ordinary-certificate/cold-optimized-0001/RESULT.json", + "bytes": 1100, + "sha256": "490dae20dcc610d06fbdd5dc0e419393d1fa35e16a98bc55c88484ff934adcdc" + }, + "admitted": "217256899/62500000000", + "comparator": "1737729/500000000", + "relative_gain": "40774/217216125", + "relative_gain_percent_decimal": "0.01877116627506360312799061303574953286732", + "whole_kappa": null, + "PR_created": false, + "next": "Root independent exact proof/source/stock/fee review; private future bundle only. Do not decimal-tighten or rewrite old sealed manifests." +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/MANIFEST.json b/research/bit-g20-nine-owned-relations/vendor/g20/MANIFEST.json new file mode 100644 index 0000000000..c4ee5d28a4 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/MANIFEST.json @@ -0,0 +1,75 @@ +{ + "status": "SEALED_PRIVATE_NATIVE_GATE_NO_ORDINARY_BOUND", + "files": [ + { + "relative_path": "README.md", + "bytes": 2534, + "sha256": "ff4c7f3acccc3991c918e2f8381712e988878a84f8c6615760e57177278ff380" + }, + { + "relative_path": "PROOF.md", + "bytes": 8163, + "sha256": "b079c3ea085c531ef64e280dc3ca0b15d8f63012125c16abfc0a280ab21f4bad" + }, + { + "relative_path": "RESULT.json", + "bytes": 3789, + "sha256": "f169477a3312a00436f7a88ba51a2316fb0d88b28de76114ebd4d3bbd7f23cc9" + }, + { + "relative_path": "REPORT.txt", + "bytes": 2034, + "sha256": "ae8d177f19c76ec0bcfec07da3a2dcbd13d52455ce926a93b8291300e444522c" + }, + { + "relative_path": "SOURCEPINS.json", + "bytes": 19690, + "sha256": "2d3f3795be9e4e9e9edf48e2a9d2a985505eacd927382b3d30a27a3713f2a258" + }, + { + "relative_path": "RESTART.json", + "bytes": 1875, + "sha256": "1a005affb5e9607b74eadae954672edc978b5107613cdc5dbb8536f73ed75876" + }, + { + "relative_path": "INPUT-PINS.json", + "bytes": 8913, + "sha256": "5377cdc7d7cef0718ab25cfc383453db4e8260cd4e95e190ee596f31dfaf7c9c" + }, + { + "relative_path": "intake.py", + "bytes": 3205, + "sha256": "5ca233e5fd96978228614b5fc2340bf0862f5386264101b1a894598f52a360ad" + }, + { + "relative_path": "seal.py", + "bytes": 1422, + "sha256": "ba29a0b7e9635109bbc9924bde67a1f5f3f2b4e07554e75730fc6e5d896424c5" + }, + { + "relative_path": "finish.py", + "bytes": 8998, + "sha256": "3b78f7a9c8493ad784056d8f698daecd636637022aebf8870d5f538cc160aeb9" + }, + { + "relative_path": "provider/MANIFEST.json", + "bytes": 8823, + "sha256": "15034901fb7641ff6cf154e3d8e3e82d1f02332a1f54ed52a90bef9667648ca3" + }, + { + "relative_path": "verification-normal-0002/RESULT.json", + "bytes": 4259, + "sha256": "5583a98fab22d5e0195440d4bb5361dbe38c90104b7f5fadfcbb4f945b707957" + }, + { + "relative_path": "verification-optimized-0001/RESULT.json", + "bytes": 4259, + "sha256": "f43b3b49f72bfc2b9371f7cb8debaa55eeb288b9700cb3fee9be61b5de435433" + }, + { + "relative_path": "development/attempt-0001/CORRECTION.json", + "bytes": 660, + "sha256": "78bd2852d129ae4449d86bd59db262ddb72d30da14929fc672963dae6dd24c37" + } + ] +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/PROOF.md b/research/bit-g20-nine-owned-relations/vendor/g20/PROOF.md new file mode 100644 index 0000000000..a39906a78c --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/PROOF.md @@ -0,0 +1,143 @@ +# Native function and ownership certificate + +## One changed window + +The old helper464 schedule has `Q(0,B,1)`, an aligned ADD from SOURCE0 at +`B=frame2`, then `Q(B,C,3)` with `C=frame507`. SOURCE0 later has its own +`Q(B,C,3)`. Between the old ADD and that SOURCE move there is no SOURCE0 +VALUE write. Its later write is outside the window. The old local capture +slot658 and its immutable-source ticket are retained unchanged. + +Allocate independent owned slot659, initialize its entire payload to zero, +and copy SOURCE0 at B by one paid pointwise XOR. Move SOURCE0 B to C at +the old ADD location. The two remaining B-frame reads of SOURCE0 use the +shadow. At the former helper move, move helper464 directly 0 to C (rank4) +and then add the current SOURCE0 at C. The former later SOURCE move is +deleted; the shadow receives a paid whole-payload CLEAR after its last +use. These are exact common-FRAME operations. For arbitrary functions, + + old: h_C = D_(C-B)(D_B h_0 + D_B x_0) + = D_C h_0 + D_C x_0 + new: h_C = D_C h_0 + D_C x_0. + +Here nested orthogonal projectors satisfy the actual paired ADDRESS +identity D_(C-B)D_B=D_C. A FRAME identifier is not a query rank. All +projectors, nested ranks and the fresh rank4 matcher S Q4 S^-1 are checked +over Q from the pinned frame basis. The window replaces ranks [1,3,3] +with [3,4]. It removes one occurrence while preserving rank mass 7. + +No rank8 LOCAL call is introduced, and no ticket for a different SOURCE or +version is inherited. Field659 is a private workspace, not an extra DATA +job. It remains live alongside slot658, so the new peak is two complete +arrays instead of one. + +## Inverse and rawdual + +The inverse is independently correct; it is not obtained by reversing a +noninvertible CLEAR. At the old inverse SOURCE move, a shadow of SOURCE0 +at C is acquired. The SOURCE move back to B stays in its old position. +At the old helper ADD the helper at C is XORed with that C shadow and +then moved directly C to 0 by the same rank4 involution. All owned payload +is explicitly cleared. Both decoded compositions are the identity on all +658 originals. The entry/exit coframes are interchanged exactly. + +The rawdual is the physical FUNCTION transpose of this true inverse. +Primitive ADD transposes by exchanging source and destination; SOURCE +QUERY transposes to its literal inverse ADDRESS permutation of the same +proper rank. An owned COPY is expanded into its physical assignment and +query before transposition. The zero map CLEAR is self-transpose; this +does not invert CLEAR. The reverse-mode programme begins with whole +owned zero and uses paid CLEAR plus zero-only reheaders. It has 22 paid +CLEAR operations and ten zero reheaders, the same query profile, and a +fresh 30-bit majorant. ADDRESS inverse-transpose is a different operation +and is not used here. The original argument arrays are never erased. + +Every replay checks all 658 independent F2 columns, exact same-FRAME ADDs, +SOURCE ownership and version leases, proper nested QUERYs, and complete +owned return. Finite q=101 and q=101^2 all-symbol sparse controls exercise +the full 16-coordinate paired HEAD/TAIL operator. Arbitrary-function +correctness comes from the exact FRAME induction and rational projector +identities, not from extrapolating the finite controls. + +## Actual global caller + +The pinned p16 controller has 18 thick local calls and 15 thin readout +stages. Each thick call uses its prescribed SOURCE and TARGET banks and +436 fresh arbitrary helper functions; inverse calls use the true inverse +and prescribed bank assignment. The replaced local operator has exactly +the same original entry/exit law. SOURCE/Pi, TARGET/Ki and the four partial +helper end frames are unchanged. + +For each port the central Pi and the 17 fresh, disjoint seven-dimensional +stage blocks commute. The global checker independently evaluates the +32-bank coefficient laws as sets of (initial bank, orthogonal phase), and +obtains the prescribed diagonal monomial for every bank. It separately +checks all 11,400 decoded independent RAW columns, original helper +identity, actual coframes, leases and owner histories. This is a finite +exact function proof on the inherited full ROW, not a character-only +comparison. Different ports are not assigned a common free Pi. + +The local port chart is the literal rational involution rho on 8+7 axes; +all 111 charts are reconstructed from the actual SOURCE roots. Internal +entry/return routes number 7,548. Whole-job canonical matching is a +separate paid wrapper: 7,104 MAIN routes and 144 partial-helper routes, +7,248 in all. MAIN matcher recipes cover every original SOURCE-line plus +selected-stage target, and the three distinct partial rank4 geometries +have explicit rational matchers. Inherited whole-fiber right-ROW routing +is charged; no dense ADDRESS map is declared free. Identity matcher cases +may be charged by the same conservative bound. + +Each emitted SOURCE descriptor records the event-prefix hash, current +owner epoch/version, actual geometry and current RAW bitmap hash. A bitmap +hash is offline control metadata, not a runtime oracle or an assertion +that a physical function is merely a scalar row. The complete literal +prefix plus the current owner defines the actual function. Compound COPY +descriptors explicitly bind their assignment-before-query step. All +57,321 descriptors are replayed independently. + +## DOMAIN, ROW, stock and charges + +The operator acts on complete arrays with the inherited common GLOBAL +domain, valid low unit types, ordered HEAD fields and paired TAIL in +C_(N f) order. Spectators and whole ROW coordinates are carried along. +For column width f each fixed local rational geometry tensors I_f; the +ordered lowerers, field scans, low-type/high-carry fallback, and whole +fiber row transformations are the pinned finite-precompilation/stream +contracts. Their positive finite constants must be regenerated for this +programme. A current owned SUM is a legitimate correlated actual child +input after normalization; arbitrary-input correctness of a child does +not require independence from other parent arrays. This supplies no +additional parent DATA credit. Child-owned regions remain separate from +exposed ancestor arrays. + +The packet explicitly charges 378,039 XOR passes, 1,827 compound pointwise +COPY assignments, 18 shadow acquisitions, 1,845 owned clears, two initial +owned zero scans and two final teardown scans. Shadow copy ADDs are +already in the XOR count. Positive conservative parking is counted as +4*(11400+2) field passes for each paid child call, with restore and head +return, and no ancestor-region scan. This is a fixed finite-program +bound, not a saving. All fixed rational normalizers and all routes have +additional positive costs C_normalizer(N,q,P) and C_route(N,q,S). + +Two complete owned banks are reserved for every compiled unit instance or +simultaneously live unit. A suspended recursive unit does not share its +reserve with another unit at the same depth. Owned jobs are not added to +the 11,400 productive ROW classes. The inherited stock proof with new +fixed finite constants, q and rank cutoff is a pending ordinary-certificate +obligation; no old numerical precision/H threshold is asserted. + +The new global positive integer envelope is 485 bits; local forward, +inverse and rawdual envelopes are respectively 27,30,30 bits. These are +regenerated cancellation-free bounds, not integer-valued endpoint claims. +The all-in fee constant is a positive fixed expression from this new +programme. The 1e9 raw-record cap is not an all-in cap: even the deliberately +conservative parent parking count is larger. No bound is inferred by +silently reusing old numeric constants. + +The scientific claim of this packet stops at native operator/lifecycle, +literal raw profile, and the existence of positive finite programme fees. +The existing three-tail/finite compiler and finite bootstrap must be +instantiated separately with the new profiles and constants. In particular, +the minimum target rank is 4 while some paid ranks are 63; an unrelated +strict r_max --output +python -I -O -B provider/verify.py --provider --output +``` + +The script uses only the standard library and local byte-pinned files. +`INPUT-PINS.json` records origins for attribution; runtime verification never +follows those paths. `provider/MANIFEST.json` pins all runtime code, input +bytes and generated native data. No network, Git checkout or old cache is +needed. Rebuilding generated files is not part of verification. + +The literal 446,436-event global stream is `provider/data/GLOBAL.jsonl.gz`. +Its decompressed SHA-256 is +`0cb03eb11c2d8f511d495f3767e55e48156ed31094697d4e58a82f15be33c203`, +exactly the former G23 digest. Each of the 57,321 paid queries has a fresh +current-function descriptor in `SOURCE-DESCRIPTORS.jsonl.gz`. + +The 18 local calls use 658 arbitrary original functions each, with fresh +helper owners. The global original count remains 11,400. Two owned whole +arrays are allocated per live compiled unit and returned to zero; neither +receives independent-input or productive-output credit. The raw profile has +18 fewer query occurrences than the frozen partial436 baseline, with the +same rank mass and target profile. The local proper-rank request remains +at most 7; the new rank-4 request is explicitly normalized rather than +inheriting the old rank-3 ticket. + +`PROOF.md` explains the function/coframe argument, inverse and rawdual. +`provider/data/FULL-FEES.json` counts the new scans, copies, clears, +whole-fiber routes, conservative parent parking and owned reserve. The +normalizer and ROW costs are positive fixed-program costs, not free rank +admission. In particular, the old raw-record cap of 1e9 is not asserted to +bound all new parking/normalizer passes. + +The historical raw root is approximately .003476110419631239, a +.01877034747% improvement over the same raw baseline. It is below the +.1% publication guard and is not an ordinary saving. The new three-tail, +finite-compiler, prime-fallback and finite-bootstrap certificate is a +separate pending gate. Frozen PR4760/PR4814 inputs are unchanged. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/REPORT.txt b/research/bit-g20-nine-owned-relations/vendor/g20/REPORT.txt new file mode 100644 index 0000000000..0a0af3f66e --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/REPORT.txt @@ -0,0 +1,7 @@ +The private G20/G23 native candidate is materialized and reproducible. Isolated normal and optimized cold replays pass on all 11,400 arbitrary original RAW functions, 57,321 current SOURCE descriptors, 1,845 owned lifetimes and exact parent endpoints. The complete 446,436-event emitted stream has the old G23 decompressed digest 0cb03eb11c2d8f511d495f3767e55e48156ed31094697d4e58a82f15be33c203. Every new helper464 query is a fresh proper-rank4 request. Forward, independently correct inverse and physical rawdual have the same rank mass5089; every owned payload is returned whole zero with paid lifecycle operations. The rawdual uses22 paid clears and10 zero reheaders. The global cancellation-free majorant is freshly485bits. + +The full original job profile is unchanged. Private peak grows from1 to2; private arrays receive no original or output credit. Fee records retain378039 XOR passes,1827 compound pointwise assignments,18 new shadow acquisitions,1845 clears,7548 internal MAIN routes and7248 separate canonical job-matching routes. Parent parking is explicitly bounded by 2614296168 FIELD passes; normalizers/ROW routes have additional positive fixed costs. Thus1e9 is only a raw-record cap and is not silently promoted to an all-in bound. The old source inputs remain byte unchanged. + +Normal cold CPU 5.359375s and peak working set 101199872bytes; optimized CPU 5.171875s and peak 101294080bytes. All mathematical receipts match. The first CLI comparison failed only on integer dictionary keys versus JSON string keys; its code/manifest and correction receipt are preserved before the successful runtime seal. + +Historical raw root .00347611041963123910561 has relative gain .01877034747025 percent, below the0.1 percent guard. It is not an ordinary saving. New tails, finite source compiler/prime fallback, live-unit stock and finite-bootstrap parameters remain a separate certificate obligation, with parent independent validation. Frozen PR4760/4814 artefacts are not modified. No PR or whole-kappa claim is made. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/RESTART.json b/research/bit-g20-nine-owned-relations/vendor/g20/RESTART.json new file mode 100644 index 0000000000..885d0dc4c6 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/RESTART.json @@ -0,0 +1,33 @@ +{ + "status": "PRIVATE_NATIVE_GATE_COMPLETE_NEXT_ORDINARY_CERTIFICATE_PENDING", + "read_first": [ + "README.md", + "PROOF.md", + "RESULT.json", + "provider/data/INVOICE.json", + "provider/data/FULL-FEES.json" + ], + "cold_commands": [ + "python -I -B provider/verify.py --provider --output ", + "python -I -O -B provider/verify.py --provider --output " + ], + "next_concrete_gate": "Instantiate the existing productive partial-target three-tail/finite compiler/finite-bootstrap pipeline in a NEW independently owned directory with this new P/T and regenerated positive constants; parent independent review first. No edits to frozen PR4760/4814 inputs.", + "must_keep": [ + "11400 original jobs, all helpers arbitrary DIRTY, including 72 partial rank4 targets", + "57321 actual current SOURCE requests, 18 new proper rank4 geometries", + "Two owned banks per compiled live unit and explicit 1845 clears", + "Whole-fiber internal7548 plus separate canonical matching7248 routes", + "All positive normalizer/ROW/parking/headreturn costs; raw cap1e9 is not all-in", + "New 485bit global envelope and fixed prime/reserve/precision constants", + "Future rawdual remains inverse-transpose, not ADDRESS inverse-transpose or inverse CLEAR" + ], + "must_not_claim": [ + "rawroot is ordinary saving", + "0.01877 percent qualifies the0.1 percent public guard", + "all-in fees bounded by the old1e9 cap", + "rmax --output ','python -I -O -B provider/verify.py --provider --output '],'next_concrete_gate':'Instantiate the existing productive partial-target three-tail/finite compiler/finite-bootstrap pipeline in a NEW independently owned directory with this new P/T and regenerated positive constants; parent independent review first. No edits to frozen PR4760/4814 inputs.','must_keep':['11400 original jobs, all helpers arbitrary DIRTY, including 72 partial rank4 targets','57321 actual current SOURCE requests, 18 new proper rank4 geometries','Two owned banks per compiled live unit and explicit 1845 clears','Whole-fiber internal7548 plus separate canonical matching7248 routes','All positive normalizer/ROW/parking/headreturn costs; raw cap1e9 is not all-in','New 485bit global envelope and fixed prime/reserve/precision constants','Future rawdual remains inverse-transpose, not ADDRESS inverse-transpose or inverse CLEAR'],'must_not_claim':['rawroot is ordinary saving','0.01877 percent qualifies the0.1 percent public guard','all-in fees bounded by the old1e9 cap','rmax=8) for b in range(15)] for a in range(15)] + need(mm(rho,rho)==eye(15) and mm(mm(rho,local8),rho)==expected,'same finite15D wholefiber route, no free dense currentview') + ports.append(dict(port=i,root=[str(x) for x in q],chart_sha256=digest([[str(x) for x in row] for row in rho]))) + jobs={'independent_roles':[dict(role=i,initial_frame=word['start'][i],job_frame=word['final'][i],rank=frames[str(word['final'][i])]['dim']) for i in range(222,658)]} + need(all(row['initial_frame']==0 for row in jobs['independent_roles']),'all helpers cold ordinary originals') + need(len(jobs['independent_roles'])==436,'alloriginal helper roles') + matchers={} + for f in sorted({row['job_frame'] for row in jobs['independent_roles']}): + H=project(f);rank=frames[str(f)]['dim'] + need(mm(H,H)==H and sum(H[i][i] for i in range(8))==rank,'exact helperoutput idempotent rank') + if rank==8: + need(H==I,'fullhelpers');continue + B=[[Q(x) for x in row] for row in frames[str(f)]['B']];A=[[Q(x) for x in row] for row in frames[str(f)]['A']] + need(rank==4 and len(B)==len(A)==4,'actual image/kernel rank4 basis') + S=list(map(list,zip(*(B+A))));SI=matrix_inverse(S) + Q4=[[Q(i==j and i<4) for j in range(8)] for i in range(8)] + need(mm(mm(S,Q4),SI)==H,'explicit image+kernel output job matcher') + matchers[str(f)]=dict(rank=rank,projector=[[str(x) for x in row] for row in H],S=[[str(x) for x in row] for row in S],S_inverse=[[str(x) for x in row] for row in SI]) + need(len(matchers)==3,'three distinct actual rank4 helperjobs') + return dict(ports=ports,matchers=matchers,all_f='Every head projector/matcher embeds in one final ambient and tensorsI_f; use retained C_Nf for the reversed tail, not a runtime relabeling.', + helper_cover='Helpers are independent fields at the localinvocation cover rowh, not per-port-routed main fields. No rho_q is silently applied to a helperjob.', + matcher_direction='Stored S satisfies S Q4 S^-1=H4. To use childH4 as canonicalparentQ4, route input wholefiber g->g S^-1, finish wholeunit, undo route. For arbitrary parentP use B_P B_H4^-1.', + partial_job_routes='72 output roles need wholefiber matcher/inverse when used by the finite compiler:144 positive fixed routes, no extra input/output credit.') + + +def build(repo_root, local_dir, out): + repo_root,local_dir,out=map(Path,(repo_root,local_dir,out)) + out.mkdir(parents=True,exist_ok=True) + need(not any(out.iterdir()),'fresh GLOBAL output directory required') + SOURCE,LOCAL,HERE=repo_root,local_dir,out + started=time.process_time();cp=SOURCE/'research/query-thinned-controllers/BIT-CONTROLLER.json' + need(sha256(cp.read_bytes()).hexdigest()=='39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d','exact current p16controller pin') + controller=json.loads(cp.read_bytes());thick=controller['invoice']['thick_stages'] + need(len(thick)==18 and len(set(thick))==18,'actual thickstage roster') + active_embedding=[dict(stage=s,kind='central K_q=I8-P_q' if j==0 else 'fresh orthogonal rank7 B_s', + active_block=j,axes=list(range(8)) if j==0 else list(range(8+7*(j-1),8+7*j))) for j,s in enumerate(thick)] + need(max(a for row in active_embedding for a in row['axes'])==126,'actual127-axis injective thin-stage deletion') + wpath=LOCAL/'WORD.json.gz';need(sha256(gzip.decompress(wpath.read_bytes())).hexdigest()=='6f8516694bd0067897e91311fb16a749eea8fdd2eb3761bfa3f8eb2740d5c6a6','actual partialLOCAL canonical content pin') + word=json.loads(gzip.decompress(wpath.read_bytes()));fpath=SOURCE/'research/kappa-rebuild/bit/sources/pr589-regenerated/records/frames.json' + need(sha256(fpath.read_bytes()).hexdigest()=='d006b3bfe0c04afecfea7aecfa59dfe4298b99501c70da3938e40289bc2f5010','exact current frame source') + refpath=SOURCE/'research/kappa-rebuild/bit/sources/pr589-regenerated/WORD.json.gz' + need(sha256(refpath.read_bytes()).hexdigest()=='e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f','exact current reference WORD') + frames=json.loads(fpath.read_bytes())['frames'];reference=json.loads(gzip.decompress(refpath.read_bytes())) + formal=formal_main(controller);binding=port_and_helper_proofs(word,frames,reference) + values=[1<>1).bit_count()]+=V + expected_paid={1: 25407, 2: 24156, 3: 1404, 4: 702, 5: 1836, 6: 180, 7: 324, 14: 444, 21: 444, 28: 444, 35: 444, 42: 444, 49: 444, 56: 444, 63: 222} + expected_targets={4: 72, 8: 7776, 15: 444, 22: 444, 29: 444, 36: 444, 43: 444, 50: 444, 57: 444, 64: 222, 127: 222} + need(dict(sorted(profile.items()))==expected_paid,'actualexpandedpaid ledger') + need(dict(sorted(targets.items()))==expected_targets,'every actual independent helper/main outputcredit') + need(max(profile)<127 and sum(targets.values())==N,'proper requests, no private orghost Wcredit') + result=dict(status='PASS_CURRENT_PARTIAL436_THIN_CONTROLLER_ALL11400_RAW_AND_INDEPENDENT_JOBS',at_utc=datetime.now(timezone.utc).isoformat(), + raw_scalar_columns=N,main_original_fields=3552,helper_original_fields=7848, + raw_column_scope='Inline all11400 decodedF2 columns plus exact per-LOCAL frame/function invariant, rational mainportcharts and every physical main polynomial coefficient. Not only coefficient-row SOURCE projection.', + paid=dict(sorted(profile.items())),targets=dict(sorted(targets.items())),query_count=sum(profile.values()), + rank_surplus=sum(r*n for r,n in targets.items())-sum(r*n for r,n in profile.items()), + helper_full8=7776,helper_partial4=72,private_original_credit=0,private_peak=1,private_episodes=len(private_episodes), + nonidentity_mainport_routes=counts['PAID_PORT_ROUTE'],additional_partial_outputmatcher_routes=144, + event_counts=dict(counts),expanded_event_count=event_index,expanded_event_sha256=stream_hash.hexdigest(), + expanded_gzip_sha256=sha256((HERE/'EXPANDED-PROGRAM.jsonl.gz').read_bytes()).hexdigest(), + cancellation_free_integer_majorant=peak,cancellation_free_majorant_bits=peak.bit_length(), + raw_scalar_record_bound=10**9,source_type_lift='Single delayed wholeGL ambient, common externalweight independent of freshroles/cover, allfixed projectors tensorI_f and retained C_Nf tail. No free dense reframe or inherited changedROWconstants.', + fee_scope='All localCOPY/clear,thinCOPY/query/clear,bridge/swaps,wholeidle retained;144 new wholefiber matcher routes plus newrow/stock/normalizer/precision constants must be charged in root strictification.', + complete_ordinary_or_whole_claim=False,CPU_seconds=time.process_time()-started, + sourcepins=[dict(path=str(p),sha256=sha256(p.read_bytes()).hexdigest()) for p in [cp,wpath,fpath,refpath]]) + need(event_index+2*sum(profile.values())+2*N+144<10**9,'conservative finite rawrecord/route accounting fits declared bound') + for name,data in [('RESULT.json',result),('MAIN-PHYSICAL-COEFFICIENTS.json',formal),('OWNERS.json',owners),('CALLS.json',calls),('PRIVATE-EPISODES.json',private_episodes),('RATIONAL-BINDING.json',binding),('ACTIVE-AXES.json',active_embedding)]: + (HERE/name).write_text(json.dumps(data,indent=2)+'\n',encoding='utf-8') + return result + + +def main(): + p=argparse.ArgumentParser() + p.add_argument('--repo-root',type=Path,required=True) + p.add_argument('--local-dir',type=Path,required=True) + p.add_argument('--out',type=Path,required=True) + args=p.parse_args();result=build(args.repo_root,args.local_dir,args.out) + print(json.dumps({k:result[k] for k in ['status','raw_scalar_columns','query_count','rank_surplus','helper_full8','helper_partial4','expanded_event_count','cancellation_free_majorant_bits','CPU_seconds']})) + + +if __name__=='__main__':main() diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/inputs/4814-independent_native.py.txt b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/4814-independent_native.py.txt new file mode 100644 index 0000000000..bb41064dd1 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/4814-independent_native.py.txt @@ -0,0 +1,133 @@ +"""Separate Boolean/raw interpreter and rational helper-job matching. + +The state is all658 original symbols, never just the111 SOURCE symbols. +Frames specify actual ADDRESS pullbacks; equality of VALUE rows alone is +insufficient. The rank7 owned-copy backend is inherited, charged and leased. +""" +from fractions import Fraction as F +from collections import Counter + +N=658;V=111 +LOCAL={1:1319,2:1342,3:78,4:39,5:102,6:10,7:18} + +def need(c,m): + if not c:raise ValueError(m) + +def rank(a): + a=[[F(v)for v in row]for row in a] + if not a:return 0 + r=0 + for j in range(len(a[0])): + k=next((i for i in range(r,len(a))if a[i][j]),None) + if k is None:continue + a[r],a[k]=a[k],a[r];x=a[r][j];a[r]=[v/x for v in a[r]] + for i in range(r+1,len(a)): + if a[i][j]: + x=a[i][j];a[i]=[v-x*w for v,w in zip(a[i],a[r])] + r+=1 + if r==len(a):break + return r + +def inverse(a): + n=len(a);a=[[F(x)for x in row]+[F(i==j)for j in range(n)]for i,row in enumerate(a)] + for j in range(n): + k=next(i for i in range(j,n)if a[i][j]);a[j],a[k]=a[k],a[j] + q=a[j][j];a[j]=[v/q for v in a[j]] + for i in range(n): + if i!=j and a[i][j]: + q=a[i][j];a[i]=[v-q*w for v,w in zip(a[i],a[j])] + return [row[n:]for row in a] + +def mm(a,b):return [[sum(x*y for x,y in zip(row,col))for col in zip(*b)]for row in a] + +def project(frame): + b=[[F(x)for x in row]for row in frame['B']] + if not b:return [[F(0)]*8 for _ in range(8)] + bt=list(map(list,zip(*b))) + return mm(mm(bt,inverse(mm(b,bt))),b) + +def verify(word,frames,reference,reverse=False): + need(word['active_ordinary_roles']==word['namespace']==N,'Original namespace658') + need(len(word['start'])==len(word['final'])==N,'All original boundaries') + need(word['start'][:222]==reference['start'][:222]and word['final'][:222]==reference['final'][:222], + 'Exact main SOURCE/Y interface, including coordinate flags') + need(all(f==0 for f in word['start'][222:]),'All436 helper inputs start arbitrary and cold') + expected_helpers=Counter(frames[str(f)]['dim']for f in word['final'][222:]) + need(expected_helpers=={4:4,8:432},'Actual independent partial-target ranks') + used={f for f in word['start']+word['final']} + for e in word['records']: + if e[0]==0:used.update(e[2:4]) + else:used.add(e[4]) + for f in used: + frame=frames[str(f)];b,a=frame['B'],frame['A'];d=frame['dim'] + need(len(b)==d and len(a)==8-d and rank(b+a)==8,'Complete actual frame bases') + need(all(sum(x*y for x,y in zip(u,v))==0 for u in b for v in a),'Frame orthogonal complement') + state=list(word['final']if reverse else word['start'])+[None] + rows=[1<=222 and f!=1] + need(found==[(462,506),(463,506),(466,508),(468,509)],'four genuine rank4 partialendpoints') + completion=[] + for role,f in found: + P=project(frames[str(f)]);I=[[Q(i==j) for j in range(8)] for i in range(8)] + C=[[I[i][j]-P[i][j] for j in range(8)] for i in range(8)] + need(mm(P,P)==P and mm(C,C)==C and sum(C[i][i] for i in range(8))==4,'actual rational rank4 completion projector') + completion.append(dict(role=role,from_frame=f,to_frame=1,rank=4,projector=[[str(x) for x in row] for row in C])) + if not partial: + word['records'].append([0,role,f,1,4,0]);word['final'][role]=1 + if partial: + word['format']='compact436-productive-partial/1' + word['productive_interface']=dict(SOURCE_ports=111,TARGET_ports=111,independent_helpers=436,helper_job_ranks={'4':4,'8':432},private_index=658,old_word_sha256=sha256(raw).hexdigest(),paid_completion_count=0) + else: + word['format']='compact436-productive-full8/1' + word['productive_interface']=dict(SOURCE_ports=111,TARGET_ports=111,independent_helpers=436,helper_job_rank=8,private_index=658,old_word_sha256=sha256(raw).hexdigest(),paid_completion_count=4) + expected_profile=dict(EXPECTED) + if partial:expected_profile[4]-=4 + forward,fw=replay(word,frames,expected_profile=expected_profile) + reverse,rv=replay(word,frames,True,expected_profile=expected_profile) + # Signed full inverse uses actual output expressions, not just modulo2. + back,_=replay(word,frames,True,forward,expected_profile) + forth,_=replay(word,frames,False,reverse,expected_profile) + identity=[{i:1} for i in range(N)]+[{}] + need(back==forth==identity,'both exact signed inverse orders onall658 independent RAW') + job_frames=sorted(set(word['final'][222:])) + helper_jobs=dict(projectors={str(f):[[str(x) for x in row] for row in project(frames[str(f)])] for f in job_frames}, + independent_roles=[dict(role=i,initial_frame=0,job_frame=word['final'][i],rank=frames[str(word['final'][i])]['dim']) for i in range(222,N)], + physical_law='Forward D_final*D_initial^-1 on own RAW; reverse uses inverse but idempotent-job involution equals itself. All helper starts0, independent own signedrow, no SOURCE/TARGET contamination.', + cover_lift='Embed exact8x8 P in local first8 ambient axes and tensor I_f; reverse tail uses retained C_Nf convention. No free coordinate adapter.') + (out/'HELPER-ENDPOINTS.json').write_text(json.dumps(helper_jobs,indent=2)+'\n',encoding='utf-8') + (out/'COMPLETIONS.json').write_text(json.dumps(completion,indent=2)+'\n',encoding='utf-8') + packed=json.dumps(word,sort_keys=True,separators=(',',':')).encode() + (out/'WORD.json.gz').write_bytes(gzip.compress(packed,mtime=0)) + (out/'SIGNED-ENDPOINTS.json').write_text(json.dumps(dict(forward=forward,reverse=reverse),indent=2)+'\n',encoding='utf-8') + result=dict(status='PASS_PARTIAL_PRODUCTIVE_LOCAL_ALL658_RAW_NATIVE_AND_SIGNED' if partial else 'PASS_FULL8_PRODUCTIVE_LOCAL_ALL658_RAW_NATIVE_AND_SIGNED',at_utc=datetime.now(timezone.utc).isoformat(), + word_sha256=sha256((out/'WORD.json.gz').read_bytes()).hexdigest(),content_sha256=sha256(packed).hexdigest(), + ordinary_columns=N,independent_helper_columns=R,all_helper_physical_jobs='432 D_I8 and4 actual D_P4, arbitraryindependent initialdata' if partial else 'D_I8, arbitraryinitialdata, no free promotions', + SOURCE_Y_interface_identical_to_current589=True,ordered_SOURCE_lines_identical=True, + forward=fw,reverse=rv,signed_inverse_both_orders=True, + completion_count=0 if partial else 4,complete_LOCAL_rankmass=5089 if partial else 5105,published_partial_LOCAL_rankmass=5089, + productive_helper_ranks={'4':4,'8':432} if partial else {'8':436}, + attribution='Reuses our published compact436/GL464 and credited public boundary/delayed retirement lineage; new mixed productive-helper ABI/current-controller requalification only.', + current_global_not_yet_executed=True, + sourcepins=[dict(path=str(p),sha256=sha256(p.read_bytes()).hexdigest()) for p in [old_word,old_geom,source/'WORD.json.gz',frame_path]],CPU_seconds=time.process_time()-start) + (out/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n',encoding='utf-8') + return result + + +def main(): + p=argparse.ArgumentParser() + p.add_argument('--out',type=Path,required=True) + p.add_argument('--completed',action='store_true',help='Paid full-rank fallback; not the submitted partial ABI') + args=p.parse_args() + result=build(ROOT,args.out,not args.completed) + print(json.dumps({k:result[k]for k in ('status','content_sha256','ordinary_columns','productive_helper_ranks')})) + +if __name__=='__main__':main() diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/inputs/ACTIVE-AXES.json b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/ACTIVE-AXES.json new file mode 100644 index 0000000000..f68307930e --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/ACTIVE-AXES.json @@ -0,0 +1,255 @@ +[ + { + "stage": 0, + "kind": "central K_q=I8-P_q", + "active_block": 0, + "axes": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7 + ] + }, + { + "stage": 1, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 1, + "axes": [ + 8, + 9, + 10, + 11, + 12, + 13, + 14 + ] + }, + { + "stage": 3, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 2, + "axes": [ + 15, + 16, + 17, + 18, + 19, + 20, + 21 + ] + }, + { + "stage": 5, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 3, + "axes": [ + 22, + 23, + 24, + 25, + 26, + 27, + 28 + ] + }, + { + "stage": 7, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 4, + "axes": [ + 29, + 30, + 31, + 32, + 33, + 34, + 35 + ] + }, + { + "stage": 9, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 5, + "axes": [ + 36, + 37, + 38, + 39, + 40, + 41, + 42 + ] + }, + { + "stage": 11, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 6, + "axes": [ + 43, + 44, + 45, + 46, + 47, + 48, + 49 + ] + }, + { + "stage": 13, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 7, + "axes": [ + 50, + 51, + 52, + 53, + 54, + 55, + 56 + ] + }, + { + "stage": 15, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 8, + "axes": [ + 57, + 58, + 59, + 60, + 61, + 62, + 63 + ] + }, + { + "stage": 17, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 9, + "axes": [ + 64, + 65, + 66, + 67, + 68, + 69, + 70 + ] + }, + { + "stage": 19, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 10, + "axes": [ + 71, + 72, + 73, + 74, + 75, + 76, + 77 + ] + }, + { + "stage": 21, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 11, + "axes": [ + 78, + 79, + 80, + 81, + 82, + 83, + 84 + ] + }, + { + "stage": 23, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 12, + "axes": [ + 85, + 86, + 87, + 88, + 89, + 90, + 91 + ] + }, + { + "stage": 25, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 13, + "axes": [ + 92, + 93, + 94, + 95, + 96, + 97, + 98 + ] + }, + { + "stage": 27, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 14, + "axes": [ + 99, + 100, + 101, + 102, + 103, + 104, + 105 + ] + }, + { + "stage": 29, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 15, + "axes": [ + 106, + 107, + 108, + 109, + 110, + 111, + 112 + ] + }, + { + "stage": 31, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 16, + "axes": [ + 113, + 114, + 115, + 116, + 117, + 118, + 119 + ] + }, + { + "stage": 32, + "kind": "fresh orthogonal rank7 B_s", + "active_block": 17, + "axes": [ + 120, + 121, + 122, + 123, + 124, + 125, + 126 + ] + } +] diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/inputs/BASELINE-GLOBAL-RESULT.json b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/BASELINE-GLOBAL-RESULT.json new file mode 100644 index 0000000000..31652ddb8a --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/BASELINE-GLOBAL-RESULT.json @@ -0,0 +1,92 @@ +{ + "status": "PASS_CURRENT_PARTIAL436_THIN_CONTROLLER_ALL11400_RAW_AND_INDEPENDENT_JOBS", + "at_utc": "2026-10-22T18:26:16.912588+00:00", + "raw_scalar_columns": 11400, + "main_original_fields": 3552, + "helper_original_fields": 7848, + "raw_column_scope": "Inline all11400 decodedF2 columns plus exact per-LOCAL frame/function invariant, rational mainportcharts and every physical main polynomial coefficient. 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the whole finite program is compiled + +Status: a constructive native-interface argument, with an exact local-ring +audit. This closes the particular common-weight mismatch identified in the +first mixed BIT proposal, conditional on the finite mixed-flow compiler +producing the stated finite projector program. It is not an independent +proof of that compiler's asymptotic termination or of integer multiplication. + +Substantial OpenAI assistance. Apache-2.0. This argument uses the arbitrary- +projector GL cover and weighted-child normal form in +[`notes/three-stage-cover-bit.tex`](../../../notes/three-stage-cover-bit.tex), +the retained PR589 local word and its predecessors, and the finite +precompilation proposal in `../architecture/FINITE-PRECOMPILATION.md`. +The decisive order of operations was proposed jointly with the architecture +research task: compile all internal jobs first; apply one common cover and +one common external weight only afterwards. + +## 1. The earlier obstruction was real + +A productive rank-eight helper is a proper projector job inside a larger +ambient address space. After an ambient GL cover, its endpoint is + +\[ +D_{gPg^{-1}}, +\] + +not the same fixed eight-coordinate interchange on every cover row. +Lowering this job immediately to a canonical recursive query introduces a +diagonal weight determined by the pivot coefficients of `g P g^-1`. +Jobs from different parents can have different such weights. The inherited +scalar word accepts one common external weight across every fresh role; +simply placing differently weighted jobs in its roles is invalid. + +The solution below does not identify these weights. It avoids creating +weighted internal jobs at all. Only leaves of the entire precompiled word +are lowered to canonical weighted calls. + +## 2. Native projector jobs before canonical lowering + +Fix an ambient rational head space of dimension `N` and the atom-reversal +matrix `C_N`. For any rational idempotent `P` put + +\[ +D_P=\begin{pmatrix} +I-P & PC_N\\ +C_NP & I-C_NPC_N +\end{pmatrix}. +\] + +For `G` invertible let + +\[ +Q_G=\operatorname{diag}(G,C_NGC_N). +\] + +Direct block multiplication gives + +\[ +Q_GD_PQ_G^{-1}=D_{GPG^{-1}},\qquad +D_PD_{I-P}=D_I. +\] + +No symmetry of `P` is required. The second identity says that any source +job and its complementary projector complete the full interchange on that +array. If a unit of rank `m` is used at column multiplicity `c`, first embed +its rational projectors into the chosen `mc`-dimensional coordinate block +of the common `N`-dimensional space. Complete unused coordinates are +spectators. All these dimensions and embeddings are constants of the +finite precompiled program. + +The local PR589 primitive, the new global controller, its pointwise boundary +adapters, and owned COPY storage can all be treated as a finite chronological +word of pointwise scalar operations, proper projector requests, restores, +and fixed right-multiplication symbols on one future cover coordinate. +Their exact finite operator identities are established independently of a +generic canonical child normalizer. An internal request may therefore be +replaced by a finite native word computing the same `D_P` on arbitrary data. + +This schematic qualification matters. The p3 construction already uses +per-port chart routes to share one local helper bank across 111 data ports. +It is not a 3,739-field word with those routes silently deleted. Before +choosing the final cover, embed every local projector and every port chart +into the common ambient `N`. Preserve all fixed right-route symbols during +substitution. Only then instantiate that single `GL_N` cover. A helper's +endpoint is the rank-eight local-space projector at its local invocation +vertex, while main data endpoints use their port-specific line and stage +projectors. `BIT-P3-NATIVE-BINDING.json` checks every fixed rational port +chart, this ownership distinction, and the complete recursive tariff. + +## 3. Equal rank gives a fixed rational matcher + +For rational idempotents `P,Q` of the same rank, choose a rational basis of +their images and kernels. Let `B_P` and `B_Q` be the corresponding full basis +matrices, with image columns first. Then + +\[ +S=B_PB_Q^{-1},\qquad SQS^{-1}=P. +\] + +This is a finite rational matrix construction. A physical execution of the +dense address map `Q_S` is **not** assumed. The matcher is used only as a +right multiplication of the full cover row, as follows. + +Choose a fixed odd prime `q` avoiding the denominators and nonzero +determinants of every native matrix and matcher in the finite program. +For atom width `w`, use one global cover + +\[ +\mathcal G=\operatorname{GL}_N(\mathbb Z/q^w\mathbb Z). +\] + +All matchers reduce to invertible matrices over this local ring. +An array role is accompanied by the full cover coordinate `g in G`. +Its entries at different `g` are independent data. + +Suppose a parent role at cover row `g` requests `D_(g P g^-1)` and a child +target role at its cover row `h` computes `D_(h Q h^-1)`. Before running +the child, route that complete target-role fiber by + +\[ +x_g\longmapsto y_{gS}=x_g. +\] + +Execute the child word on these routed inputs, then undo the role-specific +route. The endpoint on the parent's original `x_g` is exactly + +\[ +D_{(gS)Q(gS)^{-1}}=D_{gPg^{-1}}. +\] + +Every child target role can use its own fixed matcher `S`. Each mapping +`g -> gS` is a bijection of the *whole* cover fiber, so no input is copied, +discarded, or assumed zero. The child word can mix its roles at a common +child row `h`, because those routed inputs are arbitrary independent data. +After the completed word returns its independent endpoints, undoing the +routes restores the parent ordering. The finite flow's ownership and +chronology are still required; cover routing does not repair an aliased +or cyclic flow. + +## 4. One common external weight survives every internal routing + +At column multiplicity `f`, let the outer invocation's diagonal weight +`A` be any permitted generated descriptor on its `Nf` head atoms. It can +depend on exposed ancestor rows and atom indices. It must be independent +of all fresh role and cover fields of this entire compiled invocation. +Write `Lambda_A=diag(A,I)`. + +Conjugate the entire completed covered word by `Lambda_A`. Pointwise scalar +ADDs commute with this common address permutation across roles. Every +internal role route also commutes with it: a route changes only a fresh +role or the current cover row, while `A` is independent of both. Thus the +matching identity becomes + +\[ +\Lambda_A D_{(gS)Q(gS)^{-1}}\Lambda_A^{-1} +=\Lambda_A D_{gPg^{-1}}\Lambda_A^{-1}. +\] + +There is no child-specific weight to reconcile inside the precompiled +word. The source/complement product gives + +\[ +\Lambda_A D_I\Lambda_A^{-1}=F_A +\] + +on every productive source array. This is exactly the inherited weighted +full-interchange endpoint. Owned zero storage is unaffected by address +permutations and is excluded from productive output credit; its allocation, +initialization and final erasure still belong to the finite word. + +The condition on `A` is essential. The companion audit exhibits a concrete +failure when `A` is allowed to depend on the current fresh cover row. The +argument does not quietly weaken the old ancestor-only contract. + +## 5. Only the final leaves become weighted children + +After the mixed finite compiler has replaced every internal request, suppose +the remaining paid projector requests have rank one. At multiplicity `f`, +each is a rank-`f` residual on the outer atom space. Apply the inherited +generic ordered normal form to this *finished* leaf list. + +For a generic residue class, that proof produces unit lower intrabank and +cross-bank adapters around one contiguous weighted reversed interchange. +For column `j`, the resulting weight is + +\[ +A_{\rm child}[j]=A[i_0f+j]D_P[0], +\] + +with the inherited reversed tail pairing. The pivot coefficient is evaluated +from the current outer cover row and the fixed leaf projector. Those are +ancestor data when the recursive rank-`f` child is invoked. Its fresh roles +come from unused row stock, so the child's weight is independent of them. + +Different leaf calls can have different weights; the ordinary recursion +already permits this. Each such child itself receives one common weight +across all of *its* fresh roles and cover rows. This is the critical +distinction from calling a mixed unit on several already-normalized, +differently weighted parent jobs. + +Bad residue classes use the inherited genuine local-ring fallback, including +its swaps, paired scalings and reversals. This is charged explicitly rather +than declaring a nonunit pivot invertible. + +## 6. Routing is priced by the retained native lemma + +The cover row has the unique chart `g=g0+qG1`, with `g0` in `GL_N(F_q)`. +For each fixed matcher `S`, right multiplication gives a permutation of +the finite low type and a fixed affine map on the high matrix, with carry +determined by the low type. The retained proof of finite cover routing +implements this with a constant number of fixed scalings, ordered shifts +and old atom interchanges. Its cost is + +\[ +O(Vw^{1-a_{\rm old}}) +\] + +per fixed route. It is not a free address-gather operation. A precompiled +word contains finitely many matchers, so their total remains a finite +constant times this term. High matrices are streamed by fixed low type; +the number of tapes and program types does not grow with `w`. + +The same statement holds for nonintegral rational matchers: choose `q` +avoiding their fixed denominators, use their local-ring representatives, +and apply the retained fixed-rational routing lemma. The exact small audit +uses integral unimodular matchers to exercise the carry formula directly. + +## 7. Moment and row-stock consequences + +Let the finite uniform compiler have `B` productive source arrays, ambient +rank `N`, and `P` rank-one leaves, with a certified strict inequality + +\[ +\frac PB N^{-\tau}<1. +\] + +The covered, weighted word has the same normalized good-class leaf count. +Choose `q` large enough that the full fallback surcharge fits the displayed +slack. For example, the conservative inherited per-leaf bounds yield + +\[ +\mu_\tau\le +\frac PB N^{-\tau} +\left(1+\frac{2N^3}{q}\,32N^2\right)<1. +\] + +No old fixed choice of `q` or old numerical fallback envelope is reused for +the potentially enormous new `N`. Prime avoidance and a sufficiently large +prime exist because the whole precompiled program is finite. + +For the present candidate, use the exact mixed saving +`C0=69/25000=0.00276` for the finite compiler and retain +`C1=11/4000=0.00275` after covering. Put `d=C0-C1=1/100000`. +The former gives `P/B\frac{256N^5}{d}=25,600,000N^5. +\] + +Then the fallback multiplier is less than `1+d/4`, while +`N^d >= 1+d/2` for `N>=2`, using `log 2>1/2` and `exp x>=1+x`. +Thus the complete moment is strictly below +`(1+d/4)/(1+d/2)<1`. This uses an explicit exponent gap and does not +require knowing the eventual winning template's numerical moment slack. + +The cover consumes `N^2(w-1)` high-row digits plus a fixed low-type and role +reserve. Its finite owned-storage and scalar costs may be enormous. They +replace the old constants. For fixed `N` and a fixed finite word, the +ancestor reserve remains `O(w log e)`, and the previous eventual-threshold +arguments still apply after substituting those constants. They cannot be +reused numerically without that substitution. + +The existing weighted recursion can now be applied to this one uniform +supplier: every paid query has width at most `f`, the endpoint is `F_A`, and +all routing and scalar terms have the inherited permitted form. This is a +native-interface bridge. The complete final exponent still depends on the +mixed compiler's termination theorem, its exact leaf-count saving, and the +outer multiplication transfer. + +## 8. The ordinary BIT saving and explicit template constants + +The retained stopped recurrence gives + +\[ +T(n,w)=O(n+n^{1-C_1}w^{1-a_{\rm old}}),\qquad +a_{\rm old}=384599/10^{10}. +\] + +The old atom exponent `1/1000` cannot be reused here: its linear `n` term +would limit the ordinary saving to `0.001`. Instead choose +`delta=3/1000` and `w=ceil(e^delta)` from the original chunk width `e`. +For the whole compiled program set + +\[ +W(w)=B|\operatorname{GL}_N(\mathbb F_q)|q^{N^2(w-1)}. +\] + +A safe reserve is `W(w)^D * S_old`, with +`D >= floor(log_N ceil(e/w))`; all final ordinary children have rank at +most `floor(n/N)`. Therefore the borrowed high-digit count satisfies + +\[ +k\le D\left(N^2(w-1)+ +\left\lceil\log_q(B|\operatorname{GL}_N(\mathbb F_q)|)\right\rceil\right) ++\left\lceil\log_qS_{\rm old}\right\rceil+1 +=O_{N,B,q}(w\log e). +\] + +This is `o(e)`. For sufficiently large `e`, borrow `ka_BIT` and `delta<1-a_BIT` hold strictly. The linear adapter +term and the borrowed-stock logarithm are lower order. One may relax the +ordinary saving to the simpler rational `27/10000=0.0027`. +`BIT-ALLSIZE-PARAMETERS.json` records all strict rational gaps and the +exact mixed margin at `C0`. This remains conditional on the finite uniform +compiler premise; the enormous word is not materialized in this package. + +The final ambient dimension is `N`, the productive role count is `B`, and +the rank-one leaf count is `P`. They are not the old `64`, `661`, `3739`, +or the base unit's literal counts. Let `C` be the total allocated owned +array fields, `L` the literal scalar/copy/erase count, and `R` all fixed +right routes including inverses. Keep the full finite matrix and +coefficient-height list. The new fixed tape inventory can use one stream +per productive or owned role, with the inherited parking stack; it is +finite in `B+C`. Every route is charged, and every final leaf has its own +normalization and possible fallback. A rank-one generic normalizer and +its inverse use at most `4N^2-2N` elementary lower/cross-bank shears; the inherited bad +normalizer uses at most `32N^2` recursive calls of width at most `f`. + +These constants can be enormous and affect the eventual threshold. Their +dependence on the fixed compiled template does not introduce a new power +of the later input length. The mixed-flow argument is used to bound the +normalized number of paid rank-one leaves; it must not assume that dense +matrix routing costs stay uniformly bounded while the candidate template +dimension `N` is increased in the existence search. + +## 9. Exact finite audit + +Run: + +```sh +python3 -B research/kappa-rebuild/bit/delayed_cover_bridge.py +``` + +The audit enumerates every one of the 3,888 rows of `GL_2(Z/9Z)` for each +of two independently matched target roles. It checks 7,776 exact physical +projector identities, both full cover bijections, the affine high-row carry +formula, and every one of the 6,561 addresses for common-gauge scalar +commutation. Its external weight is `(2,4)`, so it is not restricted to an +unweighted or constant-across-axis input. The emitted leaf-weight histogram +is nonconstant. Two explicit negative controls reject omitting a matcher +and allowing the external weight to depend on the fresh cover row. + +These are independent checks of concrete algebra and a genuine local ring. +The general argument is the conjugacy calculation above, not an inference +from the finite sample. + +## Open next questions + +1. Independently audit that the finite lockstep compiler only substitutes + whole arbitrary-input jobs and gives each simultaneously live child role + a distinct physical array. The row matching here assumes that ownership. +2. Bind the new BIT p3 native physical projector list and its exact local + primitive into the abstract finite compiler, including all COPY centers. +3. Write the parameter substitutions for the eventual row reserve and the + final BIT/complex outer exponent. A finite numerical mixed moment alone + is still insufficient for a new multiplication claim. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/inputs/FINITE-PRECOMPILATION.md b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/FINITE-PRECOMPILATION.md new file mode 100644 index 0000000000..4badb40f09 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/FINITE-PRECOMPILATION.md @@ -0,0 +1,313 @@ +# Finite precompilation of a mixed-target rule + +Status: constructive bridge under the precise native hypotheses below, +independently audited in `../transfer-audit/AUDIT.md`. This is a written +argument, not a formal proof or a completed integer-multiplication admission. +The companion finite scheduler checks actual integer flow and ordering. +The original immediate-normalization BIT interface failed hypothesis 3. +`../bit/DELAYED-COVER-BRIDGE.md` supplies the distinct delayed-cover +implementation, with a finite local-ring check and the native binding in +`../bit/BIT-P3-NATIVE-BINDING.json`. Its fixed rational cover routes are a +costed program schema, not dense coordinate gates in a plain native word. + +Substantial OpenAI assistance. Apache-2.0. The mixed-target asymptotic flow is +Jacob Alan Sussman's Theorem 1G, PR4268, with the detailed proof at commit +`563b4e6e913625637f36ba7869bf5fcd0dd4975a` of +[`wht-power-saving-lean`](https://github.com/jacobalansussman/wht-power-saving-lean). +The source, exact scheduling code and notices are preserved under `sources/`. +The contribution proposed here is clearing the finite flow into a single +uniform native supplier before applying the inherited outer theorem. + +## 1. What needs to be assumed + +Let a job of rank `s` apply a specified tensor operator to `s` selected +coordinate blocks of one array, fixing all other coordinates. A block has +an arbitrary positive tensor multiplicity `f`. A completed rank `s` job +therefore acts on `s*f` axes. All productive inputs are arbitrary. + +Fix one mixed unit with productive targets `W_k` of ranks `k`, a chronological +list of paid child ranks `r_j`, and a finite number of scalar and routing +passes. These assumptions are required, separately from the moment inequality: + +1. **An all-column native word.** At every integer column count `c`, the unit + computes exactly its independent rank `k*c` output jobs. Its paid rounds + are rank `r_j*c` jobs in the stated order. All borrowed data return to the + declared endpoint, and owned storage is explicitly initialized and erased. + Its finite operation count is uniform in `c`. +2. **Disjoint splitting and spectators.** A rank `a+b` job is a rank `a` job + followed by a rank `b` job on disjoint coordinates. The resulting programs + preserve arbitrary complete spectator fields and accept arbitrary data. +3. **Whole-job adapters.** Any job passed between two units has an explicitly + priced, permitted embedding into its destination. For the intended complex + application these are fixed monomial binary address maps and unit quadratic + phases, together with role permutations. The adapters must work at every + tensor multiplicity. Rank equality by itself is insufficient. +4. **Finite-program closure.** A finite composition of these words and + adapters is again a permitted finite supplier. Constantly many owned fields + may be supplied with their full cost and no productive output credit. + The eventual ordinary recursion must have the same arbitrary-input, + restoration, scalar and precision interface as the retained supplier. + +Put `m=max{k:W_k>0}`, `k_min=min{k:W_k>0}`, and +`r_max=max{r_j}`. Require `r_max g*S`, keeps one +external weight throughout the entire finite circuit, and lowers only its +final rank-one leaves. All rational matchers, role routes and their inverses +are fixed before choosing the odd prime and its exclusions. Every route +uses complete equal-multiplicity cover fibers and the retained, costed row +permutation primitive. This gives the same finite DAG argument in the +rational-cover program category. The BIT binding supplies the actual native +projectors; a rank count alone would not provide this implementation. + +## 2. Proposed conclusion + +Suppose the preceding hypotheses hold and the mixed balance has root +`tau` in `(0,1)`: + +``` +sum_j r_j^tau = sum_k W_k k^tau. +``` + +For every `z` with `tau=2`, a fixed number `B_N` of productive arrays, +and only rank-one paid children, whose number `P_N` satisfies + +``` +P_N < B_N * N^z. +``` + +Every productive output is the full rank-`N` job. The construction may have +an enormous finite scalar word, role inventory and owned-storage requirement. +Those quantities affect constants and the eventual input threshold. They are +not omitted and are not credited as extra output jobs. + +If this uniform supplier is admitted under the retained native, precision and +fixed-tape premises, the existing uniform recursion applies directly. A new +dynamic RAM-to-Turing-machine simulation is not being assumed here. + +## 3. The integer lockstep flow at a fixed rank + +This is the part of Theorem 1G used by the compiler. At one fixed top rank +`N`, its units, source jobs and exit jobs have integer multiplicities. +For a multi-index `a` on the target types define + +``` +c(a) = product_k k^(a_k), +u(a) = multinomial(|a|;a) * product_k W_k^(a_k). +``` + +The exact Pascal identity is + +``` +u(b) = sum_{k:b_k>0} W_k*u(b-e_k). +``` + +Let `G` be the largest `|a|` with `m*c(a)<=N`. A class is indexed by a +sequence of paid rounds `s` of length `d<=G`; its dilation is +`rho_s=product r_j`. It contains `u(a)` units at column `rho_s*c(a)` for +each `a` with `|a|=G-d` and `m*rho_s*c(a)<=N`. + +For one parent paid round, the Pascal bijection matches its job copies to +target roles of the child class, at exactly equal integer ranks. Missing +demands are top sources. Separation ensures every parent job is consumed. +The source ranks lie in `(N/m,N]`; only the deepest classes produce exit +jobs, all strictly smaller than `N` once `N` is outside the finite base range. + +Process a class in word order. At round `j`, suspend every unit of that +class, complete the entire child class fed by that round, and only then +advance the parents to round `j+1`. This forbids a unit from requiring both +an earlier and a later round of the same suspended parent. The resulting +dependency graph is finite and acyclic. Its edges carry complete array jobs, +not individual scalar values copied for free. + +These integer quantities exist before normalizing the sources to total +weight one. Let `S_s` be the number of source jobs of rank `s`, let +`S=sum_s S_s`, and let the ordered exit batches be `(e,t)` with `t` jobs +of rank `e` each. This finite integer flow is the compiler input. + +## 4. Clear every batch denominator constructively + +Induct on the integer top rank `N`. For each smaller rank `e` the compiler +has already constructed a uniform program on `B_e` arbitrary arrays, +computing full rank `e` with `P_e` paid rank-one calls. For a sufficiently +small rank use the ordinary sequential program: `B_e=1`, `P_e=e`. + +For the current flow choose an integer `a` divisible by every `B_e` needed +for an exit and every `B_(N-s)` needed for a nonzero source remainder. +The product of those finitely many positive integers is a valid choice; +their least common multiple is a smaller optional choice. Set + +``` +B_N = a*S. +``` + +Assign `a*S_s` of the input arrays to each source rank `s`. On each of those +arrays, first complete its `N-s` complementary coordinates using the +already-compiled smaller uniform program. All such batches are integral +because `a` is divisible by their program widths. This preliminary action +commutes with the intended `s`-coordinate job and fixes its input coordinates. + +Make `a` copies of the integer lockstep flow. Route its source arrays to +their exact input slots using permitted whole-array adapters. At a deepest +exit batch, `a*t` is divisible by `B_e`; replace that batch by copies of +the smaller uniform rank-`e` program. Restore its role ordering and adapters +before resuming the suspended parent class. Execute the finite DAG in the +lockstep order, and finally restore the original source-array ordering. + +Every array has now received its disjoint complementary job and source job, +hence the full rank-`N` transform. No copied scalar input or blank helper is +treated as another independent output. Every original array occurs exactly +once as a source; interior target slots are jobs on those arrays, not new +productive inputs. + +Induction removes all recursive calls: the only remaining paid children +have rank one. Clearing denominators multiplies productive arrays and paid +operations equally, so it preserves the per-array leaf count. In formulas, + +``` +P_N/B_N = (1/S) * [ + sum_s S_s * (P_(N-s)/B_(N-s)) + + sum_(ordered exit batches e,t) t * (P_e/B_e) +]. +``` + +Zero-rank terms vanish. Any plain rank-one exits are the ordinary base +program. Scalar and routing passes have their own analogous nonnegative +count and must be included in the asymptotic cost used to choose `N`. + +This construction uses full integer batches; it does not assume that +fractional pieces of a physical array can be routed at zero cost. Its exact +replication factors can be impractically large, which is acceptable for a +fixed finite supplier existence statement but must be disclosed. + +## 5. Why some fixed N has the required saving + +The independent audit sharpened this step to a direct count of paid leaves. +It does not require a running-time comparison between a RAM flow and native +tapes. Let `L(n)=P_n/B_n`, let `w_s=S_s/S`, and let `x_e` be the exit counts +normalized by the number S of source arrays. The actual integer compiler +satisfies + +``` +L(n) = sum_s w_s L(n-s) + sum_e x_e L(e), +sum_s w_s = 1, +sum_e x_e e^tau = sum_s w_s s^tau. +``` + +The last equality follows by canceling every internal matched job in the +exact tau-potential balance. The source ranks satisfy `n/m0`, concavity gives + +``` +n^z0 - sum_s w_s (n-s)^z0 >= eta * sum_s w_s s^z0. +``` + +Indeed, for `t=s/n` in `[1/m,1]`, +`1-(1-t)^z0 >= z0*t >= eta*t^z0`. For every sufficiently large n the +exit coefficient is less than `eta/2`. Every complement and exit has +smaller rank than n, so strong induction on the exact recurrence proves +`L(n)<=A*n^z0`, with finite A chosen to cover the smaller ranks. 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Full new scalar/owned FIELD/ROW/normalizer constants and tail/ordinary strictification not rerun." +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/inputs/INVERSE.json.gz b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/INVERSE.json.gz new file mode 100644 index 0000000000..ba1518613d Binary files /dev/null and b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/INVERSE.json.gz differ diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/inputs/REFERENCE111.json.gz b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/REFERENCE111.json.gz new file mode 100644 index 0000000000..85a4499bf9 Binary files /dev/null and b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/REFERENCE111.json.gz differ diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/inputs/three-stage-cover-bit.tex b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/three-stage-cover-bit.tex new file mode 100644 index 0000000000..f05225d21f --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/inputs/three-stage-cover-bit.tex @@ -0,0 +1,264 @@ +\subsection{Atom contract and common endpoint} +Fix an odd prime $q$, chosen below, and put $R_w=\mathbb Z/q^w\mathbb Z$. +An atom is a complete consecutive $w$-digit address field. Write $C_n$ for +reversal of the $n$ atom positions, without reversing digits inside an atom. +The recursive contract is the involution +\[ + F_A(H,D)=(AC_nD,C_nA^{-1}H), +\] +where $A$ is a diagonal array of units on the head atoms. Its entries may +depend on exposed ancestor row fields and the atom index, but not on the +fresh role fields of this invocation or on the head/data values. Only the +polynomial-time descriptors generated by the construction are required; +no constant-cost oracle for arbitrary functions of a prefix is assumed. +Every call preserves all complete spectator fields and restores its row +coordinate. The original unweighted call has $A=I$. + +For a split idempotent $P$ on the head coordinates set +\[ + D_P=\begin{pmatrix}I-P&PC_n\\C_nP&I-C_nPC_n\end{pmatrix}, + \qquad F=D_I. +\] +These are involutions, and $D_P-I$ has split rank $\operatorname{rank}P$. +Nested commuting-projector identities are polynomial identities and require +no symmetry of $P$. For $n=mf$ and $G=g\otimes I_f$ define +\[ + Q_g=\operatorname{diag}(G,C_nGC_n). +\] +Then $Q_gF=FQ_g$ and $Q_gD_PQ_g^{-1}=D_{GPG^{-1}}$. +Consequently conjugating every base frame by any $g\in\operatorname{GL}_m(R_w)$ +leaves the same full physical endpoint $F$. + +Put $Q_A=\operatorname{diag}(A,I)$. Conjugate the entire completed scalar +word by $Q_A$. Scalar gates mix roles having the same address map, so they +commute with $Q_A$. A current role routing also commutes with $Q_A$, since +it changes only fresh fields. Thus only address residuals change, and the +completed endpoint is $Q_AFQ_A^{-1}=F_A$. More explicitly, when a port +changes charts from $g$ to $gR_s$, its local label changes from $M$ to +$R_s^{-1}MR_s$, and +\[ + (gR_s)(R_s^{-1}MR_s)(gR_s)^{-1}=gMg^{-1}. +\] +This routing is a change of row/chart, not an uncharged dense address map. +The adapted chart $Q_AQ_gQ_A^{-1}$ commutes with $F_A$. None of these +conjugations is executed as an extra normalization pass. + +\subsection{Explicit rational three-stage geometry} +Use the retained PR97 local producer with +\[ + h=23,\qquad v=1771,\qquad R_{\rm loc}=28866,\qquad \ell=506. +\] +Its physical projector ranks and scalar word are unchanged. On +$\mathcal A=\mathbb Q^{23}$ take the form $H_0=(I-J/9)/2$. +For a triple $S$ let $q_S=\chi_S$; then $q_S^tH_0q_S=1$. +Fix $q_0=\chi_{\{1,2,3\}}$ and $K=q_0^\perp$. A rational basis is +\[ + k_i=e_i-(e_i^tH_0q_0)q_0,\qquad 2\le i\le23. +\] +Projection along $q_0$ is injective on the span of $e_2,\ldots,e_{23}$, +since $q_0$ has nonzero first coordinate. Thus this is indeed a basis. +Let $\mathcal B,\mathcal C$ be orthogonal copies of $K$ and put +$\mathcal E=\mathcal A\perp\mathcal B\perp\mathcal C$, of dimension $m=67$. + +Choose a coordinate permutation $\pi_S$ taking $\{1,2,3\}$ to $S$. +It preserves $H_0$. The rational isometry $R_{12,S}$ fixes $q_S$ and +$\mathcal C$, and exchanges $\pi_Sk_i\in q_S^\perp\subset\mathcal A$ +with $k_i\in\mathcal B$. Define $R_{23,S}$ by exchanging the same vectors +with their copies in $\mathcal C$, fixing $q_S$ and $\mathcal B$. +Both maps are involutions. A hyperedge $(g,S)$ uses the invocations +$gR_{12,S},g,gR_{23,S}$, with active spaces +\[ + g(\mathcal B+\mathbb Qq_S),\qquad g\mathcal A, + \qquad g(\mathcal C+\mathbb Qq_S). +\] +Their projectors commute; their pairwise and common intersection is the +projector $P_{gq_S}$, and their sum is $I+2P_{gq_S}$. +This follows from the orthogonal decomposition +$\mathbb Qq_S\perp q_S^\perp\perp\mathcal B\perp\mathcal C$ before +conjugation. These are the cumulative-projector three-stage transfer +identities: the three scalar shears complete the interchange, with zero +interstage connectors and no rank-one endpoint correction. Each port +family visits the full cover bijectively, by right multiplication with +its displayed involution. The physical ledger is therefore three copies +of the local auxiliary, data and center histograms, and three copies of +the exterior histogram $m-\text{nullity}$. + +\subsection{One weighted child on a generic residue class} +Work first on one atom column. Let $g$ be its weighted residual involution, +of split rank $r$ relative to $I$. If the cross block has generic northeast +rank profile, unit lower row and column elimination, without normalizing +pivots, gives +\[ + Lg_{XY}R=ED_pF_0^t, + \quad E=(e_1,\ldots,e_r),\quad + F_0=(e_m,\ldots,e_{m-r+1}), +\] +with invertible diagonal $D_p$. Conjugate by $\operatorname{diag}(L,R^{-1})$. +Split rank and the unit pivot minor give a factorization +\[ + g-I=\binom EB(A_0,D_pF_0^t),\qquad + A_0E+D_pF_0^tB=-2I_r. +\] +For clarity, if $g-I=UV$, then $g^2=I$ gives +$U(VU+2I)V=0$. The unit minor supplies a left inverse of $U$ and a right +inverse of $V$, proving the identity over the local ring itself. +Set +\[ + K=-(B+F_0D_p^{-1})E^t+F_0D_p^{-1}A_0(I-EE^t), + \qquad S=\begin{pmatrix}I&0\\K&I\end{pmatrix}. +\] +The identities $KE=-B-F_0D_p^{-1}$ and +$D_pF_0^tK=A_0+E^t$ give +\[ + SgS^{-1}=\begin{pmatrix} + I-EE^t&ED_pF_0^t\\F_0D_p^{-1}E^t&I-F_0F_0^t + \end{pmatrix}. +\] +This is one weighted reversed interchange on the first $r$ head and last +$r$ tail coordinates. All other factors are unit lower intrabank maps or +lower cross-bank additive maps. Thus variable diagonal units remain in +the child's weight array rather than becoming unsupported routing passes. + +For $n=mf$, group atoms by coarse coordinate $i$ and column $j$. +If $L_P,R_P,D_P$ are unweighted normalizers for the current projector and +$A_j=\operatorname{diag}(A[if+j])$, then +$L_j=A_jL_PA_j^{-1}$ and $R_j=R_P$ are unit lower normalizers for +$A_jPC_m$. The child's exact contiguous index rule is +\[ + A_{\rm child}[kf+j]=A[i_kf+j]D_P[k]. +\] +The cross-bank atom pairing is reversed, and $C_r\otimes C_f=C_{rf}$. +Hence the middle operation is exactly one $rf$-atom call of the same +contract, with no interleaving or gathering. Its coefficients depend only +on parent prefix fields, which become ancestor spectators at the child; +the child's fresh roles come from disjoint unused row stock. + +All unit lower adapters require $O(n)$ atom passes. The retained ordered +affine lemma implements each later-target shear in $O(V)$, including +prefix-controlled offsets. The generated descriptors have polynomial cost +in $w$: good-class evaluation follows one ancestral index per level; +fallback evaluation branches by a constant per level. Since depth is +$O(\log e)$ and $w=\lceil e^{1/1000}\rceil$, this costs $e^{O(1)}=w^{O(1)}$. +Stored ancestor data use $O(w\log e)$ bits. The proof of the ordered affine +lemma still applies with these controls: polynomial preparation per prefix +is absorbed by the complete $q^w$ target fiber. Unrelated spectator counters +are incremented by ripple counting rather than read in their entirety. + +\subsection{Weighted leaves and a genuine local-ring fallback} +At one atom write $J_a=\left(\begin{smallmatrix}0&a\\a^{-1}&0\end{smallmatrix}\right)$, +$U(a)=\left(\begin{smallmatrix}1&a\\0&1\end{smallmatrix}\right)$ and +$L(b)=\left(\begin{smallmatrix}1&0\\b&1\end{smallmatrix}\right)$. +Then +\[ + J_a=\operatorname{diag}(1,-1)U(a)L(-a^{-1})U(a), + \qquad U(a)=J_1L(a)J_1. +\] +Thus a weighted leaf uses four old ordinary atom interchanges, three +prefix-controlled shifts and one fixed sign. With +$a_{\rm old}=384599/10^{10}$ it costs $O(Vw^{1-a_{\rm old}})$. +This constant occurs only at stopped leaves. + +A bad residue class cannot be treated by field Bruhat elimination: +an entry zero modulo $q$ need not vanish modulo $q^w$. Instead Gaussian +eliminate the full invertible residual of size $N_0=2m$ with unit pivots. +Each invertible Schur complement has a unit in its next pivot column; +row swaps and unnormalized additions clear that column. There are at most +$N_0(N_0-1)$ additions and $N_0$ swaps. Pivot choices are determined by +the unweighted low residue class: diagonal conjugation scales every +Schur-complement row and column by units and preserves its zero pattern. +The final diagonal has product a fixed sign, since the residual has +determinant $(-1)^r$ and row swaps change only the sign. + +A lower addition is a paid additive adapter. An upper addition is +conjugated into a lower addition by two ordinary coarse-field swaps. +For a field of $f$ atoms, let $R_{\rm tail}$ reverse the later field. +Then the ordinary weighted swap is +\[ + J_A=R_{\rm tail}F_AR_{\rm tail},\qquad + J_A(H,D)=(AD,A^{-1}H). +\] +Each $R_{\rm tail}$ is one unweighted reversed call on the first and last +$\lfloor f/2\rfloor$ atoms, fixing a possible middle atom. Thus $J_A$ +costs at most three children of widths $f,\lfloor f/2\rfloor, +\lfloor f/2\rfloor$. A paired diagonal scaling is $J_aJ_1$, at most six +children. The full diagonal is a product of $N_0-1$ such pairs and a fixed +sign. Across the two banks the reversed pairing already makes the swaps +and diagonal pairs directly reversed calls; the preceding ordinary bounds +remain conservative. Reindexing a tail weight by $j\mapsto f-1-j$ changes +only its descriptor. Charging every addition as upper therefore gives +\[ + 6N_0(N_0-1)+3N_0+6(N_0-1)<32m^2. +\] +Every child has width at most $f$, hence ratio at most $1/m$. Coefficients +are computed from constant-sized local-ring matrices and parent weight +descriptors; only units are inverted. This proves the fallback cost, +including its actual reversals, rather than assuming nonunit pivots away. + +\subsection{Finite covers, batching, and the strict moment} +Take $q>2^{80}$ avoiding all fixed rational denominators and rank witnesses. +At atom width $w$ use the finite cover $\operatorname{GL}_m(R_w)$ and its +right-multiplication edges $g\mapsto gR_s$. Every vertex has the unique chart +\[ + g=g_0+qG_1,\quad g_0\in\operatorname{GL}_m(\mathbb F_q), + \quad G_1\in(\mathbb Z/q^{w-1}\mathbb Z)^{m^2}, +\] +using fixed representatives for $g_0$. Right multiplication permutes $g_0$ +and acts affinely on $G_1$, with a carry determined by $g_0$. Its fixed +dimensional rational linear part factors into fixed scalings, ordered +shifts and a constant number of old width-$O(w)$ interchanges. Thus each +fixed port routing costs $O(Vw^{1-a_{\rm old}})$. + +Let $W_0=|\operatorname{GL}_m(\mathbb F_q)|(2v+3R_{\rm loc})$. +The full role count is $W(w)=W_0q^{m^2(w-1)}$. Split preceding rows into +low role type, high matrix and unused stock. Batch \emph{all} high matrices +for each low type in one stream. A frame edge is one child on this whole +batch, of volume $V/W_0$, and routing is executed once per fixed operation +type. Consequently neither the number of tapes nor the number of child +programs grows with $w$. High cardinality cancels in the normalized moment, +but its $m^2(w-1)$ digits are charged in the row reserve. + +For each fixed projector require the leading minors of sizes $1$ through +$r$ to be units. Each cleared minor polynomial in $g_0$ is nonzero: +similarity to $\operatorname{diag}(I_r,0)$ supplies a witness after the +fixed rank is preserved modulo $q$. Their total degree is at most $m^3$. +The polynomial zero bound and conditioning on invertibility (a factor at +most two) give bad fraction at most $2m^3/q<10^{-16}$ for each edge type. +No simultaneous union bound over edge types is needed, since their moments +are averaged separately. Good classes use the whole-rank child; bad +classes use the full $32m^2$-child fallback just proved. + +Let $H_r$ be the three-stage histogram described above and +$W=2v+3R_{\rm loc}=90140$. The retained ledger gives +\[ + \sum_r rH_r=6037356,\qquad Wm-\sum_r rH_r=2024=2v-3\ell, + \qquad \max\{r:H_r>0\}=66. +\] +For $a=747/2000000$, $\tau=1-a$, and $b=10^{-16}$ the conservative moment is +\[ + \mu_\tau\le + \sum_r\frac{H_r}{W}(r/m)^\tau+ + b\frac{32m^2\sum_rH_r}{W}(1/m)^\tau<1. +\] +The entire fallback is added; no displaced good contribution is subtracted. +The exact script \path{scripts/three_stage_cover_network.py} and certificate +\path{certificates/three-stage-cover-network.json}, from the retained axis +\path{certificates/three-stage-cover-bit-input.json}, give +$1-\mu_\tau>6.3397366396\cdot10^{-7}$. +The certificate uses the 32-term positive atanh logarithm series with its +geometric tail, $\exp(u)\le1+u+u^2/(2(1-u/3))$, and upward rounding to +the grid $2^{-120}$. All inputs have $0\le u<3$; these are rational upper +bounds, not floating-point root estimates. Since every child ratio is at +most one and $\tau<1$, this same strict bound implies $\mu_1<1$. + +With $T(n,w)$ denoting time divided by logical volume, the fixed low-type +profile $\{c_r\}$, including fallback classes, satisfies +\[ + T(n,w)\le\sum_rc_rT(r\lfloor n/m\rfloor,w)+Cn+Cw^{1-a_{\rm old}} + \quad(n\ge m),\qquad + T(n,w)\le Cw^{1-a_{\rm old}}\quad(na_{\rm bit}$ and $\beta<1-a_{\rm bit}$ make both +the atom-adapter and borrowing terms lower order. The remainder cost +$O(Vw^{1-a_{\rm old}})$ is also covered. Thus the ordinary radix-$q$ +interchange has cost $O(Ve^{1-a_{\rm bit}})$, without an externally supplied +superpolynomial stock of rows. + +For an original binary chunk range $[2^e]$, let +$t=\lceil e/\log_2q\rceil$ and embed it numerically into $[q^t]$. +Pad both exchanged ranges while retaining every spectator. The total +logical-volume increase is below $q^2$. Execute the completed ordinary +radix-$q$ interchange, then remove the padding. Its endpoint preserves the +rectangular genuine set $[2^e]\times[2^e]$; intermediate maps may mix genuine +and padded addresses, which does not affect this endpoint justification. +As $q$ is fixed and $t=\Theta(e)$, the binary interchange has the same +saving exponent. All schedules use a fixed number of finite-alphabet +tapes; low residue tables and port types are fixed independently of $w$. + +The conclusion retains the original local-producer, ordered-affine, +ordinary-leaf and multiplication-framework hypotheses. It adds no free +unit-scaling, dense chart transformation, or external row-stock primitive. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/intake.py b/research/bit-g20-nine-owned-relations/vendor/g20/intake.py new file mode 100644 index 0000000000..8ebf350a07 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/intake.py @@ -0,0 +1,45 @@ +"""Copy exact immutable local inputs; no network or edits to old packages.""" +from pathlib import Path +from datetime import datetime,timezone +import hashlib,json +ROOT=Path(__file__).resolve().parent;RUN=ROOT.parent;H=RUN/'center-bit-extension' +def need(c,m): + if not c:raise ValueError(m) +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +def main(): + dest=ROOT/'inputs';dest.mkdir(exist_ok=True);provider=ROOT/'provider';provider.mkdir(exist_ok=True);sources=RUN/'source4359/current-main-repository';pub=RUN/'bootstrap-publication/gitfree-0003/research/bit-compact-productive-controller' + mapping={ + 'BASELINE-LOCAL.json.gz':RUN/'native-small/gate0003/local-partial/WORD.json.gz', + 'FORWARD.json.gz':H/'gate0020-shadow-assisted-query-fusion/WORD.json.gz', + 'INVERSE.json.gz':H/'gate0022-shadow-fusion-inverse-and-requests/INVERSE-WORD.json.gz', + 'FRAMES.json':H/'gate0001-native-coupled667/FRAMES.json', + 'CONTROLLER.json':sources/'research/query-thinned-controllers/BIT-CONTROLLER.json', + 'REFERENCE111.json.gz':sources/'research/kappa-rebuild/bit/sources/pr589-regenerated/WORD.json.gz', + 'BASELINE-GLOBAL-RESULT.json':RUN/'native-small/gate0004/RESULT.json', + 'BASELINE-RATIONAL-BINDING.json':RUN/'native-small/gate0004/RATIONAL-BINDING.json', + 'ACTIVE-AXES.json':RUN/'native-small/gate0004/ACTIVE-AXES.json', + 'G20-WINDOW.json':H/'gate0020-shadow-assisted-query-fusion/SELECTED-WINDOW.json', + 'G22-FRESH-REQUESTS.json':H/'gate0022-shadow-fusion-inverse-and-requests/FRESH-QUERY-REQUESTS.json', + 'G23-EXPECTED.json':H/'gate0023-shadow-fusion-controller/RESULT.json', + 'G23-RAW-PRICE.json':H/'gate0023-shadow-fusion-controller/PRICE.json', + 'DELAYED-COVER-BRIDGE.md':sources/'research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md', + 'FINITE-PRECOMPILATION.md':sources/'research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md', + 'three-stage-cover-bit.tex':sources/'notes/three-stage-cover-bit.tex', + 'three-stage-cover-rows.tex':sources/'notes/three-stage-cover-rows.tex', + '02-streams.tex':RUN.parent/'20261020/framework/openai109/02-streams.tex', + '4814-local_word.py.txt':pub/'local_word.py', + '4814-global_word.py.txt':pub/'global_word.py', + '4814-audit_stream.py.txt':pub/'audit_stream.py', + '4814-independent_native.py.txt':pub/'independent_native.py', + } + pins=[] + for name,source in mapping.items(): + b=source.read_bytes();target=dest/name + if target.exists():need(target.read_bytes()==b,'Refuse changed input '+name) + else:target.write_bytes(b) + pins.append({'relative_path':'inputs/'+name,'sha256':sha(target),'bytes':len(b),'read_only_origin':str(source)}) + out=ROOT/'INPUT-PINS.json' + if out.exists():need(json.loads(out.read_bytes())['files']==pins,'Inputs immutable') + else:out.write_text(json.dumps({'schema':'g20-private-candidate-inputs/1','at_utc':datetime.now(timezone.utc).isoformat(),'files':pins,'scope':'Historical4760/4814 and research proof bytes are copied read-only. Runtime provider uses these relative local paths only. No publication/ordinary claim.'},indent=2)+'\n',encoding='utf-8') + print(json.dumps({'status':'PINNED_LOCAL_READONLY_INPUTS','files':len(pins),'bytes':sum(p['bytes']for p in pins)})) +if __name__=='__main__':main() diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/FEE-BOUNDS.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/FEE-BOUNDS.json new file mode 100644 index 0000000000..fbd8925661 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/FEE-BOUNDS.json @@ -0,0 +1,53 @@ +{ + "status": "PASS_EXPLICIT_POSITIVE_FIXED_PROGRAM_FEE_BOUNDS", + "base_counts": { + "raw_records": 446436, + "scan_assign_CLEAR_INIT_passes": 381733, + "parent_parking_FIELD_passes": 2614296168, + "all_internal_plus_canonical_routes": 14796, + "coarse_base_primitive_descriptions_including_local_dimension_work": 971523007765, + "verified_less_than": "18446744073709551616" + }, + "fixed_tensor_unit": { + "v": 1024, + "upper_K": "2^262144", + "meaning": "K bounds all fixed integer ranks, role/round/operation inventories after chronological tensor product, charged target completion and paid splitting. No owned array is a productive role." + }, + "finite_compiler_count_bound": { + "top_rank_N": "2^262304923748800276275201", + "J(n)": "(n+1)^4 * K^(4*n+4)", + "A(1)": "K^4", + "A(n)": "(J(n)+2)^4 * (A(n-1)+2)^(4*n+8), for2<=n<=N", + "bounds": "A(n) bounds productive roles, paid leaves, compiled unit instances, primitive/route descriptors, owned banks, and coefficient-construction descriptions. Allocate2 banks for EVERY unit instance; C_N<=2*A(N). A(n) is a concrete finite recursive integer, not expanded or assumed small.", + "replication": "At n, the denominator-clearer product of smaller widths is <=A(n-1)^(n-1); source/exit flow inventories are <=J(n). The displayed recurrence dominates their products, smaller-program inlining and two owned banks per unit." + }, + "rational_height_and_prime": { + "base_input_height_bits_upper": 1024, + "arithmetic_step_bound_T": "(2*N+2)^4 * (A(N)+2)^2", + "rational_height_bits_H": "1026 * 4^(T+1)", + "meaning": "Each exact rational arithmetic operation increases numerator/denominator bit height by at most4*(height+1). This includes fixed rational matchers/Gaussian eliminations, not only VALUE coefficients. Every fixed matrix/witness is compiled first.", + "choose_q": "An odd prime q>max(2^45*N^5, 2^(2*H)), excluding the finite completed-program witnesses. No previous numerical prime/H/precision threshold is reused." + }, + "all_in_primitive_fee": { + "low_types_upper": "q^(N^2)", + "single_fixed_route_or_leaf_normalizer_bound": "(q+2)^(16*(N+1)^2) retained primitive invocations, including low-type dispatch, carry and polynomially many fixed affine/scaling/old-atom operations. Rank-one leaf shears<=4*N^2-2*N; bad classes charged<=32*N^2 ordinary calls separately in moment.", + "compiled_primitive_multiplier_F": "(q+2)^(32*(N+1)^2) * (A(N)+2)^8", + "actual_cost": "F times a positive maximum retained completed-backend/stream primitive constant. The latter is fixed at each finite level, never declared1 or free. This is a constructive finite bound schema, not a materialized all-in machine constant.", + "parking": "At most4*(B_N+C_N) FIELD passes per query plus initialization/teardown. B_N, P_N, C_N and all route counts are bounded above by the explicit A(N) expressions. The F bound dominates these positive products." + }, + "stock": { + "uniform_B": "B_N<=A(N)", + "owned_C": "C_N<=2*A(N), full owned INIT/CLEAR charged", + "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend", + "depth_D": "floor(log_N ceil(e/w))+1 is safe", + "borrowed_digits_bound": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1; =O_new(w loge)", + "nested_backend": "Each completed finite backend restores all outer ROW/spectators and its own stock before return; it supplies no externally assumed empty space." + }, + "eventual_threshold_rule": { + "stage_constant": "K_j>=16 times the sum of F*all positive inherited primitive constants, reserve/adapter bounds and the already frozen backend constant globalized to ALL widths by its finite fallback. K_j is newly fixed before e varies.", + "stage_gap": "eta_j=min(rho-a_j,1-rho-a_j,a_j-b_j)>0", + "sufficient_form": "A new integer e_j dominates E_backend^(ceil(2/rho)), the borrow threshold, and ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).", + "justification": "For fixed positive eta, loge<=2/eta * e^(eta/2); the displayed oversized threshold absorbs every fixed coefficient in the three root costs and k 0, + +all original and completion tails fit. After these explicitly paid +operations the exit/child separation follows from17^64<18^63, not from +the false base assertion63<4. The raw127-dimensional ambient is below256. + +Put z=1-C0,z0=(t+z)/2,h=1/64 and d=z0-t. Exact rational ceilings give + + H0=377296594739200, + H1=262304923748800276275201, + N=2^H1. + +The checked source inequalities are + + H0>=8192, + H0*h*d >= d*(5+8*h)*1024 + 1+8*1024*(1-z0), + H1*(z-z0)>H0*(1-z0). + +These are effective **rank-compiler** thresholds. They are not claims +about old tape, semantic precision or running-time thresholds. The old +PR4814 H0 fails the new induction and is explicitly rejected. The source +finite integer batching clears all denominators with real independent +owners, inlines smaller whole jobs in chronological lockstep, and produces +one fixed uniform program with B_N originals and P_N rank1 leaves such +that P_N/B_Nmax(2^45*N^5,2^(2*H)), avoiding that finite list. +There is no reliance on the old numeric q or precision cutoff. Right +routes use the actual inherited complete fiber permutation g->g*S, +not an unpriced ADDRESS gather. There are at most q^(N^2) low types. +Each high-row route uses polynomially many fixed affine/scaling/ordered +passes, carries and calls to the completed atom backend. With each fixed +rational coefficient smaller than sqrt(q), a finite-state carry table +has a bounded number of registers/ranges. The very loose bound + + (q+2)^(16*(N+1)^2) + +retained elementary primitive invocations per fixed route or normalizer +dominates low-type tables, carry cases and polynomial dimension work. +For example high-row right multiplication takes N independent N-field +row maps and O(N^3) elementary updates; bounded carries and low-type +dispatch are finite tables. Weighted leaf data remain ancestor inputs, +handled by the retained weighted primitive, not enumerated at q^w. +Rank1 generic lowering uses <=4*N^2-2*N shears; the bad-class <=32*N^2 +ordinary calls are separately charged by the moment surcharge. + +One conservative total multiplier for the completed finite program is + + F=(q+2)^(32*(N+1)^2)*(A(N)+2)^8. + +This dominates positive parking4*(B_N+C_N) per child, all copies/clears, +role restoration, whole-fiber routes and their normalizers. Actual +machine costs are F times a positive maximum retained backend/stream +primitive constant. The same source implementation hypotheses, including +their O(V*w^(1-b_backend)) fixed-rational route contract, are retained. +This is not a new proof of those primitive machine constants. They may +be enormous, but are fixed before the final input width varies and are +never dropped from the eventual threshold. + +## 4. Whole cover, arbitrary rows and stock + +Let d_cover=2^-36+10^-20 and C1=C0-d_cover. Exactly + + C1=22781037022072568293839/6553600000000000000000000. + +Since2^45*d_cover>256, the delayed whole-GL cover's full bad-class +surcharge is below1+d_cover/4, whereas N^d_cover>=1+d_cover/2. This +preserves strict contraction at covered saving C1, after the finite +program is compiled. All current jobs remain actual whole arrays; +canonical matcher right routes are paid before/after the complete unit. +Only final rank1 leaves are lowered. One external ancestor-only weight +is common through each compiled invocation; incompatible child-specific +weights are not silently combined. + +The uniform unit operates at every column count f and preserves complete +spectators, arbitrary current RAW correlations and ordered paired tails. +An owned SUM can serve as a child argument but earns no new parent input +credit. Every unit instance has distinct owned tags. The whole source +endpoint is unchanged by replacing the G20 window; neither FRAME +retagging nor an unproved read-only SOURCE premise is used. + +A safe borrowed stock is W(w)^D*S_backend, where + + W(w)=B_N*|GL_N(F_q)|*q^(N^2*(w-1)), + D=floor(log_N ceil(e/w))+1. + +Its borrowed digits are bounded by + + D*[N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|))] + +ceil(log_q S_backend)+1 = O_new(w loge). + +The inner completed backend keeps the entire outer row/spectators fixed, +borrows from its own complete argument, and restores that stock before +return. No external empty space or fresh DATA appears. Padding/unpadding +occurs at completed endpoints with a fixed volume factor; the backend's +prime need not equal q. The ordinary two-body wrapper and high-part +exchange are the retained completed contract, with their positive fees. + +## 5. Three fixed levels and eventual thresholds + +Use rho=1/100 and w=ceil(e^rho), starting from the completed ordinary +PR4814 A0 with b0=1737729/500000000. Freeze a *distinct* A_j after A_(j-1) +has been completed. Coarse calls decrease atom count; backend calls +decrease the finite level j. There is no self/forward reference or a +bootstrap depth tending to infinity with e. + +The three charged root terms are + + O_new(V*[e^(1-rho) + + e^((1-rho)*(1-C1)+rho*(1-b_(j-1))) + + e^rho*loge]). + +Put a_j=(1-rho)C1+rho*b_(j-1) and relax on the1e-12 grid. Exact checks give + + b1=.003476103861, + b2=.003476110320, + b3=.003476110384. + +Every step satisfies b_(j-1)0. + +A new integer threshold can dominate the previous backend threshold to +power ceil(2/rho), the borrow threshold, and + + ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)). + +The elementary bound loge<=2/eta_j*e^(eta_j/2) shows these oversized +choices absorb every finite coefficient in the three root costs and +force borrowed digits/verify.py --provider /provider --output +python -I -O -B /verify.py --provider /provider --output +``` + +Only stdlib and local byte-pinned files are read. The20 source inputs +include unchanged credited interval/series engines and PR4814's completed +backend proof/result. Provenance paths are never followed at runtime. +The new certificate checks actual literal P/T, three completely charged +tails, new finite rank thresholds, cover/prime fallback and three acyclic +completed backends. Base parking alone is2614296168 FIELD passes; +normalizer/route/owned fees have explicit positive finite bound schemas, +not the old1e9 all-in assumption. All program/tape/precision/stock constants +are newly fixed, under the same retained source contracts. + +The native data and its normal/-O cold replay remain sealed next door. +This directory is a successor; nothing in published PR4760/4814, the old +retiming gates or the first native-candidate manifest is changed. + +`PROOF.md` gives quantifiers, actual ABI, fee bounds and limitations. +`RESULT.json` contains exact arithmetic. `INDEPENDENT.json` recounts +the native stream and uses a separate rational series. `RESTART.json` +identifies the root independent review, not a new publication request. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/REPORT.txt b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/REPORT.txt new file mode 100644 index 0000000000..54a2609166 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/REPORT.txt @@ -0,0 +1,11 @@ +PRIVATE G20/G23 ordinary successor complete, conditional on the same retained PR4760/PR4814 native/compiler/precision/completed-ROW implementation premises. No new PR. + +Exact admitted ordinary BIT saving: 217256899/62500000000 = .003476110384. Comparator1737729/500000000=.003475458. Relative gain 40774/217216125 = 0.01877116627506360312799061303574953286732 percent, below0.1percent. This is distinct from the historicalrawroot .003476110419631239... and its different raw comparator. Wholekappa unchanged. + +Three frozen acyclic levels from completedPR4814: .003476103861, .003476110320, .003476110384. rho=.01, tested=.00347611041, uniform=.00347611040, covergap2^-36+1e-20, alpha_gap2^-39, v1024, primecoefficient2^45. Every completion at18^1024 and split at17^1024 is charged. ExactnewH0=377296594739200, H1=262304923748800276275201. OldH0 rejected. These are rankcompiler thresholds; new tape/stock/precision and runtime cutoffs have separate explicit finite rules. + +All original/helper jobs remain from the sealed literal provider:11400arbitraryRAW,57321actualqueries,2ownedbanks,1845episodes,18properrank4requests,485bitprefixheight. The independent arithmetic reader recounts P from the literal stream and T from actual original target owners, not a headline. All48native runtime bytes remain pinned. The independent rationalheight check reconstructs644frameprojectors, maxentry3bits and485bitresidual/VALUEenvelope, charged1024. + +Fees are positive: base parking2614296168FIELDpasses exceeds old1e9 raw allowance; both internal7548 and canonical7248routes remain paid. The new finite DAG is bounded by explicit recursively defined integers J(n),A(n); ownedC_N<=2A(N) allocates per compiled unit, not perdepth. All route/normalizer/carry/parking/control work is bounded in retained primitive invocations by F=(q+2)^(32(N+1)^2)*(A(N)+2)^8, multiplying actual positive inherited backend/stream constants. Absolute machine constants, astronomicaluniformWORD,N andq are not materialized or declared1. New prime, height and eventual cutoff rules are explicitly fixed after finite compile. Stock remainsO_new(w loge) with restored complete spectators/ROW, and every fixed coefficient is absorbed only at a new threshold. + +Isolated normal/-O cold CLI bothPASS: primaryexactintervals plus independent positive-series/census audit. CPU 2.71875s / 2.78125s. Runtime manifest 77cc1b9a69aba096466df23a180256303ee4f91d9a451d9ab42cb0a80ab427f4. Native provider manifest 15034901fb7641ff6cf154e3d8e3e82d1f02332a1f54ed52a90bef9667648ca3. Retained assumptions are explicitly conditional and root independent review is next. Published/frozen source trees and previous sealed native outputs were not edited. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/RESTART.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/RESTART.json new file mode 100644 index 0000000000..24d199100d --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/RESTART.json @@ -0,0 +1,27 @@ +{ + "status": "PRIVATE_CONDITIONAL_ORDINARY_GATE_READY_FOR_ROOT_REVIEW", + "native_provider": "../provider", + "native_manifest_sha256": "15034901fb7641ff6cf154e3d8e3e82d1f02332a1f54ed52a90bef9667648ca3", + "admitted": "217256899/62500000000", + "comparison_to": "1737729/500000000", + "relative_gain": "40774/217216125", + "whole_kappa": null, + "publication": "No newPR; below0.1percent guard; published/frozen trees unchanged.", + "review_first": [ + "PROOF.md", + "FEE-BOUNDS.json", + "RESULT.json", + "INDEPENDENT.json" + ], + "next_concrete_gate": "Root independently checks exact tails, new H0/H1, original/currentSOURCE ABI, explicit large positive fees, live-unit stock and finite completed-backend type. Only after that may this be used as a private future bundle input.", + "do_not_repeat": [ + "More decimal tightening", + "Oldretimingwindow/sourcebasis exclusions", + "Publishing subthreshold rawroot as ordinary saving" + ], + "bounds_not_materialized": [ + "Astronomical final uniform WORD", + "N=2^H1 or new q as a literal integer", + "Absolute source primitive TM constants; retained fixed implementation premises remain conditional" + ] +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/RESULT.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/RESULT.json new file mode 100644 index 0000000000..7922f2b99e --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/RESULT.json @@ -0,0 +1,194 @@ +{ + "status": "PASS_CONDITIONAL_G20_ORDINARY_THREE_FINITE_LEVELS", + "native_runtime_manifest": { + "relative_path": "provider/MANIFEST.json", + "bytes": 8823, + "sha256": "15034901fb7641ff6cf154e3d8e3e82d1f02332a1f54ed52a90bef9667648ca3" + }, + "invoice": { + "paid": { + "1": 25389, + "2": 24156, + "3": 1386, + "4": 720, + "5": 1836, + "6": 180, + "7": 324, + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + }, + "targets": { + "4": 72, + "8": 7776, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "127": 222 + }, + "originals": 11400, + "private_output_credit": 0, + "QUERYs": 57321, + "rawrank_surplus": 753, + "rawprice_reference": "inputs/G23-RAW-PRICE.json only, notordinarysaving", + "ordinary_tail_bootstrap_status": "Pendingseparatecertificatewithfreshfees/constants; old4760/4814unchanged" + }, + "params": { + "tested": "347611041/100000000000", + "uniform": "2172569/625000000", + "cover_gap": "95367431706161/6553600000000000000000000", + "alpha_gap": "1/549755813888", + "prime_coefficient": 35184372088832, + "rho": "1/100", + "v": 1024, + "cutoff": 17, + "floor": 18, + "u": "1/5", + "grid": 1000000000000 + }, + "tail": { + "alpha": { + "lower": "0.999999999990333712977496242156", + "upper": "0.999999999990333712977496242157" + }, + "gamma": { + "lower": "0.958138718122069468445491070071", + "upper": "0.958138718122069468445491070072" + }, + "delta": { + "lower": "0.948389584343131930157108110904", + "upper": "0.948389584343131930157108110905" + }, + "ratios_exact_intervals": { + "alpha": [ + "3138550867663002248396042666778813173509284240434791613149/3138550867693340381917894711603833208051177722232017256448", + "3138550867663002248396042666778813173509284240434791720435/3138550867693340381917894711603833208051177722232017256448" + ], + "gamma": [ + "3007167105132606006776902852322398945723502972917739114897/3138550867693340381917894711603833208051177722232017256448", + "6014334210265212013553805704644797891447005945835478592075/6277101735386680763835789423207666416102355444464034512896" + ], + "delta": [ + "186035559553216446344087226180572750593035623423664064275/196159429230833773869868419475239575503198607639501078528", + "372071119106432892688174452361145501186071246847328141375/392318858461667547739736838950479151006397215279002157056" + ] + }, + "normalized_surplus_lower": "536870911/576460753377165312", + "target_completion": "Every product target below18^1024 gets a paid complementary job on that SAME owner", + "paid_splitting": "Every old and added paid job split at17^1024, all pieces charged", + "new_H0": 377296594739200, + "new_H1": 262304923748800276275201, + "new_N": "2^262304923748800276275201", + "scope": "Rank-compiler bounds; positive machine/ROW/stock thresholds are newly generated separately." + }, + "C1": "22781037022072568293839/6553600000000000000000000", + "finite_backend_levels": [ + { + "level": 1, + "completed_backend": "1737729/500000000", + "ordinary_exact": "2278099426733984261090061/655360000000000000000000000", + "admitted": "3476103861/1000000000000", + "margins": { + "adapter": "4275500573266015738909939/655360000000000000000000000", + "stock": "646528300573266015738909939/655360000000000000000000000", + "relaxation": "389024261090061/655360000000000000000000000" + }, + "algorithm_order": "Freeze A_(j-1), then compile A_j with new fixed source/tape/height/ROW constants; never call A_j as its own atom backend." + }, + { + "level": 2, + "completed_backend": "3476103861/1000000000000", + "ordinary_exact": "2278103659448633861090061/655360000000000000000000000", + "admitted": "43451379/12500000000", + "margins": { + "adapter": "4275496340551366138909939/655360000000000000000000000", + "stock": "646528296340551366138909939/655360000000000000000000000", + "relaxation": "133433861090061/655360000000000000000000000" + }, + "algorithm_order": "Freeze A_(j-1), then compile A_j with new fixed source/tape/height/ROW constants; never call A_j as its own atom backend." + }, + { + "level": 3, + "completed_backend": "43451379/12500000000", + "ordinary_exact": "2278103701778336261090061/655360000000000000000000000", + "admitted": "217256899/62500000000", + "margins": { + "adapter": "4275496298221663738909939/655360000000000000000000000", + "stock": "646528296298221663738909939/655360000000000000000000000", + "relaxation": "520096261090061/655360000000000000000000000" + }, + "algorithm_order": "Freeze A_(j-1), then compile A_j with new fixed source/tape/height/ROW constants; never call A_j as its own atom backend." + } + ], + "admitted": "217256899/62500000000", + "comparator": "1737729/500000000", + "relative_gain": "40774/217216125", + "relative_gain_percent": "163096/8688645", + "qualifies_0_1_percent_public_guard": false, + "fee_bounds": { + "status": "PASS_EXPLICIT_POSITIVE_FIXED_PROGRAM_FEE_BOUNDS", + "base_counts": { + "raw_records": 446436, + "scan_assign_CLEAR_INIT_passes": 381733, + "parent_parking_FIELD_passes": 2614296168, + "all_internal_plus_canonical_routes": 14796, + "coarse_base_primitive_descriptions_including_local_dimension_work": 971523007765, + "verified_less_than": "18446744073709551616" + }, + "fixed_tensor_unit": { + "v": 1024, + "upper_K": "2^262144", + "meaning": "K bounds all fixed integer ranks, role/round/operation inventories after chronological tensor product, charged target completion and paid splitting. No owned array is a productive role." + }, + "finite_compiler_count_bound": { + "top_rank_N": "2^262304923748800276275201", + "J(n)": "(n+1)^4 * K^(4*n+4)", + "A(1)": "K^4", + "A(n)": "(J(n)+2)^4 * (A(n-1)+2)^(4*n+8), for2<=n<=N", + "bounds": "A(n) bounds productive roles, paid leaves, compiled unit instances, primitive/route descriptors, owned banks, and coefficient-construction descriptions. Allocate2 banks for EVERY unit instance; C_N<=2*A(N). A(n) is a concrete finite recursive integer, not expanded or assumed small.", + "replication": "At n, the denominator-clearer product of smaller widths is <=A(n-1)^(n-1); source/exit flow inventories are <=J(n). The displayed recurrence dominates their products, smaller-program inlining and two owned banks per unit." + }, + "rational_height_and_prime": { + "base_input_height_bits_upper": 1024, + "arithmetic_step_bound_T": "(2*N+2)^4 * (A(N)+2)^2", + "rational_height_bits_H": "1026 * 4^(T+1)", + "meaning": "Each exact rational arithmetic operation increases numerator/denominator bit height by at most4*(height+1). This includes fixed rational matchers/Gaussian eliminations, not only VALUE coefficients. Every fixed matrix/witness is compiled first.", + "choose_q": "An odd prime q>max(2^45*N^5, 2^(2*H)), excluding the finite completed-program witnesses. No previous numerical prime/H/precision threshold is reused." + }, + "all_in_primitive_fee": { + "low_types_upper": "q^(N^2)", + "single_fixed_route_or_leaf_normalizer_bound": "(q+2)^(16*(N+1)^2) retained primitive invocations, including low-type dispatch, carry and polynomially many fixed affine/scaling/old-atom operations. Rank-one leaf shears<=4*N^2-2*N; bad classes charged<=32*N^2 ordinary calls separately in moment.", + "compiled_primitive_multiplier_F": "(q+2)^(32*(N+1)^2) * (A(N)+2)^8", + "actual_cost": "F times a positive maximum retained completed-backend/stream primitive constant. The latter is fixed at each finite level, never declared1 or free. This is a constructive finite bound schema, not a materialized all-in machine constant.", + "parking": "At most4*(B_N+C_N) FIELD passes per query plus initialization/teardown. B_N, P_N, C_N and all route counts are bounded above by the explicit A(N) expressions. The F bound dominates these positive products." + }, + "stock": { + "uniform_B": "B_N<=A(N)", + "owned_C": "C_N<=2*A(N), full owned INIT/CLEAR charged", + "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend", + "depth_D": "floor(log_N ceil(e/w))+1 is safe", + "borrowed_digits_bound": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1; =O_new(w loge)", + "nested_backend": "Each completed finite backend restores all outer ROW/spectators and its own stock before return; it supplies no externally assumed empty space." + }, + "eventual_threshold_rule": { + "stage_constant": "K_j>=16 times the sum of F*all positive inherited primitive constants, reserve/adapter bounds and the already frozen backend constant globalized to ALL widths by its finite fallback. K_j is newly fixed before e varies.", + "stage_gap": "eta_j=min(rho-a_j,1-rho-a_j,a_j-b_j)>0", + "sufficient_form": "A new integer e_j dominates E_backend^(ceil(2/rho)), the borrow threshold, and ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).", + "justification": "For fixed positive eta, loge<=2/eta * e^(eta/2); the displayed oversized threshold absorbs every fixed coefficient in the three root costs and kmax(2^45*N^5, 2^(2*H)), excluding the finite completed-program witnesses. No previous numerical prime/H/precision threshold is reused." + }, + "all_in_primitive_fee": { + "low_types_upper": "q^(N^2)", + "single_fixed_route_or_leaf_normalizer_bound": "(q+2)^(16*(N+1)^2) retained primitive invocations, including low-type dispatch, carry and polynomially many fixed affine/scaling/old-atom operations. Rank-one leaf shears<=4*N^2-2*N; bad classes charged<=32*N^2 ordinary calls separately in moment.", + "compiled_primitive_multiplier_F": "(q+2)^(32*(N+1)^2) * (A(N)+2)^8", + "actual_cost": "F times a positive maximum retained completed-backend/stream primitive constant. The latter is fixed at each finite level, never declared1 or free. This is a constructive finite bound schema, not a materialized all-in machine constant.", + "parking": "At most4*(B_N+C_N) FIELD passes per query plus initialization/teardown. B_N, P_N, C_N and all route counts are bounded above by the explicit A(N) expressions. The F bound dominates these positive products." + }, + "stock": { + "uniform_B": "B_N<=A(N)", + "owned_C": "C_N<=2*A(N), full owned INIT/CLEAR charged", + "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend", + "depth_D": "floor(log_N ceil(e/w))+1 is safe", + "borrowed_digits_bound": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1; =O_new(w loge)", + "nested_backend": "Each completed finite backend restores all outer ROW/spectators and its own stock before return; it supplies no externally assumed empty space." + }, + "eventual_threshold_rule": { + "stage_constant": "K_j>=16 times the sum of F*all positive inherited primitive constants, reserve/adapter bounds and the already frozen backend constant globalized to ALL widths by its finite fallback. K_j is newly fixed before e varies.", + "stage_gap": "eta_j=min(rho-a_j,1-rho-a_j,a_j-b_j)>0", + "sufficient_form": "A new integer e_j dominates E_backend^(ceil(2/rho)), the borrow threshold, and ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).", + "justification": "For fixed positive eta, loge<=2/eta * e^(eta/2); the displayed oversized threshold absorbs every fixed coefficient in the three root costs and k0,'Contraction includes original and both completion tails') + need(p['cutoff']**640,'Fresh uniform strict gap') + H0=ceil((gap*(5+8*h)*p['v']+1+8*p['v']*(1-z0))/(h*gap));H1=(H0*(1-z0)/(z-z0)).__floor__()+1 + need(H0>=8*p['v']and H0*h*gap>=gap*(5+8*h)*p['v']+1+8*p['v']*(1-z0)and H1*(z-z0)>H0*(1-z0),'New effective integer compiler') + C1=p['uniform']-p['cover_gap'];need(p['tested']>p['uniform']>C1>0 and F(p['prime_coefficient'])*p['cover_gap']>256,'Positive uniform and full cover fallback gaps') + need(F(old['admitted'])==F(1737729,500000000),'Completed PR4814 base supplier, not raw root') + backend=F(old['admitted']);levels=[] + for j in range(1,4): + a=(1-p['rho'])*C1+p['rho']*backend;scaled=a*p['grid'];b=F(scaled.__floor__(),p['grid']) + need(backend=F(1,1000),'fee_bounds':bounds,'whole_kappa':None,'publication':'Private candidate only; no new PR or modifications of published/frozen trees.','retained_assumptions':'Same completed arbitrary-input/all-width ROW/spectator/weighted-leaf/native/finite-compiler/precision/fixed-tape contracts as PR4760/4814. Final astronomical uniform programme not materialized.'}) +if __name__=='__main__':print(json.dumps(run(),indent=2)) diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/cold-normal-0001/RESULT.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/cold-normal-0001/RESULT.json new file mode 100644 index 0000000000..dd1197839e --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/cold-normal-0001/RESULT.json @@ -0,0 +1,23 @@ +{ + "status": "PASS_COLD_CONDITIONAL_G20_ORDINARY_CERTIFICATE", + "at_utc": "2026-10-23T01:53:30.095027+00:00", + "isolated": 1, + "optimized": 0, + "python": "3.12.14 (main, Aug 25 2026, 14:01:42) [MSC v.1944 64 bit (AMD64)]", + "source_inputs": 20, + "native_runtime_pins": 48, + "admitted": "217256899/62500000000", + "comparator": "1737729/500000000", + "relative_gain": "40774/217216125", + "finite_levels": 3, + "H0": 377296594739200, + "H1": 262304923748800276275201, + "provider_manifest_sha256": "15034901fb7641ff6cf154e3d8e3e82d1f02332a1f54ed52a90bef9667648ca3", + "certificate_manifest_sha256": "77cc1b9a69aba096466df23a180256303ee4f91d9a451d9ab42cb0a80ab427f4", + "allfees_status": "PASS_EXPLICIT_POSITIVE_FIXED_PROGRAM_FEE_BOUNDS", + "retained_assumptions": "Same completed arbitrary-input/all-width ROW/spectator/weighted-leaf/native/finite-compiler/precision/fixed-tape contracts as PR4760/4814. Final astronomical uniform programme not materialized.", + "whole_kappa": null, + "new_PR": false, + "CPU_seconds": 2.71875, + "elapsed_seconds": 2.7347284000134096 +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/cold-optimized-0001/RESULT.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/cold-optimized-0001/RESULT.json new file mode 100644 index 0000000000..f2036213ed --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/cold-optimized-0001/RESULT.json @@ -0,0 +1,23 @@ +{ + "status": "PASS_COLD_CONDITIONAL_G20_ORDINARY_CERTIFICATE", + "at_utc": "2026-10-23T01:54:11.943555+00:00", + "isolated": 1, + "optimized": 1, + "python": "3.12.14 (main, Aug 25 2026, 14:01:42) [MSC v.1944 64 bit (AMD64)]", + "source_inputs": 20, + "native_runtime_pins": 48, + "admitted": "217256899/62500000000", + "comparator": "1737729/500000000", + "relative_gain": "40774/217216125", + "finite_levels": 3, + "H0": 377296594739200, + "H1": 262304923748800276275201, + "provider_manifest_sha256": "15034901fb7641ff6cf154e3d8e3e82d1f02332a1f54ed52a90bef9667648ca3", + "certificate_manifest_sha256": "77cc1b9a69aba096466df23a180256303ee4f91d9a451d9ab42cb0a80ab427f4", + "allfees_status": "PASS_EXPLICIT_POSITIVE_FIXED_PROGRAM_FEE_BOUNDS", + "retained_assumptions": "Same completed arbitrary-input/all-width ROW/spectator/weighted-leaf/native/finite-compiler/precision/fixed-tape contracts as PR4760/4814. Final astronomical uniform programme not materialized.", + "whole_kappa": null, + "new_PR": false, + "CPU_seconds": 2.78125, + "elapsed_seconds": 2.812113500025589 +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/fee_bounds.py b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/fee_bounds.py new file mode 100644 index 0000000000..7a90a75477 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/fee_bounds.py @@ -0,0 +1,28 @@ +"""Positive finite primitive-count bounds, represented without tower expansion. + +The resulting bounds multiply retained native primitive constants. They are +not a claim of a source-independent numerical Turing-machine coefficient. +""" +from fractions import Fraction as F +def need(c,m): + if not c:raise ValueError(m) +def certify(fees,invoice,H1,v=1024): + n=invoice['originals'];M=invoice['QUERYs'];park=4*(n+2)*M + need(n==11400 and M==57321 and fees['parent_parking']['total_FIELD_pass_bound']==park==2614296168,'Actual new FIELD parking bound') + need(fees['in_BODY_paid_MAINport_wholefiber_routes']==7548 and fees['canonical_job_matching_routes']==7248,'Both internal and whole-job routes charged') + need(fees['stock']['per_primitive_GLOBAL_unit_owned_banks']==2 and fees['stock']['owned_OUTPUT_credit']==0,'Two owned per compiled unit, no extra DATA credit') + scans=sum(fees[k]for k in('literal_VALUE_XOR_passes','compound_pointwiseCOPY_assignments','new_shadow_ZERO_INIT_passes','all_paid_owned_CLEAR_passes','initial_owned_bank_ZERO_scans','final_owned_bank_teardown_scans')) + routes=7548+7248;raw=fees['raw_bit_IR_records'];base=scans+park+routes+raw+M*(32*127**2+8*127**3) + need(base<2**64 and park>10**9,'Only RAW record cap1e9; new base primitive envelope fits2^64') + # K bounds ranks, roles, rounds and primitive descriptions in the fixed + # tensor/completion/splitting unit. It is an integer, not expanded here. + kexp=256*v + need(kexp>=4*v*64 and 127<256 and v==1024,'Conservative tensor/completion/splitting count envelope') + return {'status':'PASS_EXPLICIT_POSITIVE_FIXED_PROGRAM_FEE_BOUNDS', + 'base_counts':{'raw_records':raw,'scan_assign_CLEAR_INIT_passes':scans,'parent_parking_FIELD_passes':park,'all_internal_plus_canonical_routes':routes,'coarse_base_primitive_descriptions_including_local_dimension_work':base,'verified_less_than':str(2**64)}, + 'fixed_tensor_unit':{'v':v,'upper_K':f'2^{kexp}','meaning':'K bounds all fixed integer ranks, role/round/operation inventories after chronological tensor product, charged target completion and paid splitting. No owned array is a productive role.'}, + 'finite_compiler_count_bound':{'top_rank_N':'2^'+str(H1),'J(n)':'(n+1)^4 * K^(4*n+4)','A(1)':'K^4','A(n)':'(J(n)+2)^4 * (A(n-1)+2)^(4*n+8), for2<=n<=N','bounds':'A(n) bounds productive roles, paid leaves, compiled unit instances, primitive/route descriptors, owned banks, and coefficient-construction descriptions. Allocate2 banks for EVERY unit instance; C_N<=2*A(N). A(n) is a concrete finite recursive integer, not expanded or assumed small.','replication':'At n, the denominator-clearer product of smaller widths is <=A(n-1)^(n-1); source/exit flow inventories are <=J(n). The displayed recurrence dominates their products, smaller-program inlining and two owned banks per unit.'}, + 'rational_height_and_prime':{'base_input_height_bits_upper':1024,'arithmetic_step_bound_T':'(2*N+2)^4 * (A(N)+2)^2','rational_height_bits_H':'1026 * 4^(T+1)','meaning':'Each exact rational arithmetic operation increases numerator/denominator bit height by at most4*(height+1). This includes fixed rational matchers/Gaussian eliminations, not only VALUE coefficients. Every fixed matrix/witness is compiled first.','choose_q':'An odd prime q>max(2^45*N^5, 2^(2*H)), excluding the finite completed-program witnesses. No previous numerical prime/H/precision threshold is reused.'}, + 'all_in_primitive_fee':{'low_types_upper':'q^(N^2)','single_fixed_route_or_leaf_normalizer_bound':'(q+2)^(16*(N+1)^2) retained primitive invocations, including low-type dispatch, carry and polynomially many fixed affine/scaling/old-atom operations. Rank-one leaf shears<=4*N^2-2*N; bad classes charged<=32*N^2 ordinary calls separately in moment.','compiled_primitive_multiplier_F':'(q+2)^(32*(N+1)^2) * (A(N)+2)^8','actual_cost':'F times a positive maximum retained completed-backend/stream primitive constant. The latter is fixed at each finite level, never declared1 or free. This is a constructive finite bound schema, not a materialized all-in machine constant.','parking':'At most4*(B_N+C_N) FIELD passes per query plus initialization/teardown. B_N, P_N, C_N and all route counts are bounded above by the explicit A(N) expressions. The F bound dominates these positive products.'}, + 'stock':{'uniform_B':'B_N<=A(N)','owned_C':'C_N<=2*A(N), full owned INIT/CLEAR charged','reserve':'[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend','depth_D':'floor(log_N ceil(e/w))+1 is safe','borrowed_digits_bound':'D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1; =O_new(w loge)','nested_backend':'Each completed finite backend restores all outer ROW/spectators and its own stock before return; it supplies no externally assumed empty space.'}, + 'eventual_threshold_rule':{'stage_constant':'K_j>=16 times the sum of F*all positive inherited primitive constants, reserve/adapter bounds and the already frozen backend constant globalized to ALL widths by its finite fallback. K_j is newly fixed before e varies.','stage_gap':'eta_j=min(rho-a_j,1-rho-a_j,a_j-b_j)>0','sufficient_form':'A new integer e_j dominates E_backend^(ceil(2/rho)), the borrow threshold, and ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).','justification':'For fixed positive eta, loge<=2/eta * e^(eta/2); the displayed oversized threshold absorbs every fixed coefficient in the three root costs and k0,'Independent sum of original and completion tails') + z=1-u0;z0=(t+z)/2;d=z0-t;h=F(1,64);need(d>0,'Positive finite compiler gap');H0=X.ceil((d*(5+8*h)*v+1+8*v*(1-z0))/(h*d));H1=X.floor(H0*(1-z0)/(z-z0))+1 + need(H0>=8*v and H0*h*d>=d*(5+8*h)*v+1+8*v*(1-z0)and H1*(z-z0)>H0*(1-z0),'Independent finite rank compiler') + need(cut**64u0>C1>0 and F(params['prime_coefficient'])*gap>256,'Full fallback prime allowance') + backend=F(1737729,500000000);levels=[] + for j in range(3): + a=(1-rho)*C1+rho*backend;b=F(X.floor(a*params['grid']),params['grid']) + need(backendar['C1'],'Raw root overclaim would exceed covered body saving');negatives['rawroot_as_ordinary']='REJECT: exceeds even covered body C1' + old=read(HERE/'inputs'/'PR4814-RESULT.json');oldH0=old['new_H0'];t=1-F(p['tested']);z=1-F(p['uniform']);z0=(t+z)/2;d=z0-t + need(oldH0*F(1,64)*d10**9 and counts['coarse_base_primitive_descriptions_including_local_dimension_work']<2**64,'Positive parking exceeds old cap, new explicit envelope') + return {'status':'PASS_INDEPENDENT_LITERAL_P_T_THREE_TAILS_BOOTSTRAP_AND_BASE_HEIGHT','all_originals':sum(T.values()),'actual_queries':sum(P.values()),'H0':ar['H0'],'H1':ar['H1'],'admitted':str(ar['admitted']),'relative_gain':str(ar['relative_gain']),'rational_height':base_height(provider),'negative_controls':negatives,'not_materialized':'Astronomical uniform programme and new fixed machine threshold; retained source assumptions are explicit.'} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/DELAYED-COVER-BRIDGE.md b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/DELAYED-COVER-BRIDGE.md new file mode 100644 index 0000000000..a58774e237 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/DELAYED-COVER-BRIDGE.md @@ -0,0 +1,401 @@ +# Delaying the BIT cover until the whole finite program is compiled + +Status: a constructive native-interface argument, with an exact local-ring +audit. This closes the particular common-weight mismatch identified in the +first mixed BIT proposal, conditional on the finite mixed-flow compiler +producing the stated finite projector program. It is not an independent +proof of that compiler's asymptotic termination or of integer multiplication. + +Substantial OpenAI assistance. Apache-2.0. This argument uses the arbitrary- +projector GL cover and weighted-child normal form in +[`notes/three-stage-cover-bit.tex`](../../../notes/three-stage-cover-bit.tex), +the retained PR589 local word and its predecessors, and the finite +precompilation proposal in `../architecture/FINITE-PRECOMPILATION.md`. +The decisive order of operations was proposed jointly with the architecture +research task: compile all internal jobs first; apply one common cover and +one common external weight only afterwards. + +## 1. The earlier obstruction was real + +A productive rank-eight helper is a proper projector job inside a larger +ambient address space. After an ambient GL cover, its endpoint is + +\[ +D_{gPg^{-1}}, +\] + +not the same fixed eight-coordinate interchange on every cover row. +Lowering this job immediately to a canonical recursive query introduces a +diagonal weight determined by the pivot coefficients of `g P g^-1`. +Jobs from different parents can have different such weights. The inherited +scalar word accepts one common external weight across every fresh role; +simply placing differently weighted jobs in its roles is invalid. + +The solution below does not identify these weights. It avoids creating +weighted internal jobs at all. Only leaves of the entire precompiled word +are lowered to canonical weighted calls. + +## 2. Native projector jobs before canonical lowering + +Fix an ambient rational head space of dimension `N` and the atom-reversal +matrix `C_N`. For any rational idempotent `P` put + +\[ +D_P=\begin{pmatrix} +I-P & PC_N\\ +C_NP & I-C_NPC_N +\end{pmatrix}. +\] + +For `G` invertible let + +\[ +Q_G=\operatorname{diag}(G,C_NGC_N). +\] + +Direct block multiplication gives + +\[ +Q_GD_PQ_G^{-1}=D_{GPG^{-1}},\qquad +D_PD_{I-P}=D_I. +\] + +No symmetry of `P` is required. The second identity says that any source +job and its complementary projector complete the full interchange on that +array. If a unit of rank `m` is used at column multiplicity `c`, first embed +its rational projectors into the chosen `mc`-dimensional coordinate block +of the common `N`-dimensional space. Complete unused coordinates are +spectators. All these dimensions and embeddings are constants of the +finite precompiled program. + +The local PR589 primitive, the new global controller, its pointwise boundary +adapters, and owned COPY storage can all be treated as a finite chronological +word of pointwise scalar operations, proper projector requests, restores, +and fixed right-multiplication symbols on one future cover coordinate. +Their exact finite operator identities are established independently of a +generic canonical child normalizer. An internal request may therefore be +replaced by a finite native word computing the same `D_P` on arbitrary data. + +This schematic qualification matters. The p3 construction already uses +per-port chart routes to share one local helper bank across 111 data ports. +It is not a 3,739-field word with those routes silently deleted. Before +choosing the final cover, embed every local projector and every port chart +into the common ambient `N`. Preserve all fixed right-route symbols during +substitution. Only then instantiate that single `GL_N` cover. A helper's +endpoint is the rank-eight local-space projector at its local invocation +vertex, while main data endpoints use their port-specific line and stage +projectors. `BIT-P3-NATIVE-BINDING.json` checks every fixed rational port +chart, this ownership distinction, and the complete recursive tariff. + +## 3. Equal rank gives a fixed rational matcher + +For rational idempotents `P,Q` of the same rank, choose a rational basis of +their images and kernels. Let `B_P` and `B_Q` be the corresponding full basis +matrices, with image columns first. Then + +\[ +S=B_PB_Q^{-1},\qquad SQS^{-1}=P. +\] + +This is a finite rational matrix construction. A physical execution of the +dense address map `Q_S` is **not** assumed. The matcher is used only as a +right multiplication of the full cover row, as follows. + +Choose a fixed odd prime `q` avoiding the denominators and nonzero +determinants of every native matrix and matcher in the finite program. +For atom width `w`, use one global cover + +\[ +\mathcal G=\operatorname{GL}_N(\mathbb Z/q^w\mathbb Z). +\] + +All matchers reduce to invertible matrices over this local ring. +An array role is accompanied by the full cover coordinate `g in G`. +Its entries at different `g` are independent data. + +Suppose a parent role at cover row `g` requests `D_(g P g^-1)` and a child +target role at its cover row `h` computes `D_(h Q h^-1)`. Before running +the child, route that complete target-role fiber by + +\[ +x_g\longmapsto y_{gS}=x_g. +\] + +Execute the child word on these routed inputs, then undo the role-specific +route. The endpoint on the parent's original `x_g` is exactly + +\[ +D_{(gS)Q(gS)^{-1}}=D_{gPg^{-1}}. +\] + +Every child target role can use its own fixed matcher `S`. Each mapping +`g -> gS` is a bijection of the *whole* cover fiber, so no input is copied, +discarded, or assumed zero. The child word can mix its roles at a common +child row `h`, because those routed inputs are arbitrary independent data. +After the completed word returns its independent endpoints, undoing the +routes restores the parent ordering. The finite flow's ownership and +chronology are still required; cover routing does not repair an aliased +or cyclic flow. + +## 4. One common external weight survives every internal routing + +At column multiplicity `f`, let the outer invocation's diagonal weight +`A` be any permitted generated descriptor on its `Nf` head atoms. It can +depend on exposed ancestor rows and atom indices. It must be independent +of all fresh role and cover fields of this entire compiled invocation. +Write `Lambda_A=diag(A,I)`. + +Conjugate the entire completed covered word by `Lambda_A`. Pointwise scalar +ADDs commute with this common address permutation across roles. Every +internal role route also commutes with it: a route changes only a fresh +role or the current cover row, while `A` is independent of both. Thus the +matching identity becomes + +\[ +\Lambda_A D_{(gS)Q(gS)^{-1}}\Lambda_A^{-1} +=\Lambda_A D_{gPg^{-1}}\Lambda_A^{-1}. +\] + +There is no child-specific weight to reconcile inside the precompiled +word. The source/complement product gives + +\[ +\Lambda_A D_I\Lambda_A^{-1}=F_A +\] + +on every productive source array. This is exactly the inherited weighted +full-interchange endpoint. Owned zero storage is unaffected by address +permutations and is excluded from productive output credit; its allocation, +initialization and final erasure still belong to the finite word. + +The condition on `A` is essential. The companion audit exhibits a concrete +failure when `A` is allowed to depend on the current fresh cover row. The +argument does not quietly weaken the old ancestor-only contract. + +## 5. Only the final leaves become weighted children + +After the mixed finite compiler has replaced every internal request, suppose +the remaining paid projector requests have rank one. At multiplicity `f`, +each is a rank-`f` residual on the outer atom space. Apply the inherited +generic ordered normal form to this *finished* leaf list. + +For a generic residue class, that proof produces unit lower intrabank and +cross-bank adapters around one contiguous weighted reversed interchange. +For column `j`, the resulting weight is + +\[ +A_{\rm child}[j]=A[i_0f+j]D_P[0], +\] + +with the inherited reversed tail pairing. The pivot coefficient is evaluated +from the current outer cover row and the fixed leaf projector. Those are +ancestor data when the recursive rank-`f` child is invoked. Its fresh roles +come from unused row stock, so the child's weight is independent of them. + +Different leaf calls can have different weights; the ordinary recursion +already permits this. Each such child itself receives one common weight +across all of *its* fresh roles and cover rows. This is the critical +distinction from calling a mixed unit on several already-normalized, +differently weighted parent jobs. + +Bad residue classes use the inherited genuine local-ring fallback, including +its swaps, paired scalings and reversals. This is charged explicitly rather +than declaring a nonunit pivot invertible. + +## 6. Routing is priced by the retained native lemma + +The cover row has the unique chart `g=g0+qG1`, with `g0` in `GL_N(F_q)`. +For each fixed matcher `S`, right multiplication gives a permutation of +the finite low type and a fixed affine map on the high matrix, with carry +determined by the low type. The retained proof of finite cover routing +implements this with a constant number of fixed scalings, ordered shifts +and old atom interchanges. Its cost is + +\[ +O(Vw^{1-a_{\rm old}}) +\] + +per fixed route. It is not a free address-gather operation. A precompiled +word contains finitely many matchers, so their total remains a finite +constant times this term. High matrices are streamed by fixed low type; +the number of tapes and program types does not grow with `w`. + +The same statement holds for nonintegral rational matchers: choose `q` +avoiding their fixed denominators, use their local-ring representatives, +and apply the retained fixed-rational routing lemma. The exact small audit +uses integral unimodular matchers to exercise the carry formula directly. + +## 7. Moment and row-stock consequences + +Let the finite uniform compiler have `B` productive source arrays, ambient +rank `N`, and `P` rank-one leaves, with a certified strict inequality + +\[ +\frac PB N^{-\tau}<1. +\] + +The covered, weighted word has the same normalized good-class leaf count. +Choose `q` large enough that the full fallback surcharge fits the displayed +slack. For example, the conservative inherited per-leaf bounds yield + +\[ +\mu_\tau\le +\frac PB N^{-\tau} +\left(1+\frac{2N^3}{q}\,32N^2\right)<1. +\] + +No old fixed choice of `q` or old numerical fallback envelope is reused for +the potentially enormous new `N`. Prime avoidance and a sufficiently large +prime exist because the whole precompiled program is finite. + +For the present candidate, use the exact mixed saving +`C0=69/25000=0.00276` for the finite compiler and retain +`C1=11/4000=0.00275` after covering. Put `d=C0-C1=1/100000`. +The former gives `P/B\frac{256N^5}{d}=25,600,000N^5. +\] + +Then the fallback multiplier is less than `1+d/4`, while +`N^d >= 1+d/2` for `N>=2`, using `log 2>1/2` and `exp x>=1+x`. +Thus the complete moment is strictly below +`(1+d/4)/(1+d/2)<1`. This uses an explicit exponent gap and does not +require knowing the eventual winning template's numerical moment slack. + +The cover consumes `N^2(w-1)` high-row digits plus a fixed low-type and role +reserve. Its finite owned-storage and scalar costs may be enormous. They +replace the old constants. For fixed `N` and a fixed finite word, the +ancestor reserve remains `O(w log e)`, and the previous eventual-threshold +arguments still apply after substituting those constants. They cannot be +reused numerically without that substitution. + +The existing weighted recursion can now be applied to this one uniform +supplier: every paid query has width at most `f`, the endpoint is `F_A`, and +all routing and scalar terms have the inherited permitted form. This is a +native-interface bridge. The complete final exponent still depends on the +mixed compiler's termination theorem, its exact leaf-count saving, and the +outer multiplication transfer. + +## 8. The ordinary BIT saving and explicit template constants + +The retained stopped recurrence gives + +\[ +T(n,w)=O(n+n^{1-C_1}w^{1-a_{\rm old}}),\qquad +a_{\rm old}=384599/10^{10}. +\] + +The old atom exponent `1/1000` cannot be reused here: its linear `n` term +would limit the ordinary saving to `0.001`. Instead choose +`delta=3/1000` and `w=ceil(e^delta)` from the original chunk width `e`. +For the whole compiled program set + +\[ +W(w)=B|\operatorname{GL}_N(\mathbb F_q)|q^{N^2(w-1)}. +\] + +A safe reserve is `W(w)^D * S_old`, with +`D >= floor(log_N ceil(e/w))`; all final ordinary children have rank at +most `floor(n/N)`. Therefore the borrowed high-digit count satisfies + +\[ +k\le D\left(N^2(w-1)+ +\left\lceil\log_q(B|\operatorname{GL}_N(\mathbb F_q)|)\right\rceil\right) ++\left\lceil\log_qS_{\rm old}\right\rceil+1 +=O_{N,B,q}(w\log e). +\] + +This is `o(e)`. For sufficiently large `e`, borrow `ka_BIT` and `delta<1-a_BIT` hold strictly. The linear adapter +term and the borrowed-stock logarithm are lower order. One may relax the +ordinary saving to the simpler rational `27/10000=0.0027`. +`BIT-ALLSIZE-PARAMETERS.json` records all strict rational gaps and the +exact mixed margin at `C0`. This remains conditional on the finite uniform +compiler premise; the enormous word is not materialized in this package. + +The final ambient dimension is `N`, the productive role count is `B`, and +the rank-one leaf count is `P`. They are not the old `64`, `661`, `3739`, +or the base unit's literal counts. Let `C` be the total allocated owned +array fields, `L` the literal scalar/copy/erase count, and `R` all fixed +right routes including inverses. Keep the full finite matrix and +coefficient-height list. The new fixed tape inventory can use one stream +per productive or owned role, with the inherited parking stack; it is +finite in `B+C`. Every route is charged, and every final leaf has its own +normalization and possible fallback. A rank-one generic normalizer and +its inverse use at most `4N^2-2N` elementary lower/cross-bank shears; the inherited bad +normalizer uses at most `32N^2` recursive calls of width at most `f`. + +These constants can be enormous and affect the eventual threshold. Their +dependence on the fixed compiled template does not introduce a new power +of the later input length. The mixed-flow argument is used to bound the +normalized number of paid rank-one leaves; it must not assume that dense +matrix routing costs stay uniformly bounded while the candidate template +dimension `N` is increased in the existence search. + +## 9. Exact finite audit + +Run: + +```sh +python3 -B research/kappa-rebuild/bit/delayed_cover_bridge.py +``` + +The audit enumerates every one of the 3,888 rows of `GL_2(Z/9Z)` for each +of two independently matched target roles. It checks 7,776 exact physical +projector identities, both full cover bijections, the affine high-row carry +formula, and every one of the 6,561 addresses for common-gauge scalar +commutation. Its external weight is `(2,4)`, so it is not restricted to an +unweighted or constant-across-axis input. The emitted leaf-weight histogram +is nonconstant. Two explicit negative controls reject omitting a matcher +and allowing the external weight to depend on the fresh cover row. + +These are independent checks of concrete algebra and a genuine local ring. +The general argument is the conjugacy calculation above, not an inference +from the finite sample. + +## Open next questions + +1. Independently audit that the finite lockstep compiler only substitutes + whole arbitrary-input jobs and gives each simultaneously live child role + a distinct physical array. The row matching here assumes that ownership. +2. Bind the new BIT p3 native physical projector list and its exact local + primitive into the abstract finite compiler, including all COPY centers. +3. Write the parameter substitutions for the eventual row reserve and the + final BIT/complex outer exponent. A finite numerical mixed moment alone + is still insufficient for a new multiplication claim. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/FINITE-PRECOMPILATION.md b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/FINITE-PRECOMPILATION.md new file mode 100644 index 0000000000..4badb40f09 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/FINITE-PRECOMPILATION.md @@ -0,0 +1,313 @@ +# Finite precompilation of a mixed-target rule + +Status: constructive bridge under the precise native hypotheses below, +independently audited in `../transfer-audit/AUDIT.md`. This is a written +argument, not a formal proof or a completed integer-multiplication admission. +The companion finite scheduler checks actual integer flow and ordering. +The original immediate-normalization BIT interface failed hypothesis 3. +`../bit/DELAYED-COVER-BRIDGE.md` supplies the distinct delayed-cover +implementation, with a finite local-ring check and the native binding in +`../bit/BIT-P3-NATIVE-BINDING.json`. Its fixed rational cover routes are a +costed program schema, not dense coordinate gates in a plain native word. + +Substantial OpenAI assistance. Apache-2.0. The mixed-target asymptotic flow is +Jacob Alan Sussman's Theorem 1G, PR4268, with the detailed proof at commit +`563b4e6e913625637f36ba7869bf5fcd0dd4975a` of +[`wht-power-saving-lean`](https://github.com/jacobalansussman/wht-power-saving-lean). +The source, exact scheduling code and notices are preserved under `sources/`. +The contribution proposed here is clearing the finite flow into a single +uniform native supplier before applying the inherited outer theorem. + +## 1. What needs to be assumed + +Let a job of rank `s` apply a specified tensor operator to `s` selected +coordinate blocks of one array, fixing all other coordinates. A block has +an arbitrary positive tensor multiplicity `f`. A completed rank `s` job +therefore acts on `s*f` axes. All productive inputs are arbitrary. + +Fix one mixed unit with productive targets `W_k` of ranks `k`, a chronological +list of paid child ranks `r_j`, and a finite number of scalar and routing +passes. These assumptions are required, separately from the moment inequality: + +1. **An all-column native word.** At every integer column count `c`, the unit + computes exactly its independent rank `k*c` output jobs. Its paid rounds + are rank `r_j*c` jobs in the stated order. All borrowed data return to the + declared endpoint, and owned storage is explicitly initialized and erased. + Its finite operation count is uniform in `c`. +2. **Disjoint splitting and spectators.** A rank `a+b` job is a rank `a` job + followed by a rank `b` job on disjoint coordinates. The resulting programs + preserve arbitrary complete spectator fields and accept arbitrary data. +3. **Whole-job adapters.** Any job passed between two units has an explicitly + priced, permitted embedding into its destination. For the intended complex + application these are fixed monomial binary address maps and unit quadratic + phases, together with role permutations. The adapters must work at every + tensor multiplicity. Rank equality by itself is insufficient. +4. **Finite-program closure.** A finite composition of these words and + adapters is again a permitted finite supplier. Constantly many owned fields + may be supplied with their full cost and no productive output credit. + The eventual ordinary recursion must have the same arbitrary-input, + restoration, scalar and precision interface as the retained supplier. + +Put `m=max{k:W_k>0}`, `k_min=min{k:W_k>0}`, and +`r_max=max{r_j}`. Require `r_max g*S`, keeps one +external weight throughout the entire finite circuit, and lowers only its +final rank-one leaves. All rational matchers, role routes and their inverses +are fixed before choosing the odd prime and its exclusions. Every route +uses complete equal-multiplicity cover fibers and the retained, costed row +permutation primitive. This gives the same finite DAG argument in the +rational-cover program category. The BIT binding supplies the actual native +projectors; a rank count alone would not provide this implementation. + +## 2. Proposed conclusion + +Suppose the preceding hypotheses hold and the mixed balance has root +`tau` in `(0,1)`: + +``` +sum_j r_j^tau = sum_k W_k k^tau. +``` + +For every `z` with `tau=2`, a fixed number `B_N` of productive arrays, +and only rank-one paid children, whose number `P_N` satisfies + +``` +P_N < B_N * N^z. +``` + +Every productive output is the full rank-`N` job. The construction may have +an enormous finite scalar word, role inventory and owned-storage requirement. +Those quantities affect constants and the eventual input threshold. They are +not omitted and are not credited as extra output jobs. + +If this uniform supplier is admitted under the retained native, precision and +fixed-tape premises, the existing uniform recursion applies directly. A new +dynamic RAM-to-Turing-machine simulation is not being assumed here. + +## 3. The integer lockstep flow at a fixed rank + +This is the part of Theorem 1G used by the compiler. At one fixed top rank +`N`, its units, source jobs and exit jobs have integer multiplicities. +For a multi-index `a` on the target types define + +``` +c(a) = product_k k^(a_k), +u(a) = multinomial(|a|;a) * product_k W_k^(a_k). +``` + +The exact Pascal identity is + +``` +u(b) = sum_{k:b_k>0} W_k*u(b-e_k). +``` + +Let `G` be the largest `|a|` with `m*c(a)<=N`. A class is indexed by a +sequence of paid rounds `s` of length `d<=G`; its dilation is +`rho_s=product r_j`. It contains `u(a)` units at column `rho_s*c(a)` for +each `a` with `|a|=G-d` and `m*rho_s*c(a)<=N`. + +For one parent paid round, the Pascal bijection matches its job copies to +target roles of the child class, at exactly equal integer ranks. Missing +demands are top sources. Separation ensures every parent job is consumed. +The source ranks lie in `(N/m,N]`; only the deepest classes produce exit +jobs, all strictly smaller than `N` once `N` is outside the finite base range. + +Process a class in word order. At round `j`, suspend every unit of that +class, complete the entire child class fed by that round, and only then +advance the parents to round `j+1`. This forbids a unit from requiring both +an earlier and a later round of the same suspended parent. The resulting +dependency graph is finite and acyclic. Its edges carry complete array jobs, +not individual scalar values copied for free. + +These integer quantities exist before normalizing the sources to total +weight one. Let `S_s` be the number of source jobs of rank `s`, let +`S=sum_s S_s`, and let the ordered exit batches be `(e,t)` with `t` jobs +of rank `e` each. This finite integer flow is the compiler input. + +## 4. Clear every batch denominator constructively + +Induct on the integer top rank `N`. For each smaller rank `e` the compiler +has already constructed a uniform program on `B_e` arbitrary arrays, +computing full rank `e` with `P_e` paid rank-one calls. For a sufficiently +small rank use the ordinary sequential program: `B_e=1`, `P_e=e`. + +For the current flow choose an integer `a` divisible by every `B_e` needed +for an exit and every `B_(N-s)` needed for a nonzero source remainder. +The product of those finitely many positive integers is a valid choice; +their least common multiple is a smaller optional choice. Set + +``` +B_N = a*S. +``` + +Assign `a*S_s` of the input arrays to each source rank `s`. On each of those +arrays, first complete its `N-s` complementary coordinates using the +already-compiled smaller uniform program. All such batches are integral +because `a` is divisible by their program widths. This preliminary action +commutes with the intended `s`-coordinate job and fixes its input coordinates. + +Make `a` copies of the integer lockstep flow. Route its source arrays to +their exact input slots using permitted whole-array adapters. At a deepest +exit batch, `a*t` is divisible by `B_e`; replace that batch by copies of +the smaller uniform rank-`e` program. Restore its role ordering and adapters +before resuming the suspended parent class. Execute the finite DAG in the +lockstep order, and finally restore the original source-array ordering. + +Every array has now received its disjoint complementary job and source job, +hence the full rank-`N` transform. No copied scalar input or blank helper is +treated as another independent output. Every original array occurs exactly +once as a source; interior target slots are jobs on those arrays, not new +productive inputs. + +Induction removes all recursive calls: the only remaining paid children +have rank one. Clearing denominators multiplies productive arrays and paid +operations equally, so it preserves the per-array leaf count. In formulas, + +``` +P_N/B_N = (1/S) * [ + sum_s S_s * (P_(N-s)/B_(N-s)) + + sum_(ordered exit batches e,t) t * (P_e/B_e) +]. +``` + +Zero-rank terms vanish. Any plain rank-one exits are the ordinary base +program. Scalar and routing passes have their own analogous nonnegative +count and must be included in the asymptotic cost used to choose `N`. + +This construction uses full integer batches; it does not assume that +fractional pieces of a physical array can be routed at zero cost. Its exact +replication factors can be impractically large, which is acceptable for a +fixed finite supplier existence statement but must be disclosed. + +## 5. Why some fixed N has the required saving + +The independent audit sharpened this step to a direct count of paid leaves. +It does not require a running-time comparison between a RAM flow and native +tapes. Let `L(n)=P_n/B_n`, let `w_s=S_s/S`, and let `x_e` be the exit counts +normalized by the number S of source arrays. The actual integer compiler +satisfies + +``` +L(n) = sum_s w_s L(n-s) + sum_e x_e L(e), +sum_s w_s = 1, +sum_e x_e e^tau = sum_s w_s s^tau. +``` + +The last equality follows by canceling every internal matched job in the +exact tau-potential balance. The source ranks satisfy `n/m0`, concavity gives + +``` +n^z0 - sum_s w_s (n-s)^z0 >= eta * sum_s w_s s^z0. +``` + +Indeed, for `t=s/n` in `[1/m,1]`, +`1-(1-t)^z0 >= z0*t >= eta*t^z0`. For every sufficiently large n the +exit coefficient is less than `eta/2`. Every complement and exit has +smaller rank than n, so strong induction on the exact recurrence proves +`L(n)<=A*n^z0`, with finite A chosen to cover the smaller ranks. Eventually +`L(N) g S^(-1), with inverse return g -> g S. Both routes are paid. There are +72 such output jobs and144 additional routes. This protocol uses fresh +independent complete-cover rows and one common ancestor-only external weight; +it does not require a free dense operation on an uncovered ARRAY. The main +port routes and all SOURCE INDEX/lifetime conditions remain explicit. Only +final rank-one leaves use the inherited weighted normalization. + +Together with7,548 inherited nonidentity main port routes, the raw route +census is7,692. The finite full-group cover is algorithm-defined; it is not +materialized by these tests. Its legality retains the selected source's +whole-job and native implementation hypotheses. + +## 4. Strict price gain + +Write Phi(t)=sum_k T_k k^t - sum_r P_r r^t. One changed full invocation adds + + Delta(t)=4 + 3^t + 9*4^t + 6^t + 7^t - 7*8^t. + +The positive terms split seven eights into + + (1,7), (1,1,6), (1,3,4), (4,4), (4,4), (4,4), (4,4). + +Each group sums to eight. Strict subadditivity of x^t for00, while Delta(1)=0. This compares the two verified circuits' prices. +The complete p16 difference is18 Delta(t); main, query-only and idle terms +are unchanged. Independent exact intervals put the new raw crossing in + + (0.003475458064076428997514, 0.003475458064076428997515), + +against the old + + (0.003464248972023961106948, 0.003464248972023961106949). + +The raw improvement is about0.323565%. It is a changed paid/target inventory. + +## 5. Charged completion, splitting and finite rank compiler + +Rank-four targets overlap the large idle ranks. Apply the source chronological +tensor product and higher-moment theorem, retaining distinct physical owners, +whole-job normalizers and every live owned bank. Complete every product target +below18^1024 with a paid disjoint-axis job on that same owner, and split every +original and added paid job at17^1024. New input credit is never created by +completion. + +At C=0.00347545, t=1-C, u=1/5 and v=1024, use the complete bound + + alpha^v + 2 gamma^v + 2 delta^v, + alpha=P_t/T_t, + gamma=P_(t+u)/(17^u T_t), + delta=11400*18/(17^C T_t). + +Two retained rational interval engines and a separately implemented positive- +series engine verify alpha<1-2^-32, gamma<31/32 and delta<19/20. +Both latter bounds raised to128 are below1/16, and + + 1/(1+1024*2^-32) + 4*2^-32 < 1. + +Thus both tails, including all target completion, fit. The new uniform saving +before covering is C0=0.00347544. The source integer compiler inequalities, +with17^64<18^63 and raw ambient127<256, give + + H0=377227157504, + H1=262206447682297857, + N=2^H1. + +These are sufficient rank-compiler arithmetic bounds. They are not a claim +that the predecessor's numerical precision, tape or stock thresholds apply +unchanged to the new word. + +## 6. Cover, stock, finite constants and ordinary saving + +Set d=C0-C1=2^-18+10^-10, so + + C1=8887360519/2560000000000. + +The same odd-prime rule q>2^26 N^5, avoiding the fixed denominators and rank +witnesses, satisfies q>(256/d)N^5 and pays the full bad-class fallback. Fix +all new finite word, route, height and owned-bank lists before varying the +input chunk width e. The new raw cancellation-free integer prefix bound +uses485 bits; the old21-bit bound is not inherited. The bound10^9 is a coarse +raw-record allowance, not a final normalizer or machine-instruction count. +After tensoring, completion, splitting and finite compilation, regenerate +their fixed counts and heights by those source algorithms. In particular, +tensor/normalizer multipliers do not remain bounded by10^9. + +These fixed constants multiply the source lower-order adapter, old-atom and +ROW terms. The source proof permits this dependence on the fixed new +(N,B,q,program). No route or normalizer is assigned zero cost. The borrowed +reserve is the product W(w)^D S_old with + + W(w)=B |GL_N(F_q)| q^(N^2(w-1)), + D >= floor(log_N ceil(e/w)). + +Its borrowed digits are O_(N,B,q)(w log e). Choose atom exponent +rho=0.00346 and w=ceil(e^rho). With the retained old saving +a_old=0.0000384599, the three root costs are + + O(V[e^(1-rho) + +e^((1-rho)(1-C1)+rho(1-a_old)) + +e^rho log e]). + +Consequently the exact ordinary saving is + + a=(1-rho)C1+rho a_old + =17713901828029/5120000000000000. + +The exact positive gaps are + + rho-a=1298171971/5120000000000000, + 1-a-rho=5084570898171971/5120000000000000, + a-0.0034597=237828029/5120000000000000. + +They absorb the linear adapter and borrowed-stock logarithm for sufficiently +large e with the newly generated finite constants. This admits the simpler +ordinary BIT saving34597/10000000=0.0034597. The massive winning word and its +full machine execution are not materialized. This is the same conditional +native/compiler setting as the selected supplier, with the changed ABI and +new finite constants stated explicitly. No larger complex or multiplication +kappa follows from this BIT-only contribution. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4760-price.py.txt b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4760-price.py.txt new file mode 100644 index 0000000000..07ac039f35 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4760-price.py.txt @@ -0,0 +1,87 @@ +"""Fully paid p16 invoice and ordinary BIT conversion; no global kappa claim. + +Uses credited source-bound tail engines of Cinna Davis and zxv. The changed +helper ABI retains arbitrary independent rank4 endpoints, rather than paying +to complete them to rank8. Jacob Alan Sussman's mixed-target recursion and +Mark/Matarener's PR4697 parameter derivation are explicit predecessors. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter +import importlib.util,json,sys + +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +THIN=ROOT/'research/query-thinned-controllers' +LOCAL={1:1319,2:1342,3:78,4:39,5:102,6:10,7:18} +OLD_LOCAL={1:1323,2:1342,3:79,4:44,5:102,6:11,7:19} +HELPERS={4:4,8:432} +PARAMS={'tested':F('.00347545'),'uniform':F('.00347544'), + 'cover_gap':F(1,2**18)+F(1,10**10),'atom':F('.00346'), + 'admitted':F('.0034597'),'old_backend':F('.0000384599'), + 'alpha_gap':F(1,2**32),'prime_coefficient':2**26} + +def need(c,m): + if not c:raise ValueError(m) + +def load(p,n): + s=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(s) + sys.modules[n]=m;s.loader.exec_module(m);return m + +def source_engines(): + sys.path.insert(0,str(THIN)) + v=load(THIN/'verify.py','compact_productive_credited_tail') + e=load(ROOT/'research/higher-moment-strictification/verify.py','compact_productive_exact_intervals') + return v,e + +def invoice(local,helpers): + need(local==LOCAL and helpers==HELPERS,'Actual local paid/target profile required') + row=json.loads((THIN/'BIT-CONTROLLER.json').read_bytes()) + old=row['invoice'];calls=old['thick_calls'] + need(calls==18 and old['thin_queries']==1665,'Literal p16 full/query inventory') + targets=Counter({int(k):v for k,v in old['targets'].items()}) + paid=Counter({int(k):v for k,v in old['paid'].items()}) + targets[8]-=calls*439 + targets.update({k:calls*v for k,v in helpers.items()}) + for k,n in OLD_LOCAL.items():paid[k]-=calls*n + paid.update({k:calls*v for k,v in local.items()}) + need(all(v>=0 for v in targets.values())and all(v>=0 for v in paid.values()),'No negative jobs') + targets={k:v for k,v in sorted(targets.items())if v} + paid={k:v for k,v in sorted(paid.items())if v} + need(sum(targets.values())==11400 and sum(paid.values())==57339,'All independent originals and actual queries') + need(targets[4]==72 and targets[8]==7776 and paid[4]==702,'Partial helper physical jobs') + surplus=sum(k*v for k,v in targets.items())-sum(k*v for k,v in paid.items()) + need(surplus==753==old['rank_surplus'],'No new first-moment credit') + return {'targets':targets,'paid':paid,'rank_surplus':surplus, + 'thick_calls':calls,'thin_queries':1665,'original_fields':11400, + 'main_original_fields':3552,'helper_original_fields':7848} + +def certify(inv,params=None): + p=dict(PARAMS if params is None else params) + V,E=source_engines() + tail=V.tail(E,inv,p['tested'],p['uniform'],17,18,p['alpha_gap']) + c1=p['uniform']-p['cover_gap'];d=p['atom'];old=p['old_backend'] + ordinary=(1-d)*c1+d*old;b=p['admitted'] + need(p['tested']>p['uniform']>c1>0,'Tested/uniform/covered strict gaps') + need(d>ordinary>b>0 and d<1-ordinary,'Ordinary adapter, recurrence and stock costs') + need(p['prime_coefficient']>256/p['cover_gap'],'Actual bad-class fallback prime allowance') + comparison={'current_admitted':F('.0034'),'current_exact_ordinary':F('.0034363538396')} + old_c1=F('.003459')-F(1,2**18) + comparison['PR4697_fixed_C0_prime_saturated_sup']=old_c1/(1+old_c1-old) + gains={k:b/v-1 for k,v in comparison.items()} + need(gains['current_exact_ordinary']>F(1,1000),'At least0.1% actual ordinary improvement') + return {'params':p,'after_cover':c1,'ordinary_exact':ordinary,'admitted':b, + 'tail':tail,'comparators':comparison,'relative_gains':gains, + 'margins':{'adapter':d-ordinary,'ordinary_relaxation':ordinary-b, + 'stock':1-ordinary-d,'prime_allowance':p['prime_coefficient']-256/p['cover_gap']}, + 'WORD_changed':True,'new_whole_kappa':None, + 'scope':'Conditional ordinary BIT supplier only; main selected/complex result unchanged.'} + +def encode(x): + if isinstance(x,F):return str(x) + if isinstance(x,dict):return {str(k):encode(v)for k,v in x.items()} + if isinstance(x,(tuple,list)):return [encode(v)for v in x] + return x + +if __name__=='__main__': + inv=invoice(LOCAL,HELPERS);result=certify(inv) + print(json.dumps(encode({'invoice':inv,'certificate':result}),indent=2)) diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-PROOF.md b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-PROOF.md new file mode 100644 index 0000000000..7db6805f8a --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-PROOF.md @@ -0,0 +1,90 @@ +# Finite ordinary backend replacement on the productive BIT supplier + +Scope. This is a conditional composition of the completed ordinary BIT +contracts retained by PR4760 and its source. The raw local/global WORD, its +11400 independent originals, all helper jobs, projector routes and raw mixed +moment are unchanged. The new claim is ordinary BIT b=1737729/500000000. +The complex supplier and selected whole multiplication kappa are unchanged. + +Attribution. Finite acyclic ordinary-leaf bootstrapping and its nested row +restoration argument are prior work: rohanarun's PR185, followed by PR199 and +PR204. Their exact historical heads are identified in SOURCES.json and linked in README.md. +They are not claimed as merged or as a new theorem here. We rederive the +composition on the current productive/delayed-cover contract instead of +reusing their historical numerical constants, tapes or acceptance arithmetic. + +1. Fixed uniform program and paid cover. +On the unchanged PR4760 native invoice, new exact tail verification at tested +saving0.00347545806 and alpha_gap=2^-39 supplies C0=0.00347545805, +H0=377228190883840, H1=262208150916063859466241 and N=2^H1, under its existing +finite compiler and implementation premises. Set d=2^-36+10^-20 and C1=C0-d. +Choose one fixed odd q>2^45*N^5 avoiding all denominators, determinants and +rank witnesses of this completed finite program. Since 2^45*d>256, its full +bad-class multiplier is below 1+d/4, whereas N^d>=1+d/2. Thus the cover +retains the claimed strict moment. Regenerate all q-dependent route, stock, +precision, semantic-height and machine constants. They may be enormous. +No old 21-bit/raw1e9/tape threshold is reused as a bound for this new program. + +2. Backend interface and order of quantifiers. +A_0 is the already completed ordinary BIT supplier of PR4760 with saving +b0=0.0034597. It operates on arbitrary widths and complete chunks, keeps all +preceding/intervening complete spectators, and internally borrows and returns +its row stock. These completed-interface conclusions retain the same source +analytic/native/compiler/tape assumptions; a scalar exponent alone is not +enough. Weighted leaves use four unweighted ordinary atom interchanges, so +this completed A_0 has the required type. Fixed radix ranges are numerically +padded to binary ranges and unpadded at completed endpoints, with volume +factor below four. The backend's internal prime need not equal the outer q. + +For j=1,2,3 define a distinct finite algorithm A_j. Use the fixed uniform +supplier above, w=ceil(e^(1/100)), and only the already frozen A_(j-1) for +ordinary atom, routing and high-part exchanges. Freeze its new constants and +eventual threshold before varying e. Coarse recursive calls decrease atom +count; backend calls decrease j. There is no forward/self-reference and no +depth tending to infinity with the input size. + +3. Costs and separators. +Put rho=1/100. The three retained root costs of A_j are + O(V[e^(1-rho) + + e^((1-rho)*(1-C1)+rho*(1-b_(j-1))) + + e^rho*log(e)]). +Thus a_j=(1-rho)*C1+rho*b_(j-1). On the1e-10 grid choose + b1=0.0034753004, + b2=0.0034754564, + b3=0.0034754580. +Exact rational checks give, at each j, + b_(j-1)0. +Completion at18^1024 and splitting at17^1024 remain fully charged. +The integer compiler uses z=1-C0, z0=(t+z)/2, h=1/64; +H0*h*(z0-t)>=(z0-t)*(5+8*h)*1024+1+8*1024*(1-z0), +and H1*(z-z0)>H0*(1-z0). Old H0/H1 fail these new inequalities. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-RESULT.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-RESULT.json new file mode 100644 index 0000000000..0d5096a143 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-RESULT.json @@ -0,0 +1,234 @@ +{ + "C1": "22776761781112568293839/6553600000000000000000000", + "admitted": "1737729/500000000", + "base_completed_backend": "34597/10000000", + "finite_backend_levels": 3, + "levels": [ + { + "admitted": "8688251/2500000000", + "certificate": { + "admitted": "8688251/2500000000", + "after_cover": "22776761781112568293839/6553600000000000000000000", + "completed_backend_replaced": true, + "margins": { + "adapter": "4276027093749855738909939/655360000000000000000000000", + "ordinary_relaxation": "36106144261090061/655360000000000000000000000", + "prime_allowance": "1677721602305843009213693952/95367431706161", + "stock": "646528827093749855738909939/655360000000000000000000000" + }, + "new_whole_kappa": null, + "ordinary_exact": "2277572906250144261090061/655360000000000000000000000", + "params": { + "admitted": "8688251/2500000000", + "alpha_gap": "1/549755813888", + "atom": "1/100", + "cover_gap": "95367431706161/6553600000000000000000000", + "old_backend": "34597/10000000", + "prime_coefficient": 35184372088832, + "tested": "173772903/50000000000", + "uniform": "69509161/20000000000" + }, + "raw_moment_word_changed": false, + "scope": "Conditional ordinary BIT supplier only; main selected/complex result unchanged.", + "tail": { + "alpha": { + "lower": "0.999999999995907969119219873828", + "upper": "0.999999999995907969119219873829" + }, + "compiler_H0": 377228190883840, + "cutoff_base": 17, + "delta": { + "lower": "0.948389240822963884322396564019", + "upper": "0.948389240822963884322396564020" + }, + "gamma": { + "lower": "0.958113122911614897909836201269", + "upper": "0.958113122911614897909836201270" + }, + "normalized_surplus_lower": "536870911/576460753377165312", + "tail_exponent": "1/5", + "target_floor_base": 18, + "tensor_power": 1024, + "tested_saving": "173772903/50000000000", + "uniform_H1": 262208150916063859466241, + "uniform_N": "2^262208150916063859466241", + "uniform_saving": "69509161/20000000000", + "winning_word_materialized": false + } + }, + "completed_backend_saving": "34597/10000000", + "level": 1, + "ordinary_exact": "2277572906250144261090061/655360000000000000000000000" + }, + { + "admitted": "8688641/2500000000", + "certificate": { + "admitted": "8688641/2500000000", + "after_cover": "22776761781112568293839/6553600000000000000000000", + "completed_backend_replaced": true, + "margins": { + "adapter": "4275924854968415738909939/655360000000000000000000000", + "ordinary_relaxation": "38727584261090061/655360000000000000000000000", + "prime_allowance": "1677721602305843009213693952/95367431706161", + "stock": "646528724854968415738909939/655360000000000000000000000" + }, + "new_whole_kappa": null, + "ordinary_exact": "2277675145031584261090061/655360000000000000000000000", + "params": { + "admitted": "8688641/2500000000", + "alpha_gap": "1/549755813888", + "atom": "1/100", + "cover_gap": "95367431706161/6553600000000000000000000", + "old_backend": "8688251/2500000000", + "prime_coefficient": 35184372088832, + "tested": "173772903/50000000000", + "uniform": "69509161/20000000000" + }, + "raw_moment_word_changed": false, + "scope": "Conditional ordinary BIT supplier only; main selected/complex result unchanged.", + "tail": { + "alpha": { + "lower": "0.999999999995907969119219873828", + "upper": "0.999999999995907969119219873829" + }, + "compiler_H0": 377228190883840, + "cutoff_base": 17, + "delta": { + "lower": "0.948389240822963884322396564019", + "upper": "0.948389240822963884322396564020" + }, + "gamma": { + "lower": "0.958113122911614897909836201269", + "upper": "0.958113122911614897909836201270" + }, + "normalized_surplus_lower": "536870911/576460753377165312", + "tail_exponent": "1/5", + "target_floor_base": 18, + "tensor_power": 1024, + "tested_saving": "173772903/50000000000", + "uniform_H1": 262208150916063859466241, + "uniform_N": "2^262208150916063859466241", + "uniform_saving": "69509161/20000000000", + "winning_word_materialized": false + } + }, + "completed_backend_saving": "8688251/2500000000", + "level": 2, + "ordinary_exact": "2277675145031584261090061/655360000000000000000000000" + }, + { + "admitted": "1737729/500000000", + "certificate": { + "admitted": "1737729/500000000", + "after_cover": "22776761781112568293839/6553600000000000000000000", + "completed_backend_replaced": true, + "margins": { + "adapter": "4275923832606815738909939/655360000000000000000000000", + "ordinary_relaxation": "12513184261090061/655360000000000000000000000", + "prime_allowance": "1677721602305843009213693952/95367431706161", + "stock": "646528723832606815738909939/655360000000000000000000000" + }, + "new_whole_kappa": null, + "ordinary_exact": "2277676167393184261090061/655360000000000000000000000", + "params": { + "admitted": "1737729/500000000", + "alpha_gap": "1/549755813888", + "atom": "1/100", + "cover_gap": "95367431706161/6553600000000000000000000", + "old_backend": "8688641/2500000000", + "prime_coefficient": 35184372088832, + "tested": "173772903/50000000000", + "uniform": "69509161/20000000000" + }, + "raw_moment_word_changed": false, + "scope": "Conditional ordinary BIT supplier only; main selected/complex result unchanged.", + "tail": { + "alpha": { + "lower": "0.999999999995907969119219873828", + "upper": "0.999999999995907969119219873829" + }, + "compiler_H0": 377228190883840, + "cutoff_base": 17, + "delta": { + "lower": "0.948389240822963884322396564019", + "upper": "0.948389240822963884322396564020" + }, + "gamma": { + "lower": "0.958113122911614897909836201269", + "upper": "0.958113122911614897909836201270" + }, + "normalized_surplus_lower": "536870911/576460753377165312", + "tail_exponent": "1/5", + "target_floor_base": 18, + "tensor_power": 1024, + "tested_saving": "173772903/50000000000", + "uniform_H1": 262208150916063859466241, + "uniform_N": "2^262208150916063859466241", + "uniform_saving": "69509161/20000000000", + "winning_word_materialized": false + } + }, + "completed_backend_saving": "8688641/2500000000", + "level": 3, + "ordinary_exact": "2277676167393184261090061/655360000000000000000000000" + } + ], + "new_H0": 377228190883840, + "new_H1": 262208150916063859466241, + "params_shared": { + "alpha_gap": "1/549755813888", + "atom": "1/100", + "cover_gap": "95367431706161/6553600000000000000000000", + "prime_coefficient": 35184372088832, + "tested": "173772903/50000000000", + "uniform": "69509161/20000000000" + }, + "previous_exact_ordinary": "17713901828029/5120000000000000", + "raw_invoice": { + "helper_original_fields": 7848, + "main_original_fields": 3552, + "original_fields": 11400, + "paid": { + "1": 25407, + "14": 444, + "2": 24156, + "21": 444, + "28": 444, + "3": 1404, + "35": 444, + "4": 702, + "42": 444, + "49": 444, + "5": 1836, + "56": 444, + "6": 180, + "63": 222, + "7": 324 + }, + "rank_surplus": 753, + "targets": { + "127": 222, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "4": 72, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "8": 7776 + }, + "thick_calls": 18, + "thin_queries": 1665 + }, + "raw_moment_word_changed": false, + "relative_gain_over_previous_exact": "80443131971/17713901828029", + "schema": 1, + "scope": "Same raw native WORD; tightened effective rank compiler, new fixed prime/cover constants and three acyclic completed ordinary backends. Retains completed arbitrary-width/spectator/ROW and source implementation premises. Not a materialized uniform program or a new whole multiplication theorem.", + "source_PR": 4760, + "source_full_receipt_sha256": "552bd59e681d2d53461318eaf788e2d2e49ae78853265c30607834359fe9b118", + "source_inputs_authenticated": 43, + "status": "PASS_CONDITIONAL_ORDINARY_BIT_003475458", + "whole_kappa_changed": false +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-independent.py.txt b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-independent.py.txt new file mode 100644 index 0000000000..498ebb37a3 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-independent.py.txt @@ -0,0 +1,113 @@ +"""Independent tight tail/rank-compiler/bootstrap arithmetic successor. + +Uses the separately implemented PR4760 census and positive-series engine. +No primary price/tail/interval module is imported or called. +""" +from pathlib import Path +# Apache-2.0. Internal independent OpenAI Codex check for ai-nanachi. +from fractions import Fraction as F +from decimal import Decimal,localcontext +from hashlib import sha256 +import importlib.util,json,sys + +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +PKG=HERE.parent/'bit-compact-productive-controller' +PRIMARY=HERE/'RESULT.json' +TESTED=F('.00347545806');UNIFORM=F('.00347545805') +ETA=F(1,2**39);V=1024;U=F(1,5);RHO=F(1,100) +COVER_GAP=F(1,2**36)+F(1,10**20);C1=UNIFORM-COVER_GAP +PRIME=2**45;B0=F('.0034597');OLD_EXACT=F(17713901828029,5120000000000000) + + +def need(v,m): + if not v:raise ValueError(m) + + +def ceil(x):return -((-x.numerator)//x.denominator) +def floor(x):return x.numerator//x.denominator + + +def decimal(x): + with localcontext() as c: + c.prec=60;return str(Decimal(x.numerator)/x.denominator) + + +def encode(x): + if isinstance(x,F):return str(x) + if isinstance(x,dict):return {str(k):encode(v) for k,v in x.items()} + if isinstance(x,(list,tuple)):return [encode(v) for v in x] + return x + + +def main(): + ipath=PKG/'independent_price.py' + spec=importlib.util.spec_from_file_location('separate_PR4760_tight_census',ipath);I=importlib.util.module_from_spec(spec);spec.loader.exec_module(I) + T,P,local,helpers,baseline=I.census();X=I.X + need(sum(T.values())==11400 and sum(P.values())==57339 and helpers=={4:4,8:432},'unchanged actual productive unit') + t=1-TESTED;target=X.moment(T,t);paid=X.moment(P,t) + alpha=X.div(paid,target) + gamma=X.div(X.moment(P,t+U),X.mul(X.power(17,U),target)) + delta=X.div((F(sum(T.values())*18),)*2,X.mul(X.power(17,TESTED),target)) + need(alpha[1]<1-ETA,'tight strict raw alpha gap') + need(gamma[1]0,'alpha Bernoulli bound plus both tails strictly contracts') + h=F(1,64);z=1-UNIFORM;z0=(t+z)/2;g=z0-t + overhead=(5+8*h)*V;debt=1+8*V*(1-z0) + H0=ceil((g*overhead+debt)/(h*g));H1=floor(H0*(1-z0)/(z-z0))+1 + need(g>0 and H0>=8*V and H0*h*g>=g*overhead+debt,'new effective compiler induction') + need(H1*(z-z0)>H0*(1-z0),'new uniform rank bound') + need(17**64<18**63 and max(T)<256,'strict completed rank separation') + need(F(PRIME)>256/COVER_GAP,'complete delayed-cover fallback prime budget') + previous=B0;levels=[] + for level in range(1,4): + exact=(1-RHO)*C1+RHO*previous;admitted=F(floor(exact*10**10),10**10) + if exact==admitted:admitted-=F(1,10**10) + row=dict(level=level,backend_level=level-1,completed_backend_saving=previous,ordinary_exact=exact,ordinary_exact_decimal=decimal(exact),admitted=admitted,admitted_decimal=decimal(admitted),adapter_gap=RHO-exact,stock_gap=1-exact-RHO,ordinary_relaxation_gap=exact-admitted,improvement_gap=admitted-previous) + need(all(row[k]>0 for k in('adapter_gap','stock_gap','ordinary_relaxation_gap','improvement_gap')),'all finite ordinary stage gaps') + need((1-RHO)*(1-C1)+RHO*(1-previous)==1-exact,'actual ordinary body exponent') + levels.append(row);previous=admitted + need(previous==F(1737729,500000000),'independently derived final finegrid saving') + # Only now read and compare the primary table, including every level's tail. + primary=json.loads(PRIMARY.read_bytes()) + need(F(primary['C1'])==C1 and primary['new_H0']==H0 and primary['new_H1']==H1,'primary newrank constants agree') + shared={'tested':TESTED,'uniform':UNIFORM,'cover_gap':COVER_GAP,'atom':RHO,'alpha_gap':ETA,'prime_coefficient':F(PRIME)} + need(all(F(primary['params_shared'][k])==v for k,v in shared.items()),'all primary shared parameters') + need(len(primary['levels'])==3,'three completed finite levels') + for computed,root in zip(levels,primary['levels']): + for k in('level','completed_backend_saving','ordinary_exact','admitted'): + need(F(root[k])==computed[k],'independent stage agreement '+k) + cert=root['certificate'];tail=cert['tail'];need(tail['compiler_H0']==H0 and tail['uniform_H1']==H1,'all levels use the newcompiler bounds') + need(all(F(cert['params'][k])==v for k,v in shared.items()),'all per-level shared parameters') + need(F(cert['params']['old_backend'])==computed['completed_backend_saving'] and F(cert['params']['admitted'])==computed['admitted'],'actual predecessor/admission at each level') + need(F(cert['after_cover'])==C1 and F(cert['ordinary_exact'])==computed['ordinary_exact'] and F(cert['admitted'])==computed['admitted'],'nested certificate exact values') + need(F(tail['tested_saving'])==TESTED and F(tail['uniform_saving'])==UNIFORM and tail['tensor_power']==V and tail['cutoff_base']==17 and tail['target_floor_base']==18 and F(tail['tail_exponent'])==U,'entire tail and cutoff parameters') + need(F(tail['normalized_surplus_lower'])==surplus,'primary strict tail surplus') + for name,bounds in [('alpha',alpha),('gamma',gamma),('delta',delta)]: + display=tail[name] + need(F(display['lower'])<=bounds[0]<=bounds[1]<=F(display['upper']),'independent series enclosure contained in primary '+name) + margins=cert['margins'] + need(F(margins['adapter'])==computed['adapter_gap'] and F(margins['stock'])==computed['stock_gap'] and F(margins['ordinary_relaxation'])==computed['ordinary_relaxation_gap'],'all stage margins agree') + need(F(margins['prime_allowance'])==F(PRIME)-256/COVER_GAP,'all per-stage full prime allowances') + gain=previous/OLD_EXACT-1 + need(F(primary['relative_gain_over_previous_exact'])==gain,'comparison against actual previous exact') + controls={} + def reject(label,condition): + need(not condition,'bad control unexpectedlypasses '+label);controls[label]='REJECT' + reject('old_alpha_gap_2^-32',alpha[1]<1-F(1,2**32)) + reject('weaker_alpha_gap_2^-40_same_tailbudget',1-1/(1+V*F(1,2**40))-F(4,2**32)>0) + reject('old_H0',377227157504*h*g>=g*overhead+debt) + reject('old_H1',262206447682297857*(z-z0)>H0*(1-z0)) + reject('old_atom_00346',F('.00346')>levels[-1]['ordinary_exact']) + reject('closed_covered_limit',levels[-1]['ordinary_exact']>C1) + reject('unfunded_prime_2^36',F(2**36)>256/COVER_GAP) + rawlo=F('.003475458064076428997514');rawhi=F('.003475458064076428997515') + result=dict(status='PASS_INDEPENDENT_TIGHT_TAIL_NEW_COMPILER_AND_THREE_FINITE_LEVELS',targets=T,paid=P,local=local,helpers=helpers,tested=TESTED,uniform=UNIFORM,t=t,alpha_gap=ETA,alpha=alpha,gamma=gamma,delta=delta,tail_surplus=surplus,compiler_H0=H0,uniform_H1=H1,uniform_N_symbolic='2^'+str(H1),cover_gap=COVER_GAP,C1=C1,prime_coefficient=PRIME,prime_allowance_margin=F(PRIME)-256/COVER_GAP,levels=levels,admitted=previous,relative_gain_over_PR4760_exact=gain,percent_gain_over_PR4760_exact=decimal(100*gain),raw_crossing_minus_admitted=[rawlo-previous,rawhi-previous],negative_controls=controls,primary_price_imported=False,actual_backend_API_independently_verified=False,new_WORD=False,new_whole_kappa=False,sourcepins={p.relative_to(ROOT).as_posix():sha256(p.read_bytes()).hexdigest() for p in(ipath,PKG/'exact_series.py',PKG/'SOURCES.json',PRIMARY)},scope='Same rawSOURCE unit; new tested/uniform exponents require NEW compiled rankN,q/ROW/height/tape/stock constants. Numeric finite stages only; actual completebackend API/algorithm freezing remains under same sourcebridge conditional framework. No infinite-limit or materialized uniformWORD claim.') + encoded=encode(result);target=HERE/'INDEPENDENT.json' + if '--write'in sys.argv:target.write_bytes((json.dumps(encoded,sort_keys=True,indent=2)+'\n').encode()) + else:need(encoded==json.loads(target.read_bytes()),'Deterministic independent certificate') + print(json.dumps(dict(status=result['status'],H0=H0,H1=H1,tail_surplus=str(surplus),separators=[r['admitted_decimal'] for r in levels],percent_gain=result['percent_gain_over_PR4760_exact'],controls=len(controls)))) + + +if __name__=='__main__':main() diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-verify.py.txt b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-verify.py.txt new file mode 100644 index 0000000000..f72f8dedfc --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/PR4814-verify.py.txt @@ -0,0 +1,88 @@ +#!/usr/bin/env python3 +"""Rebind completed finite ordinary backends to PR4760's productive supplier. + +Apache-2.0. Prepared for ai-nanachi with substantial OpenAI Codex assistance. +Finite leaf bootstrapping: rohanarun/PR185 and the credited PR199/204 lineage. +Native/compiler/cover sources and their notices remain frozen in the input. +""" +from pathlib import Path +from fractions import Fraction as F +import argparse,hashlib,importlib.util,json,sys +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +PREVIOUS=HERE.parent/'bit-compact-productive-controller' + +def need(value,message): + if not value:raise ValueError(message) + +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);sys.modules[name]=module + spec.loader.exec_module(module);return module + +def encode(value): + if isinstance(value,F):return str(value) + if isinstance(value,dict):return {str(k):encode(v)for k,v in value.items()} + if isinstance(value,(list,tuple)):return [encode(v)for v in value] + return value + +def authenticate(): + manifest=json.loads((HERE/'SOURCES.json').read_bytes());count=0 + for item in manifest['files']: + if item['usage']!='input':continue + path=ROOT/item['path'];raw=path.read_bytes() + need(not path.is_symlink(),'No aliased source') + need(hashlib.sha256(raw).hexdigest()==item['sha256'],'Changed input '+item['path']) + need(hashlib.sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()==item['git_blob'],'Changed source blob') + count+=1 + return count + +def run(): + inputs=authenticate() + # One source-identical full native/caller/RAW replay, not another legacy suite. + source=load(PREVIOUS/'verify.py','bootstrap_previous_complete_verifier') + previous=source.run() + need(previous==json.loads((PREVIOUS/'RESULT.json').read_bytes()),'Source-identical complete PR4760 result') + price=source.price + inv=price.invoice(price.LOCAL,price.HELPERS) + need(price.encode(inv)==previous['invoice'],'Exact native invoice, not copied headline') + common=dict(price.PARAMS) + common.update(tested=F('.00347545806'),uniform=F('.00347545805'),alpha_gap=F(1,2**39), + cover_gap=F(1,2**36)+F(1,10**20),atom=F(1,100),prime_coefficient=2**45) + covered=common['uniform']-common['cover_gap'];backend=F('.0034597');levels=[] + for index in range(1,4): + exact=(1-common['atom'])*covered+common['atom']*backend + scaled=exact*10**10;admitted=F(scaled.numerator//scaled.denominator,10**10) + params={**common,'old_backend':backend,'admitted':admitted} + cert=price.certify(inv,params) + # The inherited changed-word label and variable historical comparator + # do not describe a fixed-word finite-backend replacement. + for key in ('WORD_changed','comparators','relative_gains'):cert.pop(key,None) + cert.update(raw_moment_word_changed=False,completed_backend_replaced=True) + need(cert['ordinary_exact']==exact,'Actual body exponent') + need(backendF(1,1000),'Publication preparation margin over previous exact') + source_receipt=hashlib.sha256(json.dumps(previous,sort_keys=True,separators=(',',':')).encode()).hexdigest() + return encode({'schema':1,'status':'PASS_CONDITIONAL_ORDINARY_BIT_003475458', + 'source_PR':4760,'source_inputs_authenticated':inputs,'source_full_receipt_sha256':source_receipt, + 'raw_invoice':inv,'raw_moment_word_changed':False,'whole_kappa_changed':False, + 'C1':covered,'params_shared':{k:v for k,v in common.items()if k not in ('admitted','old_backend')},'levels':levels,'admitted':backend, + 'new_H0':levels[0]['certificate']['tail']['compiler_H0'], + 'new_H1':levels[0]['certificate']['tail']['uniform_H1'], + 'previous_exact_ordinary':old_exact,'relative_gain_over_previous_exact':backend/old_exact-1, + 'base_completed_backend':F('.0034597'),'finite_backend_levels':3, + 'scope':'Same raw native WORD; tightened effective rank compiler, new fixed prime/cover constants and three acyclic completed ordinary backends. Retains completed arbitrary-width/spectator/ROW and source implementation premises. Not a materialized uniform program or a new whole multiplication theorem.'}) + +if __name__=='__main__': + parser=argparse.ArgumentParser();parser.add_argument('--write',action='store_true');args=parser.parse_args() + result=run();target=HERE/'RESULT.json' + if args.write:target.write_bytes((json.dumps(result,sort_keys=True,indent=2)+'\n').encode()) + else:need(result==json.loads(target.read_bytes()),'Deterministic finite-backend certificate') + print(json.dumps({'status':result['status'],'ordinary_BIT':result['admitted'],'finite_levels':3, + 'raw_WORD_changed':False,'whole_kappa_changed':False})) diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/credited_intervals.py b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/credited_intervals.py new file mode 100644 index 0000000000..4b24a50961 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/credited_intervals.py @@ -0,0 +1,421 @@ +#!/usr/bin/env python3 +"""Higher-moment strictification and a polynomial-logarithm compiler bound. + +New arithmetic is independent of predecessor interval code. The unchanged +invoice replay and two outer ledgers are credited, byte-pinned oracles. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import ast +from collections import Counter +from contextlib import redirect_stdout +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256, sha1 +import io +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +GRID = 2**192 +C = Q('0.00268648') +KAPPA = Q('0.00268647') +T = {5:420, 6:270, 7:840, 8:1395, 9:3195, + 25:448, 41:448, 57:448, 121:224} +P = {1:37305, 2:10695, 3:3360, 4:1530, 5:300, + 8:1464, 16:448, 32:448, 48:448} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def down(x): + return Q((x*GRID).__floor__(), GRID) + + +def up(x): + return Q(-((-x*GRID).__floor__()), GRID) + + +def rounded(lo, hi): + return down(lo), up(hi) + + +def mul(a, b): + products = [x*y for x in a for y in b] + return rounded(min(products), max(products)) + + +def scale(a, x): + return mul(a, (x, x)) + + +def divide(a, b): + need(b[0] > 0, 'positive interval denominator') + return mul(a, rounded(1/b[1], 1/b[0])) + + +@lru_cache(None) +def log_bounds(n): + """Exact atanh series, binary reduction; round only the final interval.""" + need(isinstance(n, int) and n >= 1, 'positive integer logarithm') + + def series(x): + u = (x-1)/(x+1) + term, total = u, Q(0) + for j in range(80): + total += 2*term/(2*j+1) + term *= u*u + tail = 2*term/(161*(1-u*u)) + return total, total+tail + + k = n.bit_length()-1 + a, b = series(Q(2)) + c, d = series(Q(n, 2**k)) + return rounded(k*a+c, k*b+d) + + +def exp_point(x): + """Outward fixed-point Taylor enclosure, with binary scaling/squaring.""" + need(abs(x) < 16, 'bounded exponential argument') + if x < 0: + a, b = exp_point(-x) + return rounded(1/b, 1/a) + divisions = 0 + while x > Q(1, 2): + x /= 2 + divisions += 1 + term = total = (Q(1), Q(1)) + for j in range(1, 65): + term = scale(term, x/j) + total = rounded(total[0]+term[0], total[1]+term[1]) + following = scale(term, x/65) + # Every remaining ratio is <= 1/132. Twice the next term is safe. + result = rounded(total[0], total[1]+2*following[1]) + for _ in range(divisions): + result = mul(result, result) + return result + + +def exp_interval(a): + return exp_point(a[0])[0], exp_point(a[1])[1] + + +@lru_cache(None) +def power(n, exponent): + return exp_interval(scale(log_bounds(n), exponent)) + + +def moment(histogram, exponent): + low = high = Q(0) + for n, count in histogram.items(): + a, b = power(n, exponent) + low += count*a + high += count*b + return rounded(low, high) + + +def display(a): + unit = 10**30 + + def fixed(n): + sign = '-' if n < 0 else '' + s = str(abs(n)).rjust(31, '0') + return sign+s[:-30]+'.'+s[-30:] + + return {'lower': fixed((a[0]*unit).__floor__()), + 'upper': fixed(-((-a[1]*unit).__floor__()))} + + +def encoded(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): encoded(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [encoded(v) for v in x] + return x + + +def source_environment(path): + env = {'__file__': str(path), '__name__': 'pinned_source_oracle'} + exec(compile(path.read_bytes(), str(path), 'exec'), env) + return env + + +def authenticate(): + result = {} + for row in json.loads((HERE/'VENDOR.json').read_text())['files']: + path = HERE/'vendor'/Path(row['path']).relative_to( + 'research/higher-moment-strictification/vendor') + digest = sha256(path.read_bytes()).hexdigest() + need(digest == row['sha256'], 'changed source: '+row['path']) + raw = path.read_bytes() + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() + == row['git_blob'], 'changed Git source blob') + result[row['path']] = digest + return result + + +def invoice_oracle(): + """Run #4426 unchanged, rebinding only its two file-location globals.""" + path = HERE/'vendor/invoice-review/verify.py' + env = source_environment(path) + env.update(ROOT=path.parent, PHASES='DATA-PHASES.json') + output = io.StringIO() + with redirect_stdout(output): + env['main']() + result = json.loads(output.getvalue()) + need(result['status'] == 'PASS_PR4416_INVOICE_REBUILD', 'source invoice oracle') + need({int(k): v for k, v in result['targets'].items()} == T + and {int(k): v for k, v in result['paid'].items()} == P, + 'exact literal-word invoice') + return result + + +def tail_certificate(v=150, cutoff=10, floor=15, u=Q(3, 10)): + t = 1-C + need(v >= 1 and 1 < cutoff < floor < 121, 'strict finite ranks') + need(t+u >= 1, 'tail moment exponent at least one') + target, paid = moment(T, t), moment(P, t) + alpha = divide(paid, target) + gamma = divide(moment(P, t+u), mul(power(cutoff, u), target)) + delta = divide((Q(sum(T.values())*floor),)*2, + mul(power(cutoff, C), target)) + limits = (1-Q(1, 10**8), Q(181, 200), Q(439, 500)) + for name, bounds, limit in zip(('alpha', 'gamma', 'delta'), + (alpha, gamma, delta), limits): + need(0 < bounds[0] <= bounds[1] < limit < 1, name+' certified limit') + a, g, d = limits + bound = 1/(1+v*(1-a))+2*g**v+2*d**v + need(bound < 1, 'complete charged normalized moment') + old_gamma = divide((Q(sum(k*n for k, n in P.items())),)*2, + mul(power(cutoff, C), target)) + old_lower = alpha[0]**v+2*old_gamma[0]**v + need(old_lower > 1, 'rank-one-tail estimate fails at this tensor power') + return {'tensor_power': v, 'cutoff_base': cutoff, 'floor_base': floor, + 'paid_moment_exponent': t+u, 'tail_offset_u': u, + 'tested_saving': C, 'alpha': display(alpha), 'gamma': display(gamma), + 'delta': display(delta), 'rational_upper_limits': limits, + 'normalized_paid_upper': bound, 'strict_moment_gap': display((1-bound,)*2), + 'old_rank_one_gamma': display(old_gamma), + 'old_rank_one_bound_lower': display((old_lower, old_lower)), + 'ambient': '121^'+str(v), 'minimum_target': str(floor)+'^'+str(v), + 'maximum_paid': str(cutoff)+'^'+str(v), + 'productive_fields_before_uniform_compiler': '7688^'+str(v), + 'rank_one_surplus': '131723^'+str(v)+'-131115^'+str(v), + 'materialized_product_or_uniform_word': False} + + +def uniform_rank(v): + t, p, theta = 1-C, 13, Q(6, 7) + gap = (C-KAPPA)/7 + uniform_saving = C-gap + need(10**7 < 15**6, 'theta upper bound') + need(2*(10**v)**7 <= (121**v)**6, 'shifted logarithm inequality') + eta = scale(exp_interval(scale(log_bounds(121), -v*C)), t) + need(eta[0] > theta**p, 'exit contraction below complement capacity') + base = exp_interval(scale(log_bounds(121), v*C)) + need(base[1] < 2**p, 'entire ordinary base range fits') + # Integer grid: gap*H is integral, avoiding enormous rational powers. + step = gap.denominator + need(gap.numerator == 1, 'chosen rational gap grid') + + def passes(j): + H = step*j + return (H+1)**p < 2**j + + lo, hi = 1, 2 + while not passes(hi): + lo, hi = hi, 2*hi + while hi-lo > 1: + mid = (lo+hi)//2 + if passes(mid): + hi = mid + else: + lo = mid + H = step*hi + need(H > 7*v and passes(hi) and not passes(hi-1), 'final integer comparison') + need(eta[1] < theta**(p-1), 'one smaller logarithmic power fails') + return {'t': t, 'uniform_saving': uniform_saving, 'gap': gap, + 'logarithm_power': p, 'theta_upper': theta, 'eta': display(eta), + 'eta_minus_theta_to_p': display((eta[0]-theta**p, eta[1]-theta**p)), + 'm_to_saving': display(base), 'H': H, 'N': '2^'+str(H), + 'integer_test': {'left_base': H+1, 'left_exponent': p, + 'right_base': 2, 'right_exponent': hi}, + 'grid_step': step, 'previous_grid_point_rejected': True, + 'smaller_logarithmic_power_rejected': True} + + +def power_majorant_comparison(v, uniform_saving): + """Retain #4416's older power proof, changing only the new unit's ranks.""" + t, z, h = 1-C, 1-uniform_saving, Q(1, 7) + z0 = (t+z)/2 + delta = z0-t + B, debt = (4+7*h)*v, 1+7*v*(1-z0) + ratio = (delta*B+debt)/(h*delta) + H0 = -((-ratio.numerator)//ratio.denominator) + ratio = H0*(1-z0)/(z-z0) + H1 = ratio.numerator//ratio.denominator+1 + need(H0 >= 7*v and H0*h*delta >= delta*B+debt, 'power majorant threshold') + need((H0-1)*h*delta < delta*B+debt, 'previous power threshold rejected') + need(H1*(z-z0) > H0*(1-z0) >= (H1-1)*(z-z0), + 'strict power-majorant comparison and previous-rank control') + return {'H0': H0, 'H1': H1, 'N': '2^'+str(H1), 'theta_upper': 1-h, + 'scope': 'Tail transformation alone, retaining the older power majorant.'} + + +def outer_ledger(uniform_saving): + d = (C-KAPPA)/7 + params = {'kappa': KAPPA, 'tested_saving': C, + 'complex_uniform_saving': uniform_saving, 'b': KAPPA+5*d, + 'a': KAPPA+4*d, 'q': KAPPA+3*d, 'bit_saving': Q('0.0027'), + 'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10, + 'stop': d, 'layout': d, 'd': d} + env = source_environment(HERE/'vendor/outer_endpoint.py') + row = env['ledger'](params) + need(len(row['strict_checks']) == 54 and len(row['functional_checks']) == 3, + 'complete first outer ledger') + need(all(v > 0 for group in ('strict_checks', 'functional_checks') + for v in row[group].values()), 'all outer predicates') + frozen = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['outer'] + need(encoded(row) == frozen, 'unchanged full p7 endpoint ledger') + parsed = ast.parse((HERE/'vendor/check_ledger.py').read_bytes()) + function = next(n for n in parsed.body + if isinstance(n, ast.FunctionDef) and n.name == 'ledger') + constants = [n for n in parsed.body if isinstance(n, ast.Assign) + and any(isinstance(t, ast.Name) and t.id.startswith('KAPPA_') + for t in n.targets)] + eps, beta, q, a = (params[k] for k in ('epsilon', 'beta', 'q', 'a')) + grid = 10**10 + backoff = Q((eps*q*grid).__floor__(), grid)-KAPPA + need(backoff > 0, 'strict derived oracle grid backoff') + oracle = {'Q': Q, 'R0': params['r0'], 'ZETA': Q(1, 10**8), + 'SLACK': d, 'STOP': d, 'FLOOR': grid, 'BACKOFF': backoff, + 'EPS': eps, 'BETA': beta, 'THETA_POWER': Q(2), + 'HALO_POWER': 48, 'CORE_POWER': 128, 'STRASSEN_TAU': Q(45, 16), + 'b': params['b'], 'q': q, 'a': a, 'bit': params['bit_saving'], + 'online': Q('0.001730970419199163702738'), + 'old': Q('0.001730970419199163702738')} + code = ast.fix_missing_locations(ast.Module(body=constants+[function], type_ignores=[])) + exec(compile(code, 'pinned 63-predicate ledger', 'exec'), oracle) + second = oracle['ledger']('higher_moment_smaller_ranks') + need(second['kappa'] == KAPPA and second['margins'] == row['margins'], + 'all nine rows match both ledgers') + need(len(second['strict_checks']) == 63 and + all(v > 0 for v in second['strict_checks'].values()), 'all 63 legacy predicates') + controls = {} + for name, updates in [('closed_epsilon', {'epsilon': Q(1)}), + ('missing_layout', {'layout': Q(0)}), + ('unfunded_kappa', {'kappa': C}), + ('closed_uniform_gap', {'complex_uniform_saving': params['b']}), + ('insufficient_BIT', {'bit_saving': Q('0.0023')})]: + bad = env['ledger'](dict(params, **updates)) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'outer control rejected: '+name) + controls[name] = failed + for name, options in [('old_per_axis_scan', {'old_scan': True}), + ('group_equals_dimension', {'beta_': eps})]: + bad = oracle['ledger']('reject_'+name, **options) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'legacy control rejected: '+name) + controls[name] = failed + return {'ledger': row, 'legacy_63_checks': second['strict_checks'], + 'legacy_grid': grid, 'legacy_backoff': backoff, + 'minimum_margin_minus_kappa': min(row['margins'].values())-KAPPA, + 'rejected_controls': controls} + + +def finite_controls(): + def tensor(histogram): + out = Counter() + for k, n in histogram.items(): + for h, b in histogram.items(): + out[k*h] += n*b + return out + + def split(histogram, cutoff): + out = Counter() + for k, n in histogram.items(): + q, r = divmod(k, cutoff) + out[cutoff] += q*n + if r: + out[r] += n + return +out + + target, paid = tensor({2:1, 5:1}), tensor({1:2, 4:1}) + padded, completion = Counter(), Counter() + for k, n in target.items(): + padded[max(k, 9)] += n + if k < 9: + completion[9-k] += n + final = split(paid+completion, 4) + mass = lambda x: sum(k*n for k, n in x.items()) + need(mass(padded)-mass(final) == 7**2-6**2 == 13, 'exact paid padding mass') + need(min(padded) > max(final), 'exact toy separation') + need(final == Counter({1:5, 4:9}), 'literal toy expanded inventory') + # t=1/2, sigma=3/4, R=100, J=1 refutes a sublinear tail extension. + invalid = power(100, Q(1, 2))[1]+2*power(100, Q(3, 4))[1] + need(invalid < 100, 'sublinear upper-tail moment cannot bound splitting') + return {'toy_targets': padded, 'toy_paid': final, 'rank_one_surplus': 13, + 'sublinear_tail_counterexample': {'R': 100, 'J': 1, 't': '1/2', + 'sigma': '3/4', 'actual_charge': 100, + 'invalid_upper': display((invalid, invalid))}} + + +def verify(): + sources = authenticate() + invoice = invoice_oracle() + tail = tail_certificate() + rank = uniform_rank(tail['tensor_power']) + endpoint = outer_ledger(rank['uniform_saving']) + controls = finite_controls() + rejected = [] + for name, updates, expected in [ + ('too_short_product', {'v': 100}, 'complete charged normalized moment'), + ('sublinear_tail', {'u': C/2}, 'tail moment exponent at least one'), + ('lost_separation', {'floor': 10}, 'strict finite ranks'), + ]: + try: + tail_certificate(**updates) + except ValueError as error: + need(str(error) == expected, 'wrong rejection: '+name) + rejected.append({'mutation': name, 'failed_at': str(error)}) + else: + raise ValueError('accepted mutation: '+name) + old = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['compiler'] + return encoded({'schema': 'higher-moment-native-strictification/1', + 'status': 'PASS_HIGHER_MOMENT_STRICTIFICATION', 'kappa': KAPPA, + 'invoice_oracle': invoice, 'strictification': tail, + 'uniform_rank': rank, 'outer': endpoint, + 'tail_only_power_majorant': power_majorant_comparison( + tail['tensor_power'], rank['uniform_saving']), + 'finite_controls': controls, 'rejected_mutations': rejected, + 'predecessor_H': old['H1'], + 'rank_exponent_reduction_factor': Q(old['H1'], rank['H']), + 'tensor_power_reduction_factor': Q(6240, tail['tensor_power']), + 'source_sha256': sources, + 'verifier_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'scope': 'Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.'}) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = verify() + if args.out: + need(not args.out.exists(), 'new output path required') + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt') + print(json.dumps({'status': result['status'], 'tensor_power': result['strictification']['tensor_power'], + 'uniform_rank': result['uniform_rank']['N'], + 'strict_moment_gap': result['strictification']['strict_moment_gap'], + 'kappa': result['kappa']})) + + +if __name__ == '__main__': + main() diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-FULL-FEES.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-FULL-FEES.json new file mode 100644 index 0000000000..c26f46eb21 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-FULL-FEES.json @@ -0,0 +1,55 @@ +{ + "status": "POSITIVE_FINITE_PROGRAM_FEE_SCHEMA_NO_ORDINARY_SAVING_YET", + "raw_bit_IR_records": 446436, + "raw_record_cap_only": 1000000000, + "raw_cap_guard": true, + "literal_VALUE_XOR_passes": 378039, + "compound_pointwiseCOPY_assignments": 1827, + "new_shadow_ZERO_INIT_passes": 18, + "all_paid_owned_CLEAR_passes": 1845, + "initial_owned_bank_ZERO_scans": 2, + "final_owned_bank_teardown_scans": 2, + "new_shadow_copy_ADDs_already_in_VALUE_count": 18, + "in_BODY_paid_MAINport_wholefiber_routes": 7548, + "canonical_job_matching_route_pairs": 3624, + "canonical_job_matching_routes": 7248, + "of_these_partial4_helper_routes": 144, + "parent_parking": { + "paid_child_calls": 57321, + "allocated_parent_originals_plus_owned": 11402, + "safe_inactive_and_IO_FIELD_pass_bound_perQUERY": 45608, + "total_FIELD_pass_bound": 2614296168, + "meaning": "BeforeeachQUERYparkinactiveparentoriginalsandBOTHownedbanks,copyactiveARRAYtochildIO; onreturnrestoreinactiveorderandparentheads/stacktop. Parentancestorregionsareneverswept. Thisisaconservativepositivefixedconstant,notasaving." + }, + "normalizer_and_ROW_route_costs": { + "source_catalogue": "AllfixedrationalP/S/rho/targetrecipesincluded; chooseqavoidingallfiniteunits/denominators/rankwitnesses AFTERfiniteprogramcompile. No inheritednumericq/H threshold.", + "QUERY": "EachactualcurrentARRAYjobnormalizesonlyinthecompleteduniformprogram. Goodclassesuseorderedproperchild; badclassesusechargedlocal-ringfallback. Newrank4isfreshgeometricjobwithG22matcher,notoldticket.", + "wholefiber_route": "Useinheritedfixedrationalright-multiplicationstreamingprimitive,chargedO_(N,S,q)(V*w^(1-a_backend)), includinglowtypes/highcarry/counters/headreturn. NotfreeADDRESSgather.", + "symbolic_fixed_fee": "C_new(N,q)=C_stream*(rawVALUE+COPY+INIT+CLEAR+parkcounts)+SUM_FIXED_ROUTES C_route(N,q,S)+SUM_QUERY C_normalizer(N,q,P). Constantsarefinite/positiveandfixedBEFOREinputwidth. Thisreceipt doesNOTsupplyanumericalall-in1e9bound fornormalizers." + }, + "majorants": { + "LOCAL_direction_bits": { + "FORWARD": 27, + "INVERSE": 30, + "RAW-DUAL": 30 + }, + "GLOBAL_bits": 485, + "GLOBAL_majorant": "84444886942101694684170345064821097278736852236761441986693729773292029633741181968660858254765568090641736900142834132599618230804004304022958549", + "scope": "Positivecancellationfreeenvelope regeneratedfromnewprogram. Old21/30bitthresholdsareNOTreused." + }, + "stock": { + "original_productive_fields": 11400, + "owned_OUTPUT_credit": 0, + "per_primitive_GLOBAL_unit_owned_banks": 2, + "per_finite_DAG_allocation": "ReserveTWOwholeownedbanksforeachcompiledunitinstance(orconcurrentliveunit),withunit-scopedtagsandzeroINIT/CLEAR. NeverreuseoneC0perdepthwhenunits suspended.", + "child_source_on_owned": "AQUERYonacurrentownedSUMusesitastheactualchildtargetslot; correlatedvaluesarevalidarbitrary-inputinstances. ItdoesNOTaddanindependentparentinput. Descendantownbanksgetdistincttags.", + "row_split": "Originalunitrolewidthremains11400; twoownedbanksareworkstreams,notnewproductiveROWclasses. Freshdescendantrolesexcludeexposedparentfields.", + "asymptotic": "WithnewfixedfiniteN,B,q,source/park/tapeconstantsregenerated,theinheritedstocklog_q S=O_new(w loge)andborrow/restoreproofremainconditionalinputs. OldnumericH/prime/precisionthresholdsnotasserted." + }, + "pending_before_ordinary_bound": [ + "Freshthree-tensor-tail/finitecompiler/primefallbackcertificateonnewP/T", + "Actualnewfixedconstants/H/reserve/cutoffchosenandchecked", + "Finiteleafbootstrapwithfrozenalready-establishedordinarybackend", + "Parentindependentvalidationandnorecordclaimuntilthen" + ] +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-GLOBAL-RESULT.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-GLOBAL-RESULT.json new file mode 100644 index 0000000000..f943cee1c2 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-GLOBAL-RESULT.json @@ -0,0 +1,64 @@ +{ + "status": "MATERIALIZED_EXACT_G23_ALL11400_RAW", + "at_utc": "2026-10-23T01:11:30.091235+00:00", + "originals": 11400, + "private_allocated": 2, + "private_peak": 2, + "private_episodes": 1845, + "calls": 18, + "expanded_event_count": 446436, + "expanded_event_sha256": "0cb03eb11c2d8f511d495f3767e55e48156ed31094697d4e58a82f15be33c203", + "global_gzip_sha256": "d963221d1f3ad9b942adefaa048a124717d500a257f1494ac56a18ec78a8488c", + "SOURCE_descriptor_count": 57321, + "SOURCE_descriptors_sha256": "c16158be5271a857f5f543fb1e8a0342eec04bfe9f120c25d13ef15330f19f99", + "paid": { + "1": 25389, + "2": 24156, + "3": 1386, + "4": 720, + "5": 1836, + "6": 180, + "7": 324, + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + }, + "targets": { + "4": 72, + "8": 7776, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "127": 222 + }, + "rank_surplus": 753, + "operation_counts": { + "ADD": 33078, + "LOCAL_ADD": 343296, + "LOCAL_QUERY": 52164, + "SHADOW_PAID_INIT": 18, + "LOCAL_COPY_QUERY": 162, + "LOCAL_PAID_CLEAR": 162, + "SHADOW_PAID_CLEAR": 18, + "PAID_PORT_ROUTE": 7548, + "PAID_WHOLE_IDLE": 3330, + 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b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-RESULT.json @@ -0,0 +1,94 @@ +{ + "status": "PASS_PRIVATE_NATIVE_CANDIDATE_READY_FOR_ORDINARY_CERTIFICATE", + "at_utc": "2026-10-23T01:34:38.223049+00:00", + "runtime_manifest": { + "relative_path": "provider/MANIFEST.json", + "bytes": 8823, + "sha256": "15034901fb7641ff6cf154e3d8e3e82d1f02332a1f54ed52a90bef9667648ca3" + }, + "cold_modes": [ + { + "relative_path": "verification-normal-0002/RESULT.json", + "bytes": 4259, + "sha256": "5583a98fab22d5e0195440d4bb5361dbe38c90104b7f5fadfcbb4f945b707957" + }, + { + "relative_path": "verification-optimized-0001/RESULT.json", + "bytes": 4259, + "sha256": "f43b3b49f72bfc2b9371f7cb8debaa55eeb288b9700cb3fee9be61b5de435433" + } + ], + "exact_G23_stream": { + "events": 446436, + "decompressed_sha256": "0cb03eb11c2d8f511d495f3767e55e48156ed31094697d4e58a82f15be33c203", + "gzip": { + "relative_path": "provider/data/GLOBAL.jsonl.gz", + "bytes": 1407039, + "sha256": 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Private future-bundle restart point.", + "development_correction": "The first CLI stopped on int-key versus JSON string-key comparison. Preserved attempt-0001; explicit lossless serialization fixed only CLI comparison. No scientific input or generated programme changed." +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-cold-O.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-cold-O.json new file mode 100644 index 0000000000..2fa1c58085 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-cold-O.json @@ -0,0 +1,142 @@ +{ + "status": "PASS_PRIVATE_NATIVE_CANDIDATE_READY_FOR_ORDINARY_CERTIFICATE", + "runtime_manifest": { + "sha256": "15034901fb7641ff6cf154e3d8e3e82d1f02332a1f54ed52a90bef9667648ca3", + "files": 48, + "input_files": 22 + }, + "isolated": 1, + "optimized": 1, + "python": "3.12.14 (main, Aug 25 2026, 14:01:42) [MSC v.1944 64 bit (AMD64)]", + "local_all_originals": { + "FORWARD": { + "rankmass": 5089, + "paid": { + "1": 1318, + "2": 1342, + "3": 77, + "4": 40, + "5": 102, + "6": 10, + "7": 18 + }, + "private_peak": 2, + "majorant_bits": 27, + "native_moduli_all658_symbols": [ + 101, + 10201 + ], + "whole_function_proof": "Every ADD has exact common coframe, every QUERY is the nested-projector MOVE, and every owned erase/reheader has a literal lifecycle. FRAME induction supplies all functions; finite pulses are controls." + }, + "INVERSE": { + "rankmass": 5089, + "paid": { + "1": 1318, + "2": 1342, + "3": 77, + "4": 40, + "5": 102, + "6": 10, + "7": 18 + }, + "private_peak": 2, + "majorant_bits": 30, + "native_moduli_all658_symbols": [ + 101, + 10201 + ], + "whole_function_proof": "Every ADD has exact common coframe, every QUERY is the nested-projector MOVE, and every owned erase/reheader has a literal lifecycle. FRAME induction supplies all functions; finite pulses are controls." + }, + "RAW-DUAL": { + "rankmass": 5089, + "paid": { + "1": 1318, + "2": 1342, + "3": 77, + "4": 40, + "5": 102, + "6": 10, + "7": 18 + }, + "private_peak": 2, + "majorant_bits": 30, + "native_moduli_all658_symbols": [ + 101, + 10201 + ], + "whole_function_proof": "Every ADD has exact common coframe, every QUERY is the nested-projector MOVE, and every owned erase/reheader has a literal lifecycle. FRAME induction supplies all functions; finite pulses are controls." + } + }, + "local_negative_controls": { + "wrong_rank4": "Proper actual residual rank, not FRAME id", + "omit_shadow_clear": "All658originalFLAGs and ownedwholepayloadreturn", + "wrong_shadow_frame": "Actualaligned commonFRAME ADD", + "original_CLEAR": "Paid fullownedpayloadCLEAR, notoriginal/inverseSOURCE" + }, + "global": { + "status": "PASS_INDEPENDENT_LITERAL_G23_STREAM_AND_FRESH_SOURCE_HISTORY", + "original_RAW": 11400, + "calls": 18, + "query_count": 57321, + "fresh_SOURCE_descriptors": 57321, + "private_episodes": 1845, + "private_peak": 2, + "new_rank4_requests": 18, + "majorant_bits": 485, + "event_sha256": "0cb03eb11c2d8f511d495f3767e55e48156ed31094697d4e58a82f15be33c203", + "paid": { + "1": 25389, + "2": 24156, + "3": 1386, + "4": 720, + "5": 1836, + "6": 180, + "7": 324, + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + }, + "targets": { + "4": 72, + "8": 7776, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "127": 222 + } + }, + "global_negative_controls": { + "duplicate_helper_owner": "All7848fresharbitraryhelperowners, nodoublecredit", + "omit_shadow_clear": "SOURCE compoundCOPY/context binding", + "wrong_rank4": "Proper actual residual rank, not FRAME id", + "wrong_shadow_frame": "EveryactualsameFRAME ADD" + }, + "rational_source_and_job_bindings": { + "original_targets": 11400, + "canonical_matching_routes": 7248, + "internal_main_routes": 7548, + "owned_banks": 2, + "owned_original_credit": 0 + }, + "fee_schema_status": "POSITIVE_FINITE_PROGRAM_FEE_SCHEMA_NO_ORDINARY_SAVING_YET", + "ordinary_saving": null, + "whole_kappa": null, + "publication_authorized_by_this_receipt": false, + "elapsed_seconds": 5.171722600003704, + "CPU_seconds": 5.171875, + "memory": { + "available": true, + "PeakWorkingSetSize": 101294080, + "PeakPagefileUsage": 92983296 + } +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-cold-normal.json b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-cold-normal.json new file mode 100644 index 0000000000..8f78eb043e --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/provider-cold-normal.json @@ -0,0 +1,142 @@ +{ + "status": "PASS_PRIVATE_NATIVE_CANDIDATE_READY_FOR_ORDINARY_CERTIFICATE", + "runtime_manifest": { + "sha256": "15034901fb7641ff6cf154e3d8e3e82d1f02332a1f54ed52a90bef9667648ca3", + "files": 48, + "input_files": 22 + }, + "isolated": 1, + "optimized": 0, + "python": "3.12.14 (main, Aug 25 2026, 14:01:42) [MSC v.1944 64 bit (AMD64)]", + "local_all_originals": { + "FORWARD": { + "rankmass": 5089, + "paid": { + "1": 1318, + "2": 1342, + "3": 77, + "4": 40, + "5": 102, + "6": 10, + "7": 18 + }, + "private_peak": 2, + "majorant_bits": 27, + "native_moduli_all658_symbols": [ + 101, + 10201 + ], + "whole_function_proof": "Every ADD has exact common coframe, every QUERY is the nested-projector MOVE, and every owned erase/reheader has a literal lifecycle. FRAME induction supplies all functions; finite pulses are controls." + }, + "INVERSE": { + "rankmass": 5089, + "paid": { + "1": 1318, + "2": 1342, + "3": 77, + "4": 40, + "5": 102, + "6": 10, + "7": 18 + }, + "private_peak": 2, + "majorant_bits": 30, + "native_moduli_all658_symbols": [ + 101, + 10201 + ], + "whole_function_proof": "Every ADD has exact common coframe, every QUERY is the nested-projector MOVE, and every owned erase/reheader has a literal lifecycle. FRAME induction supplies all functions; finite pulses are controls." + }, + "RAW-DUAL": { + "rankmass": 5089, + "paid": { + "1": 1318, + "2": 1342, + "3": 77, + "4": 40, + "5": 102, + "6": 10, + "7": 18 + }, + "private_peak": 2, + "majorant_bits": 30, + "native_moduli_all658_symbols": [ + 101, + 10201 + ], + "whole_function_proof": "Every ADD has exact common coframe, every QUERY is the nested-projector MOVE, and every owned erase/reheader has a literal lifecycle. FRAME induction supplies all functions; finite pulses are controls." + } + }, + "local_negative_controls": { + "wrong_rank4": "Proper actual residual rank, not FRAME id", + "omit_shadow_clear": "All658originalFLAGs and ownedwholepayloadreturn", + "wrong_shadow_frame": "Actualaligned commonFRAME ADD", + "original_CLEAR": "Paid fullownedpayloadCLEAR, notoriginal/inverseSOURCE" + }, + "global": { + "status": "PASS_INDEPENDENT_LITERAL_G23_STREAM_AND_FRESH_SOURCE_HISTORY", + "original_RAW": 11400, + "calls": 18, + "query_count": 57321, + "fresh_SOURCE_descriptors": 57321, + "private_episodes": 1845, + "private_peak": 2, + "new_rank4_requests": 18, + "majorant_bits": 485, + "event_sha256": "0cb03eb11c2d8f511d495f3767e55e48156ed31094697d4e58a82f15be33c203", + "paid": { + "1": 25389, + "2": 24156, + "3": 1386, + "4": 720, + "5": 1836, + "6": 180, + "7": 324, + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + }, + "targets": { + "4": 72, + "8": 7776, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "127": 222 + } + }, + "global_negative_controls": { + "duplicate_helper_owner": "All7848fresharbitraryhelperowners, nodoublecredit", + "omit_shadow_clear": "SOURCE compoundCOPY/context binding", + "wrong_rank4": "Proper actual residual rank, not FRAME id", + "wrong_shadow_frame": "EveryactualsameFRAME ADD" + }, + "rational_source_and_job_bindings": { + "original_targets": 11400, + "canonical_matching_routes": 7248, + "internal_main_routes": 7548, + "owned_banks": 2, + "owned_original_credit": 0 + }, + "fee_schema_status": "POSITIVE_FINITE_PROGRAM_FEE_SCHEMA_NO_ORDINARY_SAVING_YET", + "ordinary_saving": null, + "whole_kappa": null, + "publication_authorized_by_this_receipt": false, + "elapsed_seconds": 5.362964399973862, + "CPU_seconds": 5.359375, + "memory": { + "available": true, + "PeakWorkingSetSize": 101199872, + "PeakPagefileUsage": 92807168 + } +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/separate_series.py b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/separate_series.py new file mode 100644 index 0000000000..7c68264455 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/separate_series.py @@ -0,0 +1,32 @@ +"""Independent positive-series rational intervals, no external numeric library.""" +from fractions import Fraction as F +from functools import lru_cache +S=10**40 +def need(c,m): + if not c:raise ValueError(m) +def floor(q):return q.numerator//q.denominator +def ceil(q):return -((-q.numerator)//q.denominator) +def grid(lo,hi):return F(floor(lo*S),S),F(ceil(hi*S),S) +def logratio(z,n=60): + need(0<=z<=F(1,3),'Reduced log domain');s=F(0);p=z + for j in range(n):s+=2*p/(2*j+1);p*=z*z + return s,s+2*p/((2*n+1)*(1-z*z)) +LN2=logratio(F(1,3)) +@lru_cache(None) +def logbound(x): + if x==1:return F(0),F(0) + k=x.bit_length()-1;a,b=logratio(F(x-2**k,x+2**k));return grid(a+k*LN2[0],b+k*LN2[1]) +@lru_cache(None) +def expbound(y): + need(0<=y<7,'Bounded exp');s=p=F(1);n=90 + for j in range(1,n+1):p=p*y/j;s+=p + return grid(s,s+(p*y/(n+1))/(1-y/(n+2))) +@lru_cache(None) +def power(x,t): + if x==1:return F(1),F(1) + a,b=logbound(x);a,b=grid(t*a,t*b);return expbound(a)[0],expbound(b)[1] +def moment(profile,t): + vv=[(n,power(k,t))for k,n in profile.items()];return sum(n*v[0]for n,v in vv),sum(n*v[1]for n,v in vv) +def mul(a,b):return a[0]*b[0],a[1]*b[1] +def div(a,b):return a[0]/b[1],a[1]/b[0] +def interval(a):return {'lower':str(a[0]),'upper':str(a[1]),'display':float(sum(a)/2)} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/tail-engine.py.txt b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/tail-engine.py.txt new file mode 100644 index 0000000000..f1114036ff --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/tail-engine.py.txt @@ -0,0 +1,202 @@ +#!/usr/bin/env python3 +"""Exact finite replay for the conditional query-thinned construction. + +Apache-2.0. Prepared for Cinna Davis with substantial OpenAI Codex assistance. +Retains zxv's native/factor/tail work and Jacob Alan Sussman's integer flow. +""" +from fractions import Fraction as Q +from hashlib import sha1, sha256 +import argparse +import json +import sys +sys.dont_write_bytecode = True +import controller as C +HERE, ROOT, need = C.HERE, C.ROOT, C.need + + +def encode(x): + if isinstance(x, Q): return str(x) + if isinstance(x, dict): return {str(k): encode(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): return [encode(v) for v in x] + return x + + +def authenticate(): + count = 0 + for row in json.loads((HERE/'SOURCES.json').read_text())['files']: + if row['usage'] != 'input': continue + path = ROOT/row['path']; raw = path.read_bytes() + need(not path.is_symlink(), 'No source alias') + need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: '+row['path']) + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == row['git_blob'], 'Changed Git blob') + count += 1 + return count + + +def controllers(): + B, E = C.engines(); result = {} + for kind, p, a in [('complex', 17, 8), ('bit', 16, 7)]: + row = json.loads((HERE/(kind.upper()+'-CONTROLLER.json')).read_text()) + thick, mask = C.thick_stages(p), C.keep_mask(p, a) + if kind == 'complex': + coefficients, events, idles = E.controller(p, mask) + coefficients = C.specialize_complex(coefficients, thick) + left = [[Q(x) for x in r] for r in row['boundaries']['left']] + right = [[Q(x) for x in r] for r in row['boundaries']['right']] + diagonal = [tuple(term) for term in row['diagonal']] + transformed = {k: B.matrix_multiply(B.matrix_multiply(left, m), right) for k, m in coefficients.items()} + expected = {k: [[Q(i == j and diagonal[i] == k) for j in range(2*p)] for i in range(2*p)] for k in set(diagonal)} + need(transformed == expected, 'All exact rational Laurent coefficients, including signs and Q powers') + for name, matrix in [('left', left), ('right', right)]: + need(E.scalar_program(matrix) == row['boundaries'][name+'_program'], 'Literal unit scalar boundary program') + changed = dict(coefficients) + k = next(iter(changed)); changed[k] = [r[:] for r in changed[k]]; changed[k][0][0] += 1 + need(B.matrix_multiply(B.matrix_multiply(left, changed[k]), right) != expected.get(k), 'A changed physical coefficient is rejected') + else: + coefficients, events, idles = B.physical_controller(p, mask) + coefficients = C.specialize_bit(coefficients, thick) + fresh = B.simultaneous_monomial_factor(coefficients) + need(fresh == row['boundaries'], 'Exact binary physical operator and scalar boundaries') + diagonal = fresh['diagonal_monomials'] + need(C.replay_events(row['physical_events'], p, kind) == coefficients, + 'Emitted native/query/idle word equals the specialized physical source') + mutant = json.loads(json.dumps(row['physical_events'])) + # Every removed stage is forward; changing its direction must change + # the actual operator rather than merely a tariff field. + next(ev for ev in mutant if ev[0] == 'QUERY_SHEAR')[3] = True + need(C.replay_events(mutant, p, kind) != coefficients, 'Wrong query orientation rejected') + invoice = C.inventories(kind, p, a, diagonal, idles) + ports = 112 if kind == 'complex' else 111 + boundary_records = (sum(len(row['boundaries'][name+'_program']) for name in ('left', 'right')) + if kind == 'complex' else row['boundaries']['boundary_unit_ADDs_per_port']) + scalar_upper = (p+2)*10**6+16*invoice['thin_queries']+32*ports*(len(row['physical_events'])+boundary_records) + need(scalar_upper < invoice['raw_scalar_record_bound'], 'Conservative complete scalar/route count fits') + need(encode(invoice) == row['invoice'], 'Literal and closed-form complete '+kind+' invoice') + result[kind] = invoice + return result + + +def native_contacts(): + n = C.load(ROOT/'research/pr4359-p7-padding/native_inventory.py', 'thinned_native_phases') + phases = json.loads((ROOT/'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json').read_text()) + axes = tuple(1 << i for i in range(17)); old = [(a, 1) for a in axes[:9]]; fresh = [(a, 1) for a in axes[9:]] + checks = 0 + for recipe in phases['recipes']: + q = recipe['q']; basis = recipe['idle_children'][0]['orthogonal_axes'][:8] + need(all((b&q).bit_count() % 2 == 0 for b in basis), 'Old eight-space perpendicular to q') + swaps = [b ^ axes[9+i] for i, b in enumerate(basis)] + route = tuple(e ^ n.act(swaps, sum(((e&v).bit_count() % 2) << i for i, v in enumerate(swaps))) for e in axes) + need(all(n.act(route, route[i]) == axes[i] for i in range(17)), 'Exact physical route inverse') + need(all((a&b).bit_count() % 2 == int(i == j) for i, a in enumerate(route) for j, b in enumerate(route)), 'Orthogonal physical route') + need(n.act(route, q) == q, 'Central query direction fixed') + need(n.polynomial(n.norm([(q, -1)]), 17) == n.polynomial(n.norm([(q, 1), (q, 2)]), 17), + 'Inverse thin Gaussian is one positive query and a physical translation') + for sign in (-1, 1): + raw = (n.norm(old), n.norm(old+[(q, -1)])) + entry = (n.norm(fresh+[(q, sign)]), n.norm(fresh)) + out0 = n.norm(fresh+[(a, sign) for a in axes[:9]]) + local_out = (out0, n.norm(list(out0)+[(q, -sign)])) + out = (n.norm(old+fresh), n.norm(old+fresh+[(q, -1)])) + for x, y in list(zip(raw, entry))+list(zip(local_out, out)): + n.contact(x, y, route, 17); checks += 1 + for x, y in zip(raw, out): + need(n.polynomial(n.norm(list(y)+[(a, -c) for a, c in x]), 17) == n.polynomial(n.norm(fresh), 17), 'Exactly the fresh eight-axis multiplier') + bit = C.load(ROOT/'research/kappa-rebuild/bit/bit_native_binding.py', 'thinned_binary_charts') + ports = json.loads((ROOT/'research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json').read_text())['ports'] + local = json.loads((ROOT/'research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json').read_text())['local'] + for direction in local['signed_directions']: + need({int(k): v for k, v in direction['profile'].items()} == C.engines()[0].LOCAL, + 'Every actual binary local child remains charged') + need(direction['unit_ADDs'] < 10**6 and direction['owned_COPY_episodes'] == 9, + 'Native binary scalar and owned-center bills retained') + for row in ports: + p = [[Q(x) for x in r] for r in row['central_projector']]; rho = [[Q(x) for x in r] for r in row['chart_15']] + active = [[p[i][j] if i < 8 and j < 8 else Q(i == j and i >= 8) for j in range(15)] for i in range(15)] + full = [[Q(i == j and i < 8) for j in range(15)] for i in range(15)] + need(bit.multiply(rho, rho) == bit.ident(15) and bit.multiply(bit.multiply(rho, active), rho) == full, 'BIT exact arbitrary-column chart') + need(bit.multiply(p, p) == p and sum(p[i][i] for i in range(8)) == 1, 'BIT query rank one') + # Formal independent X,Y,Z columns. Mutants execute the same word with + # an actual omitted operation; they are not merely different receipts. + for e in (-1, 1): + def execute(clear=True, erase=True): + x, y, z = {('X', 0): 1}, {('Y', 0): 1}, {('Z', 0): 1} + if clear: z = {} + for key, value in x.items(): z[key] = z.get(key, 0)+value + z = {(name, power+e): value for (name, power), value in z.items()} + for key, value in z.items(): y[key] = y.get(key, 0)+(-1 if e == 1 else 1)*value + if erase: z = {} + return x, y, z + expected = ({('X', 0): 1}, {('Y', 0): 1, ('X', e): -1 if e == 1 else 1}, {}) + need(execute() == expected, 'Completed arbitrary-input owned-query shear') + need(execute(clear=False) != expected and execute(erase=False) != expected, 'Clear/erase omission controls rejected') + return {'complex_contacts_and_inverses': checks, 'binary_charts': len(ports), + 'thin_paid_rank_per_port': 1, 'thin_productive_credit': 0, 'owned_stream_restored_zero': True} + + +def tail(E, invoice, tested, uniform, cutoff, floor, alpha_gap): + T, P = invoice['targets'], invoice['paid']; t, u, v = 1-tested, Q(1, 5), 1024 + target, paid = E.moment(T, t), E.moment(P, t) + alpha = E.divide(paid, target) + other = C.load(ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py', 'separate_rational_moment_engine') + tl, th = other.moment(T, tested); pl, ph = other.moment(P, tested) + need(tl > ph and max(target[0], tl) <= min(target[1], th) + and max(paid[0], pl) <= min(paid[1], ph), 'Separate rational interval engine agrees') + gamma = E.divide(E.moment(P, t+u), E.mul(E.power(cutoff, u), target)) + delta = E.divide((Q(sum(T.values())*floor),)*2, E.mul(E.power(cutoff, tested), target)) + need(alpha[1] < 1-alpha_gap and gamma[1] < Q(31, 32) and delta[1] < Q(19, 20), 'Three completely charged tail ratios') + need(Q(31, 32)**128 < Q(1, 16) and Q(19, 20)**128 < Q(1, 16), 'Exact decay blocks') + surplus = 1-Q(1)/(1+v*alpha_gap)-Q(4, 2**32) + need(surplus > 0, 'Original and completion tails both fit') + need(cutoff**64 < floor**63 and max(T) < 256, 'Strict ranks after completion and splitting') + h = Q(1, 64); z, z0 = 1-uniform, (t+1-uniform)/2; gap = z0-t + B, debt = (5+8*h)*v, 1+8*v*(1-z0) + x = (gap*B+debt)/(h*gap); H0 = -((-x.numerator)//x.denominator) + x = H0*(1-z0)/(z-z0); H1 = x.numerator//x.denominator+1 + need(H0 >= 8*v and H0*h*gap >= gap*B+debt and H1*(z-z0) > H0*(1-z0), 'Effective integer compiler bound') + return {'tested_saving': tested, 'uniform_saving': uniform, 'alpha': E.display(alpha), + 'gamma': E.display(gamma), 'delta': E.display(delta), 'tensor_power': v, + 'cutoff_base': cutoff, 'target_floor_base': floor, 'tail_exponent': u, + 'normalized_surplus_lower': surplus, 'compiler_H0': H0, 'uniform_H1': H1, + 'uniform_N': '2^'+str(H1), 'winning_word_materialized': False} + + +def run(): + count = authenticate(); rows = controllers(); native = native_contacts() + E = C.load(ROOT/'research/higher-moment-strictification/verify.py', 'credited_exact_intervals') + kappa, tested = Q('.00296'), Q('.00296030'); d = (tested-kappa)/7 + complex_ = tail(E, rows['complex'], tested, kappa+6*d, 20, 21, Q(1, 30000000)) + bit = tail(E, rows['bit'], Q('.00346'), Q('.003459'), 17, 18, Q(1, 250000)) + before, after, atom, old = Q('.003459'), Q('.00345'), Q('.004'), Q('.0000384599') + ordinary, admitted = (1-atom)*after+atom*old, Q('.0034') + need(before > after and atom > ordinary > admitted and atom < 1-ordinary, 'Complete ordinary BIT conversion') + need(Q('.003') < ordinary and 2**26 > 256/(before-after), 'Old atom rejected and finite prime bound') + L = C.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'complete_outer_ledger') + params = {'kappa': kappa, 'tested_saving': tested, 'complex_uniform_saving': kappa+6*d, + 'b': kappa+5*d, 'a': kappa+4*d, 'q': kappa+3*d, 'bit_saving': admitted, + 'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10, 'stop': d, 'layout': d, 'd': d} + outer = L.ledger(params) + outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta']*(1-atom) + need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete predicate inventory') + need(all(x > 0 for group in ('strict_checks', 'functional_checks') for x in outer[group].values()), 'All outer predicates') + controls = {} + for label, changes in [('old_BIT_cap', {'bit_saving': Q('.0027')}), ('closed_uniform_gap', {'complex_uniform_saving': params['b']}), + ('unfunded_kappa', {'kappa': tested}), ('closed_epsilon', {'epsilon': Q(1)}), ('missing_layout', {'layout': Q(0)})]: + bad = L.ledger(dict(params, **changes)); failed = [k for k, v in bad['strict_checks'].items() if v <= 0] + need(failed, 'Reject '+label); controls[label] = failed + return encode({'schema': 'query-thinned-productive-controllers/1', 'status': 'PASS_CONDITIONAL_QUERY_THINNED_KAPPA_00296', + 'kappa': kappa, 'relative_gain_over_p7': kappa/Q('.00268647')-1, + 'source_inputs_authenticated': count, 'native': native, 'complex_invoice': rows['complex'], 'bit_invoice': rows['bit'], + 'complex_strictification': complex_, 'bit_strictification': bit, + 'ordinary_BIT': {'before_cover': before, 'after_cover': after, 'atom': atom, 'ordinary_saving': ordinary, + 'admitted': admitted, 'prime_rule': 'odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses'}, + 'outer': outer, 'minimum_outer_margin_minus_kappa': min(outer['margins'].values())-kappa, + 'negative_controls': controls, 'old_atom_rejected': True, + 'scope': 'Conditional native construction; all-column, erasure, whole-job matching, fixed-tape, precision, analytic, prime and exact-recovery premises retained. No unconditional theorem or selected promotion.'}) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__); parser.add_argument('--write', action='store_true'); args = parser.parse_args() + result = run(); output = HERE/'RESULT.json' + if args.write: output.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: need(result == json.loads(output.read_text()), 'Complete receipt matches exact replay') + print(json.dumps({k: result[k] for k in ('status', 'kappa', 'source_inputs_authenticated', 'minimum_outer_margin_minus_kappa')}, sort_keys=True)) diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/three-stage-cover-bit.tex b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/three-stage-cover-bit.tex new file mode 100644 index 0000000000..f05225d21f --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/inputs/three-stage-cover-bit.tex @@ -0,0 +1,264 @@ +\subsection{Atom contract and common endpoint} +Fix an odd prime $q$, chosen below, and put $R_w=\mathbb Z/q^w\mathbb Z$. +An atom is a complete consecutive $w$-digit address field. Write $C_n$ for +reversal of the $n$ atom positions, without reversing digits inside an atom. +The recursive contract is the involution +\[ + F_A(H,D)=(AC_nD,C_nA^{-1}H), +\] +where $A$ is a diagonal array of units on the head atoms. Its entries may +depend on exposed ancestor row fields and the atom index, but not on the +fresh role fields of this invocation or on the head/data values. Only the +polynomial-time descriptors generated by the construction are required; +no constant-cost oracle for arbitrary functions of a prefix is assumed. +Every call preserves all complete spectator fields and restores its row +coordinate. The original unweighted call has $A=I$. + +For a split idempotent $P$ on the head coordinates set +\[ + D_P=\begin{pmatrix}I-P&PC_n\\C_nP&I-C_nPC_n\end{pmatrix}, + \qquad F=D_I. +\] +These are involutions, and $D_P-I$ has split rank $\operatorname{rank}P$. +Nested commuting-projector identities are polynomial identities and require +no symmetry of $P$. For $n=mf$ and $G=g\otimes I_f$ define +\[ + Q_g=\operatorname{diag}(G,C_nGC_n). +\] +Then $Q_gF=FQ_g$ and $Q_gD_PQ_g^{-1}=D_{GPG^{-1}}$. +Consequently conjugating every base frame by any $g\in\operatorname{GL}_m(R_w)$ +leaves the same full physical endpoint $F$. + +Put $Q_A=\operatorname{diag}(A,I)$. Conjugate the entire completed scalar +word by $Q_A$. Scalar gates mix roles having the same address map, so they +commute with $Q_A$. A current role routing also commutes with $Q_A$, since +it changes only fresh fields. Thus only address residuals change, and the +completed endpoint is $Q_AFQ_A^{-1}=F_A$. More explicitly, when a port +changes charts from $g$ to $gR_s$, its local label changes from $M$ to +$R_s^{-1}MR_s$, and +\[ + (gR_s)(R_s^{-1}MR_s)(gR_s)^{-1}=gMg^{-1}. +\] +This routing is a change of row/chart, not an uncharged dense address map. +The adapted chart $Q_AQ_gQ_A^{-1}$ commutes with $F_A$. None of these +conjugations is executed as an extra normalization pass. + +\subsection{Explicit rational three-stage geometry} +Use the retained PR97 local producer with +\[ + h=23,\qquad v=1771,\qquad R_{\rm loc}=28866,\qquad \ell=506. +\] +Its physical projector ranks and scalar word are unchanged. On +$\mathcal A=\mathbb Q^{23}$ take the form $H_0=(I-J/9)/2$. +For a triple $S$ let $q_S=\chi_S$; then $q_S^tH_0q_S=1$. +Fix $q_0=\chi_{\{1,2,3\}}$ and $K=q_0^\perp$. A rational basis is +\[ + k_i=e_i-(e_i^tH_0q_0)q_0,\qquad 2\le i\le23. +\] +Projection along $q_0$ is injective on the span of $e_2,\ldots,e_{23}$, +since $q_0$ has nonzero first coordinate. Thus this is indeed a basis. +Let $\mathcal B,\mathcal C$ be orthogonal copies of $K$ and put +$\mathcal E=\mathcal A\perp\mathcal B\perp\mathcal C$, of dimension $m=67$. + +Choose a coordinate permutation $\pi_S$ taking $\{1,2,3\}$ to $S$. +It preserves $H_0$. The rational isometry $R_{12,S}$ fixes $q_S$ and +$\mathcal C$, and exchanges $\pi_Sk_i\in q_S^\perp\subset\mathcal A$ +with $k_i\in\mathcal B$. Define $R_{23,S}$ by exchanging the same vectors +with their copies in $\mathcal C$, fixing $q_S$ and $\mathcal B$. +Both maps are involutions. A hyperedge $(g,S)$ uses the invocations +$gR_{12,S},g,gR_{23,S}$, with active spaces +\[ + g(\mathcal B+\mathbb Qq_S),\qquad g\mathcal A, + \qquad g(\mathcal C+\mathbb Qq_S). +\] +Their projectors commute; their pairwise and common intersection is the +projector $P_{gq_S}$, and their sum is $I+2P_{gq_S}$. +This follows from the orthogonal decomposition +$\mathbb Qq_S\perp q_S^\perp\perp\mathcal B\perp\mathcal C$ before +conjugation. These are the cumulative-projector three-stage transfer +identities: the three scalar shears complete the interchange, with zero +interstage connectors and no rank-one endpoint correction. Each port +family visits the full cover bijectively, by right multiplication with +its displayed involution. The physical ledger is therefore three copies +of the local auxiliary, data and center histograms, and three copies of +the exterior histogram $m-\text{nullity}$. + +\subsection{One weighted child on a generic residue class} +Work first on one atom column. Let $g$ be its weighted residual involution, +of split rank $r$ relative to $I$. If the cross block has generic northeast +rank profile, unit lower row and column elimination, without normalizing +pivots, gives +\[ + Lg_{XY}R=ED_pF_0^t, + \quad E=(e_1,\ldots,e_r),\quad + F_0=(e_m,\ldots,e_{m-r+1}), +\] +with invertible diagonal $D_p$. Conjugate by $\operatorname{diag}(L,R^{-1})$. +Split rank and the unit pivot minor give a factorization +\[ + g-I=\binom EB(A_0,D_pF_0^t),\qquad + A_0E+D_pF_0^tB=-2I_r. +\] +For clarity, if $g-I=UV$, then $g^2=I$ gives +$U(VU+2I)V=0$. The unit minor supplies a left inverse of $U$ and a right +inverse of $V$, proving the identity over the local ring itself. +Set +\[ + K=-(B+F_0D_p^{-1})E^t+F_0D_p^{-1}A_0(I-EE^t), + \qquad S=\begin{pmatrix}I&0\\K&I\end{pmatrix}. +\] +The identities $KE=-B-F_0D_p^{-1}$ and +$D_pF_0^tK=A_0+E^t$ give +\[ + SgS^{-1}=\begin{pmatrix} + I-EE^t&ED_pF_0^t\\F_0D_p^{-1}E^t&I-F_0F_0^t + \end{pmatrix}. +\] +This is one weighted reversed interchange on the first $r$ head and last +$r$ tail coordinates. All other factors are unit lower intrabank maps or +lower cross-bank additive maps. Thus variable diagonal units remain in +the child's weight array rather than becoming unsupported routing passes. + +For $n=mf$, group atoms by coarse coordinate $i$ and column $j$. +If $L_P,R_P,D_P$ are unweighted normalizers for the current projector and +$A_j=\operatorname{diag}(A[if+j])$, then +$L_j=A_jL_PA_j^{-1}$ and $R_j=R_P$ are unit lower normalizers for +$A_jPC_m$. The child's exact contiguous index rule is +\[ + A_{\rm child}[kf+j]=A[i_kf+j]D_P[k]. +\] +The cross-bank atom pairing is reversed, and $C_r\otimes C_f=C_{rf}$. +Hence the middle operation is exactly one $rf$-atom call of the same +contract, with no interleaving or gathering. Its coefficients depend only +on parent prefix fields, which become ancestor spectators at the child; +the child's fresh roles come from disjoint unused row stock. + +All unit lower adapters require $O(n)$ atom passes. The retained ordered +affine lemma implements each later-target shear in $O(V)$, including +prefix-controlled offsets. The generated descriptors have polynomial cost +in $w$: good-class evaluation follows one ancestral index per level; +fallback evaluation branches by a constant per level. Since depth is +$O(\log e)$ and $w=\lceil e^{1/1000}\rceil$, this costs $e^{O(1)}=w^{O(1)}$. +Stored ancestor data use $O(w\log e)$ bits. The proof of the ordered affine +lemma still applies with these controls: polynomial preparation per prefix +is absorbed by the complete $q^w$ target fiber. Unrelated spectator counters +are incremented by ripple counting rather than read in their entirety. + +\subsection{Weighted leaves and a genuine local-ring fallback} +At one atom write $J_a=\left(\begin{smallmatrix}0&a\\a^{-1}&0\end{smallmatrix}\right)$, +$U(a)=\left(\begin{smallmatrix}1&a\\0&1\end{smallmatrix}\right)$ and +$L(b)=\left(\begin{smallmatrix}1&0\\b&1\end{smallmatrix}\right)$. +Then +\[ + J_a=\operatorname{diag}(1,-1)U(a)L(-a^{-1})U(a), + \qquad U(a)=J_1L(a)J_1. +\] +Thus a weighted leaf uses four old ordinary atom interchanges, three +prefix-controlled shifts and one fixed sign. With +$a_{\rm old}=384599/10^{10}$ it costs $O(Vw^{1-a_{\rm old}})$. +This constant occurs only at stopped leaves. + +A bad residue class cannot be treated by field Bruhat elimination: +an entry zero modulo $q$ need not vanish modulo $q^w$. Instead Gaussian +eliminate the full invertible residual of size $N_0=2m$ with unit pivots. +Each invertible Schur complement has a unit in its next pivot column; +row swaps and unnormalized additions clear that column. There are at most +$N_0(N_0-1)$ additions and $N_0$ swaps. Pivot choices are determined by +the unweighted low residue class: diagonal conjugation scales every +Schur-complement row and column by units and preserves its zero pattern. +The final diagonal has product a fixed sign, since the residual has +determinant $(-1)^r$ and row swaps change only the sign. + +A lower addition is a paid additive adapter. An upper addition is +conjugated into a lower addition by two ordinary coarse-field swaps. +For a field of $f$ atoms, let $R_{\rm tail}$ reverse the later field. +Then the ordinary weighted swap is +\[ + J_A=R_{\rm tail}F_AR_{\rm tail},\qquad + J_A(H,D)=(AD,A^{-1}H). +\] +Each $R_{\rm tail}$ is one unweighted reversed call on the first and last +$\lfloor f/2\rfloor$ atoms, fixing a possible middle atom. Thus $J_A$ +costs at most three children of widths $f,\lfloor f/2\rfloor, +\lfloor f/2\rfloor$. A paired diagonal scaling is $J_aJ_1$, at most six +children. The full diagonal is a product of $N_0-1$ such pairs and a fixed +sign. Across the two banks the reversed pairing already makes the swaps +and diagonal pairs directly reversed calls; the preceding ordinary bounds +remain conservative. Reindexing a tail weight by $j\mapsto f-1-j$ changes +only its descriptor. Charging every addition as upper therefore gives +\[ + 6N_0(N_0-1)+3N_0+6(N_0-1)<32m^2. +\] +Every child has width at most $f$, hence ratio at most $1/m$. Coefficients +are computed from constant-sized local-ring matrices and parent weight +descriptors; only units are inverted. This proves the fallback cost, +including its actual reversals, rather than assuming nonunit pivots away. + +\subsection{Finite covers, batching, and the strict moment} +Take $q>2^{80}$ avoiding all fixed rational denominators and rank witnesses. +At atom width $w$ use the finite cover $\operatorname{GL}_m(R_w)$ and its +right-multiplication edges $g\mapsto gR_s$. Every vertex has the unique chart +\[ + g=g_0+qG_1,\quad g_0\in\operatorname{GL}_m(\mathbb F_q), + \quad G_1\in(\mathbb Z/q^{w-1}\mathbb Z)^{m^2}, +\] +using fixed representatives for $g_0$. Right multiplication permutes $g_0$ +and acts affinely on $G_1$, with a carry determined by $g_0$. Its fixed +dimensional rational linear part factors into fixed scalings, ordered +shifts and a constant number of old width-$O(w)$ interchanges. Thus each +fixed port routing costs $O(Vw^{1-a_{\rm old}})$. + +Let $W_0=|\operatorname{GL}_m(\mathbb F_q)|(2v+3R_{\rm loc})$. +The full role count is $W(w)=W_0q^{m^2(w-1)}$. Split preceding rows into +low role type, high matrix and unused stock. Batch \emph{all} high matrices +for each low type in one stream. A frame edge is one child on this whole +batch, of volume $V/W_0$, and routing is executed once per fixed operation +type. Consequently neither the number of tapes nor the number of child +programs grows with $w$. High cardinality cancels in the normalized moment, +but its $m^2(w-1)$ digits are charged in the row reserve. + +For each fixed projector require the leading minors of sizes $1$ through +$r$ to be units. Each cleared minor polynomial in $g_0$ is nonzero: +similarity to $\operatorname{diag}(I_r,0)$ supplies a witness after the +fixed rank is preserved modulo $q$. Their total degree is at most $m^3$. +The polynomial zero bound and conditioning on invertibility (a factor at +most two) give bad fraction at most $2m^3/q<10^{-16}$ for each edge type. +No simultaneous union bound over edge types is needed, since their moments +are averaged separately. Good classes use the whole-rank child; bad +classes use the full $32m^2$-child fallback just proved. + +Let $H_r$ be the three-stage histogram described above and +$W=2v+3R_{\rm loc}=90140$. The retained ledger gives +\[ + \sum_r rH_r=6037356,\qquad Wm-\sum_r rH_r=2024=2v-3\ell, + \qquad \max\{r:H_r>0\}=66. +\] +For $a=747/2000000$, $\tau=1-a$, and $b=10^{-16}$ the conservative moment is +\[ + \mu_\tau\le + \sum_r\frac{H_r}{W}(r/m)^\tau+ + b\frac{32m^2\sum_rH_r}{W}(1/m)^\tau<1. +\] +The entire fallback is added; no displaced good contribution is subtracted. +The exact script \path{scripts/three_stage_cover_network.py} and certificate +\path{certificates/three-stage-cover-network.json}, from the retained axis +\path{certificates/three-stage-cover-bit-input.json}, give +$1-\mu_\tau>6.3397366396\cdot10^{-7}$. +The certificate uses the 32-term positive atanh logarithm series with its +geometric tail, $\exp(u)\le1+u+u^2/(2(1-u/3))$, and upward rounding to +the grid $2^{-120}$. All inputs have $0\le u<3$; these are rational upper +bounds, not floating-point root estimates. Since every child ratio is at +most one and $\tau<1$, this same strict bound implies $\mu_1<1$. + +With $T(n,w)$ denoting time divided by logical volume, the fixed low-type +profile $\{c_r\}$, including fallback classes, satisfies +\[ + T(n,w)\le\sum_rc_rT(r\lfloor n/m\rfloor,w)+Cn+Cw^{1-a_{\rm old}} + \quad(n\ge m),\qquad + T(n,w)\le Cw^{1-a_{\rm old}}\quad(na_{\rm bit}$ and $\beta<1-a_{\rm bit}$ make both +the atom-adapter and borrowing terms lower order. The remainder cost +$O(Vw^{1-a_{\rm old}})$ is also covered. Thus the ordinary radix-$q$ +interchange has cost $O(Ve^{1-a_{\rm bit}})$, without an externally supplied +superpolynomial stock of rows. + +For an original binary chunk range $[2^e]$, let +$t=\lceil e/\log_2q\rceil$ and embed it numerically into $[q^t]$. +Pad both exchanged ranges while retaining every spectator. The total +logical-volume increase is below $q^2$. Execute the completed ordinary +radix-$q$ interchange, then remove the padding. Its endpoint preserves the +rectangular genuine set $[2^e]\times[2^e]$; intermediate maps may mix genuine +and padded addresses, which does not affect this endpoint justification. +As $q$ is fixed and $t=\Theta(e)$, the binary interchange has the same +saving exponent. All schedules use a fixed number of finite-alphabet +tapes; low residue tables and port types are fixed independently of $w$. + +The conclusion retains the original local-producer, ordered-affine, +ordinary-leaf and multiplication-framework hypotheses. It adds no free +unit-scaling, dense chart transformation, or external row-stock primitive. diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/seal.py b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/seal.py new file mode 100644 index 0000000000..14da304e9a --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/seal.py @@ -0,0 +1,19 @@ +"""Create fresh exact receipts and freeze this successor, never old manifests.""" +from pathlib import Path +from datetime import datetime,timezone +import hashlib,json +import certificate,independent +HERE=Path(__file__).resolve().parent +def need(c,m): + if not c:raise ValueError(m) +def put(n,x):(HERE/n).write_text(json.dumps(x,indent=2)+'\n',encoding='utf-8') +def pin(p):return {'path':p.relative_to(HERE).as_posix(),'bytes':p.stat().st_size,'sha256':hashlib.sha256(p.read_bytes()).hexdigest()} +def main(): + need(not(HERE/'MANIFEST.json').exists(),'Successor already sealed') + for row in json.loads((HERE/'INPUTS.json').read_bytes())['files']: + p=HERE/row['path'];need(hashlib.sha256(p.read_bytes()).hexdigest()==row['sha256'],'Input drift '+row['path']) + result=certificate.run();second=independent.audit(HERE.parent/'provider',result);put('RESULT.json',result);put('INDEPENDENT.json',second);put('FEE-BOUNDS.json',result['fee_bounds']) + put('RESTART.json',{'status':'PRIVATE_CONDITIONAL_ORDINARY_GATE_READY_FOR_ROOT_REVIEW','native_provider':'../provider','native_manifest_sha256':hashlib.sha256((HERE.parent/'provider'/'MANIFEST.json').read_bytes()).hexdigest(),'admitted':result['admitted'],'comparison_to':result['comparator'],'relative_gain':result['relative_gain'],'whole_kappa':None,'publication':'No newPR; below0.1percent guard; published/frozen trees unchanged.','review_first':['PROOF.md','FEE-BOUNDS.json','RESULT.json','INDEPENDENT.json'],'next_concrete_gate':'Root independently checks exact tails, new H0/H1, original/currentSOURCE ABI, explicit large positive fees, live-unit stock and finite completed-backend type. Only after that may this be used as a private future bundle input.','do_not_repeat':['More decimal tightening','Oldretimingwindow/sourcebasis exclusions','Publishing subthreshold rawroot as ordinary saving'],'bounds_not_materialized':['Astronomical final uniform WORD','N=2^H1 or new q as a literal integer','Absolute source primitive TM constants; retained fixed implementation premises remain conditional']}) + files=sorted(HERE.glob('*.py'))+sorted(HERE.glob('*.md'))+[HERE/n for n in('INPUTS.json','RESULT.json','INDEPENDENT.json','FEE-BOUNDS.json','RESTART.json')]+sorted((HERE/'inputs').glob('*')) + put('MANIFEST.json',{'schema':'g20-ordinary-private-runtime/1','at_utc':datetime.now(timezone.utc).isoformat(),'files':[pin(p)for p in files]});print(json.dumps({'status':result['status'],'admitted':result['admitted'],'manifest_sha256':hashlib.sha256((HERE/'MANIFEST.json').read_bytes()).hexdigest()})) +if __name__=='__main__':main() diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/verify.py b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/verify.py new file mode 100644 index 0000000000..f67ba019b0 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary-certificate/verify.py @@ -0,0 +1,26 @@ +"""Isolated cold arithmetic/fee/source audit; never modifies frozen inputs.""" +from pathlib import Path +from datetime import datetime,timezone +import argparse,hashlib,json,sys,time +sys.path.insert(0,str(Path(__file__).resolve().parent)) +import certificate,independent +HERE=Path(__file__).resolve().parent +def need(c,m): + if not c:raise ValueError(m) +def read(p):return json.loads(p.read_bytes()) +def check_pin(root,row,key='path'): + p=(root/row[key]).resolve();need(p.is_relative_to(root.resolve())and p.is_file()and p.stat().st_size==row['bytes'],'Local file pin '+row[key]);need(hashlib.sha256(p.read_bytes()).hexdigest()==row['sha256'],'Source bytes '+row[key]) +def main(): + parser=argparse.ArgumentParser(description=__doc__);parser.add_argument('--provider',type=Path,required=True);parser.add_argument('--output',type=Path,required=True);args=parser.parse_args();provider=args.provider.resolve();out=args.output.resolve();need(not out.exists()and not out.is_relative_to(provider)and not out.is_relative_to(HERE/'inputs'),'Fresh output outside frozen runtime/input directories');out.mkdir(parents=True) + start=time.perf_counter();cpu=time.process_time();manifest=read(HERE/'MANIFEST.json') + for row in manifest['files']:check_pin(HERE,row) + inputs=read(HERE/'INPUTS.json') + for row in inputs['files']:check_pin(HERE,row) + pinned=(HERE/'inputs'/'provider-MANIFEST.json').read_bytes();need((provider/'MANIFEST.json').read_bytes()==pinned,'Sealed native provider exact manifest') + native=read(provider/'MANIFEST.json') + for row in native['files']:check_pin(provider.parent,row,'relative_path') + result=certificate.run();need(result==read(HERE/'RESULT.json'),'Deterministic primary certificate') + second=independent.audit(provider,result);need(second==read(HERE/'INDEPENDENT.json'),'Deterministic independent census/series/height certificate') + receipt={'status':'PASS_COLD_CONDITIONAL_G20_ORDINARY_CERTIFICATE','at_utc':datetime.now(timezone.utc).isoformat(),'isolated':sys.flags.isolated,'optimized':sys.flags.optimize,'python':sys.version,'source_inputs':len(inputs['files']),'native_runtime_pins':len(native['files']),'admitted':result['admitted'],'comparator':result['comparator'],'relative_gain':result['relative_gain'],'finite_levels':3,'H0':result['tail']['new_H0'],'H1':result['tail']['new_H1'],'provider_manifest_sha256':hashlib.sha256(pinned).hexdigest(),'certificate_manifest_sha256':hashlib.sha256((HERE/'MANIFEST.json').read_bytes()).hexdigest(),'allfees_status':result['fee_bounds']['status'],'retained_assumptions':result['retained_assumptions'],'whole_kappa':None,'new_PR':False,'CPU_seconds':time.process_time()-cpu,'elapsed_seconds':time.perf_counter()-start} + (out/'RESULT.json').write_text(json.dumps(receipt,indent=2)+'\n',encoding='utf-8');print(json.dumps(receipt)) +if __name__=='__main__':main() diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/ordinary_intake.py b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary_intake.py new file mode 100644 index 0000000000..00f34be2a2 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/ordinary_intake.py @@ -0,0 +1,39 @@ +"""Append-only source intake for the ordinary certificate, never old outputs.""" +from pathlib import Path +from datetime import datetime,timezone +import hashlib,json +HERE=Path(__file__).resolve().parent;RUN=HERE.parent;OUT=HERE/'ordinary-certificate';PUB=RUN/'bootstrap-publication'/'gitfree-0003'/'research' +def need(c,m): + if not c:raise ValueError(m) +def main(): + (OUT/'inputs').mkdir(parents=True,exist_ok=True) + choices={ + 'credited_intervals.py':PUB/'higher-moment-strictification'/'verify.py', + 'separate_series.py':PUB/'bit-compact-productive-controller'/'exact_series.py', + 'PR4814-PROOF.md':PUB/'bit-finite-ordinary-bootstrap'/'PROOF.md', + 'PR4814-RESULT.json':PUB/'bit-finite-ordinary-bootstrap'/'RESULT.json', + 'PR4814-verify.py.txt':PUB/'bit-finite-ordinary-bootstrap'/'verify.py', + 'PR4814-independent.py.txt':PUB/'bit-finite-ordinary-bootstrap'/'independent.py', + 'PR4760-PROOF.md':PUB/'bit-compact-productive-controller'/'PROOF.md', + 'PR4760-price.py.txt':PUB/'bit-compact-productive-controller'/'price.py', + 'tail-engine.py.txt':PUB/'query-thinned-controllers'/'verify.py', + 'provider-MANIFEST.json':HERE/'provider'/'MANIFEST.json', + 'provider-RESULT.json':HERE/'RESULT.json', + 'provider-INVOICE.json':HERE/'provider'/'data'/'INVOICE.json', + 'provider-FULL-FEES.json':HERE/'provider'/'data'/'FULL-FEES.json', + 'provider-GLOBAL-RESULT.json':HERE/'provider'/'data'/'GLOBAL-RESULT.json', + 'provider-cold-normal.json':HERE/'verification-normal-0002'/'RESULT.json', + 'provider-cold-O.json':HERE/'verification-optimized-0001'/'RESULT.json', + 'FINITE-PRECOMPILATION.md':HERE/'inputs'/'FINITE-PRECOMPILATION.md', + 'DELAYED-COVER-BRIDGE.md':HERE/'inputs'/'DELAYED-COVER-BRIDGE.md', + 'three-stage-cover-bit.tex':HERE/'inputs'/'three-stage-cover-bit.tex', + 'three-stage-cover-rows.tex':HERE/'inputs'/'three-stage-cover-rows.tex'} + rows=[] + for name,src in choices.items(): + raw=src.read_bytes();dst=OUT/'inputs'/name + if dst.exists():need(dst.read_bytes()==raw,'Intake overwrite forbidden '+name) + else:dst.write_bytes(raw) + rows.append({'path':'inputs/'+name,'sha256':hashlib.sha256(raw).hexdigest(),'bytes':len(raw),'read_only_origin':str(src)}) + manifest=OUT/'INPUTS.json';need(not manifest.exists(),'Intake manifest already frozen') + manifest.write_text(json.dumps({'schema':'g20-ordinary-inputs/1','at_utc':datetime.now(timezone.utc).isoformat(),'files':rows},indent=2)+'\n',encoding='utf-8');print(json.dumps({'inputs':len(rows),'bytes':sum(r['bytes']for r in rows)})) +if __name__=='__main__':main() diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/provider/MANIFEST.json b/research/bit-g20-nine-owned-relations/vendor/g20/provider/MANIFEST.json new file mode 100644 index 0000000000..066c3bceeb --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/provider/MANIFEST.json @@ -0,0 +1,247 @@ +{ + "schema": "g20-private-native-runtime/1", + "created_at_utc": "2026-10-23T01:31:57.119450+00:00", + "claim": "Native literal programme and positive finite fee schema only; ordinary saving remains unproved in this packet.", + "files": [ + { + "relative_path": "INPUT-PINS.json", + "bytes": 8913, + "sha256": "5377cdc7d7cef0718ab25cfc383453db4e8260cd4e95e190ee596f31dfaf7c9c" + }, + { + "relative_path": "inputs/02-streams.tex", + "bytes": 11311, + "sha256": "606c80db61cad13aa0c3b6060dc4b88dbbe7ac60cdd831aa93f28d908fd09dab" + }, + { + "relative_path": "inputs/4814-audit_stream.py.txt", + "bytes": 8422, + "sha256": "a0a4ca5c58bf299b1c75ba93caa3cb902b179ca78dfe99e4defb42dd58dfa5dc" + }, + { + "relative_path": "inputs/4814-global_word.py.txt", + "bytes": 20395, + "sha256": "601ecd78439e65b46f357e9b2275f6f86c234506687939da1df9259e8422872e" + }, + { + "relative_path": "inputs/4814-independent_native.py.txt", + "bytes": 6726, + "sha256": "2bd775c92ae5c79f82606909078c73ccf08eebc369faae2d111f74cb4e73ee87" + }, + { + "relative_path": "inputs/4814-local_word.py.txt", + "bytes": 12478, + "sha256": "bfca7ff22066863086ebdb1cd67d26682fb167b8b11ff9be585f43ad36de06f3" + }, + { + "relative_path": "inputs/ACTIVE-AXES.json", + "bytes": 3519, + "sha256": "2ee6d3c3a4f70e8e60bc9baa9995c2619a4c0f3138e1fd060a44a315085464eb" + }, + { + "relative_path": "inputs/BASELINE-GLOBAL-RESULT.json", + "bytes": 4033, + "sha256": "8b9831ac004a16329373fbcb59e2e200de61d6824ec5b8f3f7c6fc0c9436a0af" + }, + { + "relative_path": "inputs/BASELINE-LOCAL.json.gz", + "bytes": 62568, + "sha256": "4535dde53162b426e597aea9d0106fb1405358f775d9370bd36bfb5686ed21df" + }, + { + "relative_path": "inputs/BASELINE-RATIONAL-BINDING.json", + "bytes": 41640, + "sha256": "f26610de8b3866a3c77e56fd29c83a3a466065446f77259dcba58e1f9038f6d8" + }, + { + "relative_path": "inputs/CONTROLLER.json", + "bytes": 23753, + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d" + }, + { + "relative_path": "inputs/DELAYED-COVER-BRIDGE.md", + "bytes": 16874, + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443" + }, + { + "relative_path": "inputs/FINITE-PRECOMPILATION.md", + "bytes": 15898, + "sha256": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8" + }, + { + "relative_path": "inputs/FORWARD.json.gz", + "bytes": 60673, + "sha256": "34166a521475f1868293fbd8dbbbac0a9a90d489d7cea9c8ff8d1e7801781f74" + }, + { + "relative_path": "inputs/FRAMES.json", + "bytes": 749486, + "sha256": "0d99fc6b8f45c03dfba5252a03dd9e7fe23be3a7593dfe15368e34da6629a654" + }, + { + "relative_path": "inputs/G20-WINDOW.json", + "bytes": 625, + "sha256": "13661df94b7bb595bdf9eaabdbe823cb837ddd810f9e321b79976a70022db0a4" + }, + { + "relative_path": "inputs/G22-FRESH-REQUESTS.json", + "bytes": 7997, + "sha256": "d4cdf3d78219b983fc39e1c5acfb50c8aa41682a47d96b3e62326e6a7a8ce836" + }, + { + "relative_path": "inputs/G23-EXPECTED.json", + "bytes": 2032, + "sha256": "38e1676a342fe7f0122071f45f4cc3fa47f991c854b859aaadb05f74d4d0b2b4" + }, + { + "relative_path": "inputs/G23-RAW-PRICE.json", + "bytes": 2380, + "sha256": "2ad7f7beeba05e6a5454a81466ed2720716cf0ae926b4b67e745e931ae3c8c87" + }, + { + "relative_path": "inputs/INVERSE.json.gz", + "bytes": 59078, + "sha256": "29fb50d17a58e18988df2bdb1f7c65f7a12328ac75c676d34dd31a036aeaf483" + }, + { + "relative_path": "inputs/REFERENCE111.json.gz", + "bytes": 42353, + "sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f" + }, + { + "relative_path": "inputs/three-stage-cover-bit.tex", + "bytes": 13061, + "sha256": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511" + }, + { + "relative_path": "inputs/three-stage-cover-rows.tex", + "bytes": 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"sha256": "79b9ec64ac8c07b1103900f2bbf565402fedd55f6aee280075c7afb297304202" + } + ] +} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/provider/audit_global.py b/research/bit-g20-nine-owned-relations/vendor/g20/provider/audit_global.py new file mode 100644 index 0000000000..3df454b551 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/provider/audit_global.py @@ -0,0 +1,120 @@ +"""Independent emitted-stream reader; never imports build_global.py.""" +from pathlib import Path +from collections import Counter +from hashlib import sha256 +import gzip,json +from local_ir import need,Geometry +N=11400;V=111 +def read(p):return json.loads(gzip.decompress(p.read_bytes()))if p.suffix=='.gz'else json.loads(p.read_bytes()) +def audit(root,mutant=None): + root=Path(root);inp=root.parent/'inputs';data=root/'data';base=read(inp/'BASELINE-LOCAL.json.gz');frames=read(inp/'FRAMES.json')['frames'];geom=Geometry(frames);calls=read(data/'CALLS.json');claimed=read(data/'GLOBAL-RESULT.json');controller=read(inp/'CONTROLLER.json') + if mutant=='duplicate_helper_owner':calls[1]['helper_owner_begin']=calls[0]['helper_owner_begin'] + owners=[i for c in calls for i in range(c['helper_owner_begin'],c['helper_owner_begin']+436)];need(len(calls)==18 and len(owners)==len(set(owners))==7848 and set(owners)==set(range(3552,N)),'All7848fresharbitraryhelperowners, nodoublecredit') + values=[1<=N:need(role>1).bit_count()]+=V + need(paid==expectedP and T==Counter({int(k):v for k,v in claimed['targets'].items()})and sum(T.values())==N,'Literalpaidandactualrank4/8targetcredit') + need(raw_hash.hexdigest()==claimed['expanded_event_sha256']and src_hash.hexdigest()==claimed['SOURCE_descriptors_sha256'],'ExactstreamandfreshSOURCEdescriptor digests') + need(counts==Counter(claimed['operation_counts'])and len(episodes)==1845 and privatepeak==2 and new4==18,'Actualnewstock/episodes/requests') + need(peak.bit_length()==claimed['majorant_bits']and str(peak)==claimed['majorant'],'Regeneratedcancellationfreemajorant') + # Independent representation: each row is a set(initialbank,phase), not + # the builder's phase->bitmask dictionary. + poly=[{(i,0)}for i in range(32)] + def boundary(program): + for op,d,s in program: + if op=='ADD':poly[d]^=poly[s] + else:need(op=='SWAP','Physicalboundary');poly[d],poly[s]=poly[s],poly[d] + boundary(controller['boundaries']['right_program']) + for e in controller['physical_events']: + if e[0]in('LOCAL','QUERY_SHEAR'): + typ,stage,pair,rev=e;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + poly[y]^={(i,m^1)for i,m in poly[x]} + if typ=='LOCAL': + for bank in(x,y):poly[bank]={(i,m^(1<<(stage+1)))for i,m in poly[bank]} + elif e[0]=='IDLE': + _,pair,stages=e;m=sum(1<<(s+1)for s in stages) + for bank in(2*pair,2*pair+1):poly[bank]={(i,t^m)for i,t in poly[bank]} + elif e[0]=='ADD':poly[e[1]]^=poly[e[2]] + else:need(e[0]=='SWAP','Physicalcontroller');poly[e[1]],poly[e[2]]=poly[e[2]],poly[e[1]] + boundary(controller['boundaries']['left_program']);need(poly==[{(i,int(m))}for i,m in enumerate(controller['diagonal'])],'IndependentALLphysicalmaincoefficients, no character-onlycheck') + return {'status':'PASS_INDEPENDENT_LITERAL_G23_STREAM_AND_FRESH_SOURCE_HISTORY','original_RAW':N,'calls':len(seen),'query_count':sum(paid.values()),'fresh_SOURCE_descriptors':source_no,'private_episodes':len(episodes),'private_peak':privatepeak,'new_rank4_requests':new4,'majorant_bits':peak.bit_length(),'event_sha256':raw_hash.hexdigest(),'paid':dict(sorted(paid.items())),'targets':dict(sorted(T.items()))} diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/provider/bindings_fees.py b/research/bit-g20-nine-owned-relations/vendor/g20/provider/bindings_fees.py new file mode 100644 index 0000000000..1902868b97 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/provider/bindings_fees.py @@ -0,0 +1,80 @@ +"""Explicit rational job recipes and positive finite fees; no exponent claim.""" +from pathlib import Path +from fractions import Fraction as F +from hashlib import sha256 +from collections import Counter +import gzip,json +from local_ir import need +def read(p):return json.loads(gzip.decompress(p.read_bytes()))if p.suffix=='.gz'else json.loads(p.read_bytes()) +def mm(a,b):return[[sum(x*y for x,y in zip(r,c))for c in zip(*b)]for r in a] +def eye(n):return[[F(i==j)for j in range(n)]for i in range(n)] +def inv(a): + n=len(a);w=[r[:]+[F(i==j)for j in range(n)]for i,r in enumerate(a)] + for j in range(n): + k=next(i for i in range(j,n)if w[i][j]);w[j],w[k]=w[k],w[j];z=w[j][j];w[j]=[v/z for v in w[j]] + for i in range(n): + if i!=j: + z=w[i][j];w[i]=[v-z*y for v,y in zip(w[i],w[j])] + return[r[n:]for r in w] +def project(f): + b=[[F(x)for x in r]for r in f['B']] + if not b:return[[F(0)]*8 for _ in range(8)] + bt=list(map(list,zip(*b)));return mm(mm(bt,inv(mm(b,bt))),b) +def text(a):return[[str(x)for x in r]for r in a] +def digest(a):return sha256(json.dumps(a,sort_keys=True,separators=(',',':')).encode()).hexdigest() +def construct(root,write=False): + root=Path(root);inp=root.parent/'inputs';data=root/'data';frames=read(inp/'FRAMES.json')['frames'];base=read(inp/'BASELINE-LOCAL.json.gz');ref=read(inp/'REFERENCE111.json.gz');controller=read(inp/'CONTROLLER.json');axes=read(inp/'ACTIVE-AXES.json');saved=read(inp/'BASELINE-RATIONAL-BINDING.json');glob=read(data/'GLOBAL-RESULT.json');I=eye(8);ports=[];Acols=[] + need(len(ref['lines'])==111,'Actual orderedSOURCE111') + for i,line in enumerate(ref['lines']): + v=list(map(F,line));need(sum(x*x for x in v)==4,'ActualSOURCErootnorm4');P=[[x*y/4 for y in v]for x in v];K=[[I[a][b]-P[a][b]for b in range(8)]for a in range(8)] + need(project(frames[str(base['start'][i])])==P and project(frames[str(base['final'][i])])==I and project(frames[str(base['start'][111+i])])==[[F(0)]*8 for _ in range(8)]and project(frames[str(base['final'][111+i])])==K,'Unchanged actualSOURCE/YrationalABI') + u=[F(j==0)-v[j]/2 for j in range(8)];norm=sum(x*x for x in u);S=I if norm==0 else[[F(a==b)-2*u[a]*u[b]/norm for b in range(8)]for a in range(8)];A=[row[1:]for row in S];AT=list(map(list,zip(*A))) + need(mm(list(map(list,zip(*S))),S)==I and [2*row[0]for row in S]==v and mm(A,AT)==K and mm(AT,A)==eye(7),'ExactSOURCEline/complementcoordinates') + rho=[P[j]+A[j]for j in range(8)]+[row+[F(0)]*7 for row in AT];local8=[[F(a==b and a<8)for b in range(15)]for a in range(15)];want=[[P[a][b]if a<8 and b<8 else F(a==b and a>=8)for b in range(15)]for a in range(15)] + need(mm(rho,rho)==eye(15)and mm(mm(rho,local8),rho)==want,'Actual15DwholefiberENTRY/RETURNchart') + need(digest(text(rho))==saved['ports'][i]['chart_sha256'],'Unchangedfrozenroutebytes') + ports.append({'port':i,'root':list(map(str,v)),'unit_line':list(map(str,[x/2 for x in v])),'orthogonal_complement_columns':text(A),'rho15':text(rho),'rho15_sha256':digest(text(rho))});Acols.append(A) + partial={} + for f in sorted(set(base['final'][222:])): + p=project(frames[str(f)]);rank=frames[str(f)]['dim'];need(mm(p,p)==p and sum(p[i][i]for i in range(8))==rank,'Actualhelperendjobidempotent') + if rank==8:need(p==I,'Actualfullhelper');continue + need(rank==4,'Onlyactual4partialjobs');b=[[F(x)for x in r]for r in frames[str(f)]['B']];a=[[F(x)for x in r]for r in frames[str(f)]['A']];s=list(map(list,zip(*(b+a))));si=inv(s);q4=[[F(i==j and i<4)for j in range(8)]for i in range(8)];need(mm(mm(s,q4),si)==p,'Actualcanonicalrank4wholejobmatcher') + partial[str(f)]={'rank':4,'native_P':text(p),'S_Q4_to_native':text(s),'S_inverse':text(si),'physical_input_ROW_route':'g->g*S_inverse','completed_return_route':'h->h*S'} + need(len(partial)==3,'Threeactualdistinctpartial4projectors') + templates=[];target_roles=[] + for bank,term in enumerate(controller['diagonal']): + selected=[j for j,a in enumerate(axes)if term>>(a['stage']+1)&1];need(term&1 and(sum(1<<(axes[j]['stage']+1)for j in selected)|1)==term,'Alltargetfactorsareactualretainedorthogonalaxes') + centralfull=0 in selected;image=[a for j in selected if j for a in axes[j]['axes']];kernel=[a for j in range(1,18)if j not in selected for a in axes[j]['axes']];rank=(8 if centralfull else 1)+len(image) + need(rank==1+7*len(selected)and len(image)+len(kernel)==119,'ExactMAINsourcejobrankanddisjointspectatoraxes') + # The centralblock is either I8 or(unit_line,complementA); it is already + # exactlyorthogonal above. Othercolumns are distinctcoordinatevectors. + template={'id':f'MAIN_BANK_{bank}','bank':bank,'rank':rank,'native_target_phase_mask':int(term),'central_image':'I8'if centralfull else'unit_line[port]','central_kernel':'none'if centralfull else'complementA[port]','image_fresh_axes':image,'kernel_fresh_axes':kernel,'column_order':'imagecentral;imagefresh;kernelcentral;kernelfresh;futureambientidentityspectators','S':'Columnmatrixfromtheliteralrecipe; S*Q_rank*S^-1=P_native','inverse':'TransposeoftheorthogonalS; allfutureaxes>=127fixed','physical_input_ROW_route':'g->g*S_inverse','completed_return_route':'h->h*S'} + templates.append(template) + for port in range(111):target_roles.append({'original_owner':bank*111+port,'rank':rank,'matcher':template['id'],'port':port,'operator':'D_(P_line+selectedorthogonalstageblocks)','route_pair_required_in_generic_job_matching':True}) + for call in read(data/'CALLS.json'): + begin=call['helper_owner_begin'] + for r in range(436): + frame=base['final'][222+r];rank=frames[str(frame)]['dim'];target_roles.append({'original_owner':begin+r,'rank':rank,'matcher':'IDENTITY_FULL8'if rank==8 else'PARTIAL_FRAME_'+str(frame),'native_frame':frame,'route_pair_required_in_generic_job_matching':rank!=8}) + need(len(target_roles)==11400 and len(set(x['original_owner']for x in target_roles))==11400,'Exactlyoneindependenttargetperoriginal,noownedcredit') + need(Counter(x['rank']for x in target_roles)==Counter({int(k):v for k,v in glob['targets'].items()}),'Jobrecipesexacttargetinvoice') + route_fields=[x for x in target_roles if x['route_pair_required_in_generic_job_matching']];routes=[] + for x in sorted(route_fields,key=lambda x:x['original_owner']):routes.append({'position':'BEFORE_COMPLETE_GLOBAL_BODY','owner':x['original_owner'],'matcher':x['matcher'],'port':x.get('port'),'direction':'S_inverse','whole_fiber':'g->g*S_inverse','no_live_owned':True}) + for x in reversed(sorted(route_fields,key=lambda x:x['original_owner'])):routes.append({'position':'AFTER_COMPLETE_GLOBAL_BODY','owner':x['original_owner'],'matcher':x['matcher'],'port':x.get('port'),'direction':'S','whole_fiber':'h->h*S','no_live_owned':True}) + # Evenidentitymainrecipescanbechargedbythisuniformbound; no numerical + # optimizationusesanunchargedmatcher. Allroutesarebijectionson(role,g). + n=11400;M=sum(glob['paid'].values());ops=glob['operation_counts'];raw=glob['expanded_event_count'];primitive_adds=ops['ADD']+ops['LOCAL_ADD']+ops['THIN_ADD'];copies=ops['LOCAL_COPY_QUERY']+ops['THIN_COPY'];clears=ops['LOCAL_PAID_CLEAR']+ops['SHADOW_PAID_CLEAR']+ops['THIN_PAID_CLEAR'];parking=4*(n+2)*M + fees={'status':'POSITIVE_FINITE_PROGRAM_FEE_SCHEMA_NO_ORDINARY_SAVING_YET','raw_bit_IR_records':raw,'raw_record_cap_only':10**9,'raw_cap_guard':raw+2*M+2*n+144<10**9,'literal_VALUE_XOR_passes':primitive_adds,'compound_pointwiseCOPY_assignments':copies,'new_shadow_ZERO_INIT_passes':ops['SHADOW_PAID_INIT'],'all_paid_owned_CLEAR_passes':clears,'initial_owned_bank_ZERO_scans':2,'final_owned_bank_teardown_scans':2,'new_shadow_copy_ADDs_already_in_VALUE_count':18, + 'in_BODY_paid_MAINport_wholefiber_routes':ops['PAID_PORT_ROUTE'],'canonical_job_matching_route_pairs':len(route_fields),'canonical_job_matching_routes':len(routes),'of_these_partial4_helper_routes':144, + 'parent_parking':{'paid_child_calls':M,'allocated_parent_originals_plus_owned':n+2,'safe_inactive_and_IO_FIELD_pass_bound_perQUERY':4*(n+2),'total_FIELD_pass_bound':parking,'meaning':'BeforeeachQUERYparkinactiveparentoriginalsandBOTHownedbanks,copyactiveARRAYtochildIO; onreturnrestoreinactiveorderandparentheads/stacktop. Parentancestorregionsareneverswept. Thisisaconservativepositivefixedconstant,notasaving.'}, + 'normalizer_and_ROW_route_costs':{'source_catalogue':'AllfixedrationalP/S/rho/targetrecipesincluded; chooseqavoidingallfiniteunits/denominators/rankwitnesses AFTERfiniteprogramcompile. No inheritednumericq/H threshold.','QUERY':'EachactualcurrentARRAYjobnormalizesonlyinthecompleteduniformprogram. Goodclassesuseorderedproperchild; badclassesusechargedlocal-ringfallback. Newrank4isfreshgeometricjobwithG22matcher,notoldticket.','wholefiber_route':'Useinheritedfixedrationalright-multiplicationstreamingprimitive,chargedO_(N,S,q)(V*w^(1-a_backend)), includinglowtypes/highcarry/counters/headreturn. NotfreeADDRESSgather.','symbolic_fixed_fee':'C_new(N,q)=C_stream*(rawVALUE+COPY+INIT+CLEAR+parkcounts)+SUM_FIXED_ROUTES C_route(N,q,S)+SUM_QUERY C_normalizer(N,q,P). Constantsarefinite/positiveandfixedBEFOREinputwidth. Thisreceipt doesNOTsupplyanumericalall-in1e9bound fornormalizers.'}, + 'majorants':{'LOCAL_direction_bits':{k:v['majorant_bits']for k,v in read(data/'LOCAL-INVOICE.json')['directions'].items()},'GLOBAL_bits':glob['majorant_bits'],'GLOBAL_majorant':glob['majorant'],'scope':'Positivecancellationfreeenvelope regeneratedfromnewprogram. Old21/30bitthresholdsareNOTreused.'}, + 'stock':{'original_productive_fields':11400,'owned_OUTPUT_credit':0,'per_primitive_GLOBAL_unit_owned_banks':2,'per_finite_DAG_allocation':'ReserveTWOwholeownedbanksforeachcompiledunitinstance(orconcurrentliveunit),withunit-scopedtagsandzeroINIT/CLEAR. NeverreuseoneC0perdepthwhenunits suspended.','child_source_on_owned':'AQUERYonacurrentownedSUMusesitastheactualchildtargetslot; correlatedvaluesarevalidarbitrary-inputinstances. ItdoesNOTaddanindependentparentinput. Descendantownbanksgetdistincttags.','row_split':'Originalunitrolewidthremains11400; twoownedbanksareworkstreams,notnewproductiveROWclasses. Freshdescendantrolesexcludeexposedparentfields.','asymptotic':'WithnewfixedfiniteN,B,q,source/park/tapeconstantsregenerated,theinheritedstocklog_q S=O_new(w loge)andborrow/restoreproofremainconditionalinputs. OldnumericH/prime/precisionthresholdsnotasserted.'}, + 'pending_before_ordinary_bound':['Freshthree-tensor-tail/finitecompiler/primefallbackcertificateonnewP/T','Actualnewfixedconstants/H/reserve/cutoffchosenandchecked','Finiteleafbootstrapwithfrozenalready-establishedordinarybackend','Parentindependentvalidationandnorecordclaimuntilthen']} + need(fees['raw_cap_guard']and primitive_adds==378039 and copies==1827 and clears==1845 and len(routes)==7248,'Regeneratedfinitefeeandroutecounts') + result={'ports':ports,'partial_matchers':partial,'main_matcher_templates':templates,'targets':target_roles,'canonical_route_program':routes,'fees':fees} + if write: + for name,key in [('PORT-CHARTS.json','ports'),('PARTIAL-JOB-MATCHERS.json','partial_matchers'),('MAIN-JOB-MATCHERS.json','main_matcher_templates'),('TARGET-OWNERS.json','targets'),('JOB-MATCHING-ROUTES.json','canonical_route_program'),('FULL-FEES.json','fees')]: + (data/name).write_text(json.dumps(result[key],indent=2)+'\n',encoding='utf-8') + return result +if __name__=='__main__': + result=construct(Path(__file__).resolve().parent,True);print(json.dumps({'status':'PASS_EXACT_SOURCE_CHARTS_AND_POSITIVE_FIXED_FEE_SCHEMA','target_owners':len(result['targets']),'explicit_canonical_routes':len(result['canonical_route_program']),'partial_routes':144,'new_bound':None})) diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/provider/build_global.py b/research/bit-g20-nine-owned-relations/vendor/g20/provider/build_global.py new file mode 100644 index 0000000000..adb6e21ec7 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/provider/build_global.py @@ -0,0 +1,125 @@ +"""Materialize the exact G23 stream and separate current-source descriptors.""" +from pathlib import Path +from collections import Counter +from hashlib import sha256 +from datetime import datetime,timezone +from time import process_time +import gzip,json +from local_ir import N as LN,EXPECTED,need +HERE=Path(__file__).resolve().parent;ROOT=HERE.parent;INPUT=ROOT/'inputs';DATA=HERE/'data';N=11400;V=111 +def read(p):return json.loads(gzip.decompress(p.read_bytes()))if p.suffix=='.gz'else json.loads(p.read_bytes()) +def put(p,x):p.write_text(json.dumps(x,indent=2)+'\n',encoding='utf-8') +def xor(a,b): + out=a.copy() + for k,v in b.items(): + out[k]=out.get(k,0)^v + if not out[k]:del out[k] + return out +def shift(a,s):return{k^s:v for k,v in a.items()} +def physical_main(controller): + rows=[{0:1<=658 else((x if r>1).bit_count()]+=V + need(streamhash.hexdigest()==expected['expanded_event_sha256']and eventno==expected['expanded_event_count'],'ExactG23literalstreamnotanewunboundvariant') + need(paid==Counter({int(k):v for k,v in expected['paid'].items()})and targets==Counter({int(k):v for k,v in expected['targets'].items()})and len(changed_requests)==18,'ExactG23invoiceandfreshrank4requests') + need(peak.bit_length()==expected['cancellation_free_majorant_bits']and str(peak)==expected['cancellation_free_majorant'],'Actual newmajorantfullyregenerated') + need(len(calls)==18 and len(episodes)==1845 and privatepeak==2,'Allownedepisodesandmaximumcoexistence') + result={'status':'MATERIALIZED_EXACT_G23_ALL11400_RAW','at_utc':datetime.now(timezone.utc).isoformat(),'originals':N,'private_allocated':2,'private_peak':privatepeak,'private_episodes':len(episodes),'calls':18,'expanded_event_count':eventno,'expanded_event_sha256':streamhash.hexdigest(),'global_gzip_sha256':sha256((DATA/'GLOBAL.jsonl.gz').read_bytes()).hexdigest(),'SOURCE_descriptor_count':source_count,'SOURCE_descriptors_sha256':sourcehash.hexdigest(),'paid':dict(sorted(paid.items())),'targets':dict(sorted(targets.items())),'rank_surplus':sum(k*v for k,v in targets.items())-sum(k*v for k,v in paid.items()),'operation_counts':dict(counts),'majorant_bits':peak.bit_length(),'majorant':str(peak),'newbound':None,'CPU_seconds':process_time()-clock} + put(DATA/'GLOBAL-RESULT.json',result);put(DATA/'CALLS.json',calls);put(DATA/'PRIVATE-EPISODES.json',episodes);put(DATA/'NEW-RANK4-REQUESTS.json',changed_requests);put(DATA/'MAIN-PHYSICAL-COEFFICIENTS.json',mainrows);put(DATA/'INVOICE.json',{'paid':result['paid'],'targets':result['targets'],'originals':N,'private_output_credit':0,'QUERYs':sum(paid.values()),'rawrank_surplus':result['rank_surplus'],'rawprice_reference':'inputs/G23-RAW-PRICE.json only, notordinarysaving','ordinary_tail_bootstrap_status':'Pendingseparatecertificatewithfreshfees/constants; old4760/4814unchanged'}) + print(json.dumps({k:result[k]for k in('status','expanded_event_count','expanded_event_sha256','SOURCE_descriptor_count','private_episodes','majorant_bits','CPU_seconds')})) +if __name__=='__main__':main() diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/provider/build_local.py b/research/bit-g20-nine-owned-relations/vendor/g20/provider/build_local.py new file mode 100644 index 0000000000..e151235bba --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/provider/build_local.py @@ -0,0 +1,60 @@ +"""Freeze local forward, independently correct inverse and physical rawdual.""" +from pathlib import Path +from fractions import Fraction as F +from datetime import datetime,timezone +from time import process_time +import gzip,hashlib,json +from local_ir import N,EXPECTED,need,Geometry,replay,baseline_program,ad_inverse,transpose_rows,rowproduct +HERE=Path(__file__).resolve().parent;ROOT=HERE.parent;INPUT=ROOT/'inputs';DATA=HERE/'data' +def read(p):return json.loads(gzip.decompress(p.read_bytes()))if p.suffix=='.gz'else json.loads(p.read_bytes()) +def put(p,x): + b=(json.dumps(x,indent=2)+'\n').encode();p.parent.mkdir(exist_ok=True,parents=True);p.write_bytes(gzip.compress(b,mtime=0)if p.suffix=='.gz'else b) +def verify_inputs(): + pins=read(ROOT/'INPUT-PINS.json') + for p in pins['files']: + source=ROOT/p['relative_path'];need(source.is_file()and hashlib.sha256(source.read_bytes()).hexdigest()==p['sha256'],'Readonlyinputpin '+p['relative_path']) +def mm(a,b):return [[sum(x*y for x,y in zip(r,c))for c in zip(*b)]for r in a] +def project(frame): + b=[[F(x)for x in r]for r in frame['B']] + if not b:return [[F(0)]*8 for _ in range(8)] + def inv(a): + n=len(a);w=[r[:]+[F(i==j)for j in range(n)]for i,r in enumerate(a)] + for j in range(n): + k=next(i for i in range(j,n)if w[i][j]);w[j],w[k]=w[k],w[j];x=w[j][j];w[j]=[v/x for v in w[j]] + for i in range(n): + if i!=j: + x=w[i][j];w[i]=[v-x*z for v,z in zip(w[i],w[j])] + return [r[n:]for r in w] + bt=list(map(list,zip(*b)));return mm(mm(bt,inv(mm(b,bt))),b) +def main(): + clock=process_time();verify_inputs();DATA.mkdir(exist_ok=True);base=read(INPUT/'BASELINE-LOCAL.json.gz');forward=read(INPUT/'FORWARD.json.gz');inverse=read(INPUT/'INVERSE.json.gz');frames=read(INPUT/'FRAMES.json')['frames'];geom=Geometry(frames) + need(forward['start']==base['start']and forward['final']==base['final']and inverse['start']==base['final']and inverse['final']==base['start'],'Exact old entry/exit flags') + dual,retags=ad_inverse(inverse['records'],base['start'],base['final']);rawdual={'namespace':N,'allocated_slots':660,'owned_indices':[658,659],'start':base['start'],'final':base['final'],'records':dual,'definition':'Physical FUNCTION transpose of independently correct trueinverse, withpaidzero-mapCLEAR andzero-onlyreheaders. NotADDRESSinverse-transpose.'} + result={};rows={} + for name,payload in [('FORWARD',forward),('INVERSE',inverse),('RAW-DUAL',rawdual)]: + out,stats,_=replay(payload['records'],payload['start'],payload['final'],geom);need(stats['paid']==EXPECTED,'New complete localinvoice '+name);need(stats['private_peak']<=2,'Two explicit private banks') + for modulus in(101,101**2): + nr,ns,_=replay(payload['records'],payload['start'],payload['final'],geom,modulus);need(nr==out,'All658nativecolumns '+name) + rows[name]=out;result[name]=stats + if name!='RAW-DUAL': + src=INPUT/(name+'.json.gz');(DATA/(name+'.json.gz')).write_bytes(src.read_bytes()) + else:put(DATA/'RAW-DUAL.json.gz',payload) + oldrows,oldstats,_=replay(baseline_program(base),base['start'],base['final'],geom);oldinv,_,_=replay(baseline_program(base,True),base['final'],base['start'],geom) + need(rows['FORWARD']==oldrows and rows['INVERSE']==oldinv,'Both original operators unchanged, all658RAW') + identity=[1<g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 1, + "matcher": "MAIN_BANK_0", + "port": 1, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 2, + "matcher": "MAIN_BANK_0", + "port": 2, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 3, + "matcher": "MAIN_BANK_0", + "port": 3, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 4, + "matcher": "MAIN_BANK_0", + "port": 4, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 5, + "matcher": "MAIN_BANK_0", + "port": 5, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 6, + "matcher": "MAIN_BANK_0", + "port": 6, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 7, + "matcher": "MAIN_BANK_0", + "port": 7, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 8, + "matcher": "MAIN_BANK_0", + "port": 8, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 9, + "matcher": "MAIN_BANK_0", + "port": 9, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 10, + "matcher": "MAIN_BANK_0", + "port": 10, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 11, + "matcher": "MAIN_BANK_0", + "port": 11, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 12, + "matcher": "MAIN_BANK_0", + "port": 12, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 13, + "matcher": "MAIN_BANK_0", + "port": 13, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 14, + "matcher": "MAIN_BANK_0", + "port": 14, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 15, + "matcher": "MAIN_BANK_0", + "port": 15, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 16, + "matcher": "MAIN_BANK_0", + "port": 16, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 17, + "matcher": "MAIN_BANK_0", + "port": 17, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 18, + "matcher": "MAIN_BANK_0", + "port": 18, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 19, + "matcher": "MAIN_BANK_0", + "port": 19, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + "position": "BEFORE_COMPLETE_GLOBAL_BODY", + "owner": 20, + "matcher": "MAIN_BANK_0", + "port": 20, + "direction": "S_inverse", + "whole_fiber": "g->g*S_inverse", + "no_live_owned": true + }, + { + 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"original_owner": 11322, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11323, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11324, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11325, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11326, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11327, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11328, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11329, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11330, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11331, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11332, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11333, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11334, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11335, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11336, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11337, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11338, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11339, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11340, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11341, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11342, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11343, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11344, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11345, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11346, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11347, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11348, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11349, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11350, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11351, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11352, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11353, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11354, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11355, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11356, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11357, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11358, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11359, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11360, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11361, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11362, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11363, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11364, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11365, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11366, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11367, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11368, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11369, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11370, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11371, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11372, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11373, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11374, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11375, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11376, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11377, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11378, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11379, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11380, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11381, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11382, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11383, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11384, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11385, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11386, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11387, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11388, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11389, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11390, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11391, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11392, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11393, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11394, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11395, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11396, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11397, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11398, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11399, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + } +] diff --git a/research/bit-g20-nine-owned-relations/vendor/g20/provider/local_ir.py b/research/bit-g20-nine-owned-relations/vendor/g20/provider/local_ir.py new file mode 100644 index 0000000000..2edfa7018d --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/g20/provider/local_ir.py @@ -0,0 +1,130 @@ +"""Local physical ARRAY IR and exact types; portable standard library only.""" +from collections import Counter +from fractions import Fraction as F +from functools import lru_cache +from math import gcd + +N=658;OWNED=(658,659);EXPECTED={1:1318,2:1342,3:77,4:40,5:102,6:10,7:18} +def need(c,m): + if not c:raise ValueError(m) +def transpose_rows(a,n=N):return [sum(((r>>j)&1)< (X,Y+X)` over GF(2). Each helper has the +identity logical endpoint. The source forward and reverse words have +this same logical map. + +Replay the source records in reverse order over the vector space with +661 independent input symbols. Each of its nine COPY entries is a +linear form in these symbols. Reduce these nine forms by helper columns. +The resulting pivot helpers are + +```text +222, 223, 224, 225, 226, 228, 230, 231, 233. +``` + +Each reduced form contains its own pivot and no other pivot. Every field +in its support has the full entrance frame. The relation rows are saved +in RESULT.json and are derived again from the source during every run. + +Own these nine helpers. Clear each at entry and XOR its other relation +terms into it. The nine forms are then zero. These operations use a +common frame and leave all 652 retained input fields unchanged. A +chronological replay of the original reverse word now proves that every +COPY value is zero. The copy centre stays zero. Nine rank-one moves are +also on zero values. Replace only these moves by zero frame changes. +Clear the nine owned helpers at exit, and return the centre to its empty +frame. This gives a map on arbitrary retained inputs with all owned exit +fields zero. The entry clears make the result independent of arbitrary +initial values in owned storage. + +The exact new local paid profile is + +```text +{1:1314, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:10}. +``` + +The productive helper profile is `{8:430}`. There are no new nonzero +native maps. The original rank-one and rank-seven jobs are removed in +nine pairs. Each pair loses one rank-eight target. The fixed field count +remains 662; no new physical field is required. + +## 2. Why one reverse word serves both directions + +The logical involution alone is insufficient. Check the physical address +maps as well. For a source port let P be its rank-one rational projector, +K=I-P, Q=D_P, S=D_K, and R=D_I. Here D denotes the source two-bank +interchange, with its fixed second-bank reversal included. These address +permutations commute, square to I, and satisfy QS=R. + +In this paragraph Q, S and R denote their induced data-permutation +operators. Let M be the two-field XOR shear, with block rows `(I,0)` +and `(I,I)`. The source forward physical operator is + +```text +diag(R,S) M diag(Q,I) = [[S,0],[R,S]]. +``` + +Its reverse physical operator is + +```text +diag(Q,I) M diag(R,S) = [[S,0],[R,S]]. +``` + +Both products therefore give the same physical endpoint. This endpoint +is an involution over GF(2), since RS+SR=0. Each retained helper has +endpoint D_I, also an involution. Thus the new reverse implementation +replaces either direction of the original local call with the same +caller port and role assignments. No new query, route or native map is +needed for this replacement. + +The verifier checks the source entrance line and exit complement for +every port. It checks the rational address identities `D_I D_P=D_K` +and `D_P^2=D_K^2=I`. These are identities of address matrices. The block +XOR calculation above is an identity of induced data operators; it does +not identify addition of address matrices with addition of data operators. + +## 3. Native interfaces and all column multiplicities + +All nonzero native transitions are retained source transitions. The +verifier rebuilds every source projector over the rationals and checks +both nesting products and the rank difference for each transition pair. +For each of the 111 ports it builds an exact complement basis and a +15-dimensional route. It checks that the route is an involution, fixes +the central line, and sends the local full projector to the required +line-plus-fresh-stage projector. + +For column multiplicity f, tensor each head-space projector and route +with I_f. The same products, inclusions and involutions hold. The entry +code consists of pointwise XORs and clears in a common full frame. Its +relations hold on arbitrary data arrays. The complete finite program +therefore has the same native boundary for every f under the inherited +all-column and owned-erasure premises. + +Apply the retained delayed-cover bridge only after the entire finite +program is compiled. Its one common external weight is the same for all +fresh roles. All pointwise XORs commute with that weight. The retained +whole-fibre routes preserve independent data. The new code adds no +right-route symbol, nonzero native map or denominator. This argument +retains the source compiler and native realization premises; the finite +rational tests alone do not prove them. + +## 4. Complete controller invoice + +Replay every physical event in the source p16/a7 BIT controller over the +GF(2) group ring. Verify its literal scalar boundaries and all 32 +independent main inputs per port. There are eighteen full calls and +fifteen query shears. Replace every full call by the new word, using +Section 2. Leave each thin query and idle transform in place. + +Let P_old, T_old and P_new, T_new be the full paid and target histograms. +The exact differences are + +```text +P_new - P_old = -162 H1 -162 H7 +T_new - T_old = -162 H8. +``` + +Here Hr denotes one rank-r job or target. The new total is 57,231 paid +jobs and 11,292 productive fields. The paid rank mass is 215,457 and the +target rank mass is 216,210. The surplus is 753, as before. The verifier +reconstructs both complete invoices from the literal event list; it does +not subtract a proposed saving from a stored total. + +For every 00`. An equivalent certificate for the signed paid-minus- +target difference is the hinge sum `sum(delta_r*min(r,k))`: its values +at k=1,7,8 are -162,-162,0. All tail values are zero. This charges every +lost target and proves a strict improvement for the concave rank power. + +Two rational interval engines check the new moment. The raw moment has +a positive margin at 0.003472070044 and a negative margin at +0.003472070045. This is a certified crossing, not an optimum over other +words or controller classes. + +## 5. Compiler, cover and ordinary conversion + +The new tested saving is 0.0034678 and the uniform saving is 0.0034668. +Keep the source tensor power 1024, cutoff 17, floor 18, second-moment +parameter 1/5 and reserve 1/250000. The exact interval checks give the +charged first-moment ratio below `1-reserve`, the tail ratio below +31/32 and the rounding ratio below 19/20. Both decay bounds after 128 +steps are below 1/16. The completion surplus is positive, `17^64<18^63`, +and every target rank is below 256. RESULT.json records the exact H0 and +strict H1 thresholds. The winning uniform word is not materialized. + +Keep the source cover loss 0.000009. The saving after cover is 0.0034578. +Use an odd prime `q>2^26*N^5` that avoids all fixed denominators and rank +witnesses. Keep atom fraction 0.004 and old ordinary saving 0.0000384599. +The new ordinary saving is + +```text +(1-0.004)*0.0034578 + 0.004*0.0000384599 = 0.0034441226396. +``` + +The strict admitted endpoint is 0.00344412. At the same compiler gaps, +cover loss and atom fraction, the old word gives 0.0034363538396. The +matched gain is exactly 0.0000077688. This comparison does not credit the +new relations for the old source's unused conservative headroom. + +The new local word has 25,891 pointwise records. This is 1,568 more than +the source's 24,305 XORs and eighteen COPY entry/exit records. Add all +1,568 records to the inherited complete local allowance of 1,000,000. +The new local allowance is 1,001,568. With all eighteen calls, thin +queries, physical events and boundary operations, the complete raw +nonrecursive allowance is 19,170,192, below the retained 10^9 allowance. +The new code uses only unit XOR coefficients, adds no denominator and +no storage field, and retains the source tape and cover obligations. + +## 6. Complete multiplication scope + +Use the pinned PR5398 outer parameters and replace only their ordinary +BIT saving by 0.00344412. All 54 strict and four functional predicates +pass. The actual BIT stock exponent is positive and strictly below the +active group exponent, which is below one. The complete multiplication +endpoint remains 0.00302728823. The complex supplier still binds. + +This is a complete conditional BIT component improvement. It is not a +new complete multiplication bound, a selected-frontier change, a formal +proof, or an independent replay of the consumed complex construction. +All five inherited premise classes remain explicit in RESULT.json. diff --git a/research/bit-g20-nine-owned-relations/vendor/public5421/README.md b/research/bit-g20-nine-owned-relations/vendor/public5421/README.md new file mode 100644 index 0000000000..f2914f37b9 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/public5421/README.md @@ -0,0 +1,89 @@ +# Nine owned BIT helper relations + +This conditional construction raises the ordinary BIT saving from +**0.0034363538396 to 0.0034441226396** at matched compiler and cover +parameters. It admits the strict endpoint **0.00344412**. The complete +multiplication kappa does not increase: the complex supplier still binds. + +The reverse PR589 word has nine COPY values that are linear forms of its +initial full-frame fields. Own one helper for each independent form and +set all nine forms to zero. This removes nine rank-one transitions and +nine rank-seven COPY jobs per local call. It also removes nine rank-eight +productive helper targets. All 652 retained inputs remain independent. +The ten owned fields, including the old COPY centre, accept arbitrary +entry data and finish at zero. + +[PROOF.md](PROOF.md) gives the local boundary argument, the physical +involution that permits use at all eighteen full calls, the tensor lift, +and the complete cost. [RESULT.json](RESULT.json) contains the exact +receipt. [WORD.json.gz](WORD.json.gz) contains the emitted program. +[SOURCES.json](SOURCES.json) pins all thirteen live inputs at base +`d277c97824e50782da6adbc486ca3c76c8fc687e`. The selected record in that +manifest is historical provenance. This package does not change it. + +The complete p16/a7 controller has 57,231 paid jobs and 11,292 productive +fields. Its change is minus 162 rank-one jobs, minus 162 rank-seven jobs, +and minus 162 rank-eight targets. Its rank surplus remains 753. The raw +moment crossing lies strictly between 0.003472070044 and 0.003472070045. +The complete scalar and route allowance remains below 10^9. + +## Reproduce + +Use CPython 3.12 and its standard library. From the repository root: + +```sh +python3.12 -B scripts/research_package.py --package research/bit-nine-owned-relations +python3.12 -O -B research/bit-nine-owned-relations/verify.py +``` + +The verifier prints: + +```text +PASS_BIT_NINE_OWNED_RELATIONS_00344412_NO_NEW_MULTIPLICATION_KAPPA +``` + +It authenticates every live source, rebuilds the word, checks all symbolic +input rows, and replays each of the 662 input columns with separate +Boolean state. It checks rational projectors and all 111 port charts, +the literal controller, all targets and paid jobs, two exact moment +engines, the compiler tail, the cover loss, the ordinary BIT conversion, +and the unchanged outer arithmetic. It rejects missing entry or exit +clears, a changed relation, a nonzero free transition, a missing target +debit, and the old word at the new saving. + +## Scope + +The native all-column, owned-erasure, compiler, precision/tape, and +analytic-recovery premises remain conditional. The source delayed-cover +argument supplies the common weight and recursive interface. The finite +checks do not materialize the full GL cover, the winning uniform word, +or the complete integer multiplier. No Lean or proof-kernel check is +included. The outer arithmetic consumes the pinned PR5398 receipt; it +does not replay that complex construction. No global optimum is claimed. + +## Open next questions + +A further BIT gain needs a new relation space after all nine COPY jobs +are removed. Check active claims first, then charge each lost target +against the full word. The current full-history searches supply no such +additional gain. A complete multiplication gain needs a cheaper complex +supplier with a complete caller and cost. This package supplies neither. +[TASK.json](TASK.json) records the scope and these limits. + +## Credit + +DreamingOfClouds supplied [PR #589](https://github.com/CrocSwap/integer-mult-bounds/pull/589), +the retained two-transport word. eumemic supplied +[PR #555](https://github.com/CrocSwap/integer-mult-bounds/pull/555), the +punctured 111-port, 439-helper construction, from the credited earlier +word and port construction. Their source notices remain unchanged. +Cinna Davis supplied the query-thinned controller, the native BIT binding, +and the delayed-cover bridge. The exact compiler and tail work follows +zxv and the retained mixed-target recursion of Jacob Alan Sussman. +Ali Romman's [PR #5383](https://github.com/CrocSwap/integer-mult-bounds/pull/5383) +supplies the prior owned-helper method. The unchanged complex comparison +comes from [PR #5398](https://github.com/CrocSwap/integer-mult-bounds/pull/5398). +The exact consumed source paths and pins are in SOURCES.json. + +Prepared by Ali Romman with substantial OpenAI Codex assistance; no +subagents. New work is Apache-2.0. All predecessor notices are retained. diff --git a/research/bit-g20-nine-owned-relations/vendor/public5421/SOURCES.json b/research/bit-g20-nine-owned-relations/vendor/public5421/SOURCES.json new file mode 100644 index 0000000000..ff523a2966 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/public5421/SOURCES.json @@ -0,0 +1,96 @@ +{ + "schema_version": 1, + "base_commit": "d277c97824e50782da6adbc486ca3c76c8fc687e", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b288ae44032fd84dd5564243422836cbcd29835e", + "sha256": "f9ed52bb642cd1e1486cf2743557ac5fa23cf1514a3277d786a644e39a565038" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "research/higher-moment-strictification/verify.py", + "usage": "input", + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "usage": "input", + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85" + }, + { + "path": "research/kappa-backward-controller-20261023/RESULT.json", + "usage": "input", + "git_blob": "32b2b214ae108046bb68a507939ecb8c28c4ba92", + "sha256": "9b65013f63f616f12f4bb4d96ac75429452fad8680cada4bfd570e001fcd9a34" + }, + { + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "usage": "input", + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a" + }, + { + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "usage": "input", + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443" + }, + { + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "usage": "input", + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e" + }, + { + "path": "research/kappa-rebuild/bit/sources/pr589-regenerated/WORD.json.gz", + "usage": "input", + "git_blob": "85a4499bf9e4911a705d50567a2c2ef6cf23739a", + "sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f" + }, + { + "path": "research/kappa-rebuild/bit/sources/pr589-regenerated/records/249-records.bin", + "usage": "input", + "git_blob": "bdf9ab4ca0fd74cde6837f95f5f4e88133704e0e", + "sha256": "ea44aa047a2a9cf034de8b56b2166c49cf2dbdf9cd9ed6a20299a4f2b05ef09a" + }, + { + "path": "research/kappa-rebuild/bit/sources/pr589-regenerated/records/frames.json", + "usage": "input", + "git_blob": "a9a932b9268da28af9ba4bccdab205c5bcd50ad3", + "sha256": "d006b3bfe0c04afecfea7aecfa59dfe4298b99501c70da3938e40289bc2f5010" + }, + { + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "usage": "input", + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15" + }, + { + "path": "research/query-thinned-controllers/BIT-CONTROLLER.json", + "usage": "input", + "git_blob": "89c400d5970024b3debe870c36ce43889beed001", + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d" + }, + { + "path": "research/query-thinned-controllers/PROOF.md", + "usage": "input", + "git_blob": "9068f429896112082664455ab00bab083c99d1d8", + "sha256": "5ade59641f2ed70d045d6f60e89db7d979b1d1e9967f3acbe5c56eac81312841" + }, + { + "path": "research/query-thinned-controllers/verify.py", + "usage": "input", + "git_blob": "f1114036fff66f57014e5c1256141fb78ff4c4a9", + "sha256": "07dea601d6bbaa4d90e576f20c8607c37fb01e8778c798d919fa9df435049950" + } + ] +} diff --git a/research/bit-g20-nine-owned-relations/vendor/public5421/local.py b/research/bit-g20-nine-owned-relations/vendor/public5421/local.py new file mode 100644 index 0000000000..8fb7f48ebd --- /dev/null +++ b/research/bit-g20-nine-owned-relations/vendor/public5421/local.py @@ -0,0 +1,249 @@ +"""Own nine BIT helper relations and check all input columns. + +The source word is due to DreamingOfClouds, eumemic and their predecessors. +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +""" +from collections import Counter +from fractions import Fraction +from hashlib import sha256 +from pathlib import Path +import gzip +import importlib.util +import json +import struct +import sys + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +SOURCE = ROOT / 'research/kappa-rebuild/bit/sources/pr589-regenerated' +SIZE, PORTS = 661, 111 +OLD_PAID = {1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19} +NEW_PAID = {1:1314, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:10} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, ROOT / path) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def source(): + word = json.loads(gzip.decompress((SOURCE / 'WORD.json.gz').read_bytes())) + records = list(struct.iter_unpack('<6i', (SOURCE / 'records/249-records.bin').read_bytes())) + frames = json.loads((SOURCE / 'records/frames.json').read_text())['frames'] + return word, records, frames + + +def relations(word, records): + rows = [1 << i for i in range(SIZE)] + [0] + result = [] + for op, x, y, coefficient, frame, _ in reversed(records): + if op == 1 and coefficient & 1: + rows[x] ^= rows[y] + elif op == 3: + need(y == SIZE and rows[SIZE] == 0, 'Source COPY entrance') + result.append(rows[x]) + rows[SIZE] = rows[x] + elif op == 2: + need(y == SIZE and rows[x] == rows[SIZE], 'Source COPY exit') + rows[SIZE] = 0 + want = [(1 << i) ^ ((1 << (i-PORTS)) if PORTS <= i < 2*PORTS else 0) + for i in range(SIZE)] + [0] + need(rows == want and len(result) == 9, 'Source reverse identity and all nine COPY forms') + basis = {} + for row in result: + for pivot, value in sorted(basis.items()): + if row >> pivot & 1: + row ^= value + helpers = row >> (2*PORTS) + need(helpers != 0, 'Each relation has a new helper pivot') + pivot = 2*PORTS + (helpers & -helpers).bit_length()-1 + for old in list(basis): + if basis[old] >> pivot & 1: + basis[old] ^= row + basis[pivot] = row + need(len(basis) == 9, 'Nine independent helper relations') + pivots = sum(1 << i for i in basis) + for pivot, row in basis.items(): + need(row & pivots == 1 << pivot, 'Reduced helper basis') + need(all(word['final'][i] == 1 for i in range(SIZE) if row >> i & 1), + 'Every relation input has the full entrance frame') + return dict(sorted(basis.items())) + + +def construct(word, records, basis): + frames = list(word['final']) + [None] + rows = [1 << i for i in range(SIZE+1)] + program = [['CLEAR', SIZE, None]] + rows[SIZE] = 0 + for pivot, row in basis.items(): + program.append(['CLEAR', pivot, 1]) + rows[pivot] = 0 + for i in range(SIZE): + if i != pivot and row >> i & 1: + program.append(['ADD', pivot, i, 1]) + rows[pivot] ^= rows[i] + removed = [] + for index, (op, x, y, a, b, _) in enumerate(reversed(records)): + if op == 0: + old, new, rank = a, y, b + need(frames[x] == old, 'Source MOVE entrance') + if rows[x]: + program.append(['MOVE', x, old, new, rank]) + else: + program.append(['ZERO_MOVE', x, old, new]) + if rank: + removed.append([index, 'MOVE', x, rank]) + frames[x] = new + elif op == 1: + need(frames[x] == frames[y] == b, 'Source ADD frame') + if a & 1: + rows[x] ^= rows[y] + program.append(['ADD', x, y, b]) + elif op == 3: + need(y == SIZE and frames[x] == a and rows[x] == rows[SIZE] == 0, + 'All nine source COPY values are zero') + program.append(['CLEAR', SIZE, b]) + frames[SIZE] = b + removed.append([index, 'COPY', x, 7]) + else: + need(op == 2 and y == SIZE and rows[x] == rows[SIZE] == 0, + 'Zero COPY close') + program.append(['CLEAR', SIZE, None]) + frames[SIZE] = None + for pivot in basis: + program.append(['CLEAR', pivot, word['start'][pivot]]) + return program, removed + + +def replay(word, program, basis): + owned = set(basis) | {SIZE} + rows = [1 << i for i in range(SIZE+1)] + frames = list(word['final']) + [None] + paid = Counter() + largest_row = 1 + for event in program: + op, role = event[:2] + if op == 'CLEAR': + need(role in owned, 'Only an owned field can be cleared') + rows[role], frames[role] = 0, event[2] + elif op == 'ADD': + _, dst, src, frame = event + need(dst != src and frames[dst] == frames[src] == frame, 'Common-frame XOR') + rows[dst] ^= rows[src] + largest_row = max(largest_row, rows[dst].bit_count()) + elif op in ('MOVE', 'ZERO_MOVE'): + _, role, old, new, *rank = event + need(frames[role] == old, 'Native MOVE entrance') + if op == 'ZERO_MOVE': + need(rows[role] == 0, 'Only a zero value can change frame for free') + elif rank[0]: + paid[rank[0]] += 1 + frames[role] = new + else: + raise ValueError('Unknown local operation') + for i, row in enumerate(rows): + expected = 0 if i in owned else (1 << i) ^ ((1 << (i-PORTS)) if PORTS <= i < 2*PORTS else 0) + need(row == expected, 'Every retained and arbitrary owned entry column') + need(frames[:SIZE] == word['start'] and frames[SIZE] is None, 'All exit frames') + need(dict(paid) == NEW_PAID, 'Exact changed local paid profile') + return {'paid': dict(sorted(paid.items())), 'helpers': {8:439-len(basis)}, + 'retained_inputs': SIZE-len(basis), 'arbitrary_owned_entries': len(owned), + 'events': len(program), 'scalar_events': sum(e[0] in ('ADD', 'CLEAR') for e in program), + 'maximum_binary_row_weight': largest_row, + 'word_sha256': sha256(json.dumps(program, separators=(',', ':')).encode()).hexdigest()} + + +def native(word, records, frame_data): + load('research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py', 'joint_pair_dag') + module = load('research/kappa-rebuild/bit/mixed_productive_bit.py', 'bit_source_geometry') + projectors = module.frame_projectors(frame_data) + dims = {int(f): row['dim'] for f, row in frame_data.items()} + pairs = {(e[2], e[3], e[4]) for e in records if e[0] == 0} + for a, b, rank in pairs: + p, q = projectors[a], projectors[b] + need(module.matrix_multiply(p, q) == p == module.matrix_multiply(q, p), 'Nested exact projectors') + need(dims[b]-dims[a] == rank, 'Every original and reversed child rank') + multiply = module.matrix_multiply + def eye(n): + return [[Fraction(i == j) for j in range(n)] for i in range(n)] + def swap(p): + return [[Fraction(int(i == j)-(p[i][j] if i < 8 and j < 8 else p[i-8][j-8]) + if (i < 8) == (j < 8) else p[i][j-8] if i < 8 else p[i-8][j]) + for j in range(16)] for i in range(16)] + for port in range(PORTS): + p = projectors[word['start'][port]] + complement = [[Fraction(i == j)-p[i][j] for j in range(8)] for i in range(8)] + need(dims[word['start'][port]] == 1 and word['start'][port+PORTS] == 0, + 'Actual main entrance line and empty frame') + need(word['final'][port] == 1 and projectors[word['final'][port+PORTS]] == complement, + 'Actual main full frame and complement') + q = list(map(Fraction, word['lines'][port])) + need(sum(x*x for x in q) == 4 and p == [[x*y/4 for y in q] for x in q], + 'Source root and actual entrance projector') + u = [Fraction(i == 0)-q[i]/2 for i in range(8)] + norm = sum(x*x for x in u) + g = eye(8) if norm == 0 else [[Fraction(i == j)-2*u[i]*u[j]/norm for j in range(8)] for i in range(8)] + a = [row[1:] for row in g] + at = list(map(list, zip(*a))) + need(multiply(at,a) == eye(7) and multiply(a,at) == complement, 'Fresh exact complement basis') + rho = [p[i]+a[i] for i in range(8)] + [row+[Fraction(0)]*7 for row in at] + full = [[Fraction(i == j and i < 8) for j in range(15)] for i in range(15)] + active = [[p[i][j] if i < 8 and j < 8 else Fraction(i == j and i >= 8) for j in range(15)] for i in range(15)] + central = [[p[i][j] if i < 8 and j < 8 else Fraction(0) for j in range(15)] for i in range(15)] + need(multiply(rho,rho) == eye(15), 'Fresh port route is an involution') + need(multiply(multiply(rho,full),rho) == active, 'Every port route maps the full local projector to the next active block') + need(multiply(multiply(rho,central),rho) == central, 'Every route fixes the central query projector') + need(multiply(swap(eye(8)),swap(p)) == swap(complement), 'Exact address map D_I D_P equals D_K') + need(multiply(swap(p),swap(p)) == eye(16) and multiply(swap(complement),swap(complement)) == eye(16), + 'Both physical address factors are involutions') + need(all(word['start'][i] == 0 and word['final'][i] == 1 for i in range(2*PORTS, SIZE)), + 'Every retained helper has a rank-eight target') + return {'rational_projectors': len(projectors), 'nested_transition_pairs': len(pairs), + 'main_involution_ports': PORTS, 'fresh_port_routes': PORTS, 'new_nonzero_native_maps': 0, + 'all_f_rule': 'Source projectors tensor I_f; the source address involutions and all GF(2) identities stay exact.', + 'full_GL_cover_executed': False} + + +def controls(word, program, basis): + bad = json.loads(json.dumps(program)) + bad.pop(next(i for i, e in enumerate(bad) if e[0] == 'CLEAR' and e[1] in basis)) + variants = {'missing_owned_entry_clear': bad} + bad = json.loads(json.dumps(program)) + bad.pop(next(i for i, e in enumerate(bad) if e[0] == 'ADD' and e[1] in basis)) + variants['changed_relation'] = bad + bad = json.loads(json.dumps(program)) + bad.pop(max(i for i, e in enumerate(bad) if e[0] == 'CLEAR' and e[1] in basis)) + variants['missing_owned_exit_clear'] = bad + bad = json.loads(json.dumps(program)) + i = next(i for i, e in enumerate(bad) if e[0] == 'MOVE' and e[-1] > 0) + bad[i] = ['ZERO_MOVE'] + bad[i][1:4] + variants['unearned_free_transition'] = bad + failures = {} + for name, bad in variants.items(): + try: + replay(word, bad, basis) + except ValueError as error: + failures[name] = str(error) + else: + raise ValueError('Accepted local mutation: ' + name) + return failures + + +def run(): + word, records, frames = source() + basis = relations(word, records) + program, removed = construct(word, records, basis) + result = replay(word, program, basis) + need(Counter(e[-1] for e in removed) == {1:9, 7:9}, 'All removed jobs and no others') + result.update({'relation_basis': {str(p): [i for i in range(SIZE) if row >> i & 1] for p, row in basis.items()}, + 'removed': removed, 'native': native(word, records, frames), + 'negative_controls': controls(word, program, basis)}) + return result, program diff --git a/research/bit-g20-nine-owned-relations/verify.py b/research/bit-g20-nine-owned-relations/verify.py new file mode 100644 index 0000000000..ad29ec6667 --- /dev/null +++ b/research/bit-g20-nine-owned-relations/verify.py @@ -0,0 +1,7 @@ +"""Regenerate the changed native caller and exact ordinary certificate cold.""" +from replay_common import * +def main(): + outputs=['WORD.json.gz','LOCAL-RESULT.json','GLOBAL.jsonl.gz','GLOBAL-RESULT.json','INVOICE.json','CALLS.json','PRIVATE-EPISODES.json','TARGET-OWNERS.json','SOURCE-DESCRIPTORS.json.gz','TARGET-INVOLUTIONS.json','ORDINARY-RESULT.json'] + checked=copy_and_run(['local_relations.py','global_relations.py','target_involutions.py','ordinary.py'],outputs) + print(json.dumps({'status':'PASS_G20_NINE_OWNED_RELATIONS_COLD_PRIMARY','proof_payloads':len(checked),'admitted':'435496247/125000000000','python_optimize':sys.flags.optimize,'scope':'Conditional ordinary BIT component; no whole multiplication or external acceptance claim.'})) +if __name__=='__main__':main()