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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..5f67868be5 --- /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 **0.2449166755%** 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..c85c43d4ad --- /dev/null +++ b/research/bit-g20-nine-owned-relations/REPLAY.json @@ -0,0 +1,76 @@ +{ + "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 and this receipt are added; scientific sources/wrappers/evidence are byte-identical. Final registered replay is required at publication commit.", + "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." + } + } + ] +} 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 0000000000000000000000000000000000000000..e9474fd6b3a411662ad70708049fc10144a8c5ea GIT binary patch literal 5198821 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