From dca175fed8ebde8980635fd3b4508b8cba89a1b0 Mon Sep 17 00:00:00 2001 From: Dugongue <49054532+Dugongue@users.noreply.github.com> Date: Thu, 22 Oct 2026 06:58:13 -0700 Subject: [PATCH] Construct exact typed native quotient interfaces and shared-map repair --- .../native-quotient-interface/.gitattributes | 1 + .../CONTENT-HASHES.json | 39 + .../FREE-GROUP-LIFT-REVIEW.md | 37 + research/native-quotient-interface/LICENSE | 201 + .../native-quotient-interface/OVERLAP.json | 108 + .../native-quotient-interface/PHASE-CUT.md | 80 + .../PHASE-FORM-GRAMMAR.md | 79 + .../QUOTIENT-PROGRAMS.json.gz | Bin 0 -> 197338 bytes .../QUOTIENT-WORD.json.gz | Bin 0 -> 3979 bytes research/native-quotient-interface/README.md | 49 + .../REPAIRED-WARP-PHASES.json.gz | Bin 0 -> 7157 bytes .../REPAIRED-WARP-RECEIPT.json | 484 + .../REPAIRED-WARP-WORD.json.gz | Bin 0 -> 263235 bytes .../SOURCE-CLOSURE.json | 64 + .../native-quotient-interface/SOURCES.json | 18 + research/native-quotient-interface/TASK.json | 80 + 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research/native-quotient-interface/v/research/kappa-rebuild/complex/power_two_balance.py create mode 100644 research/native-quotient-interface/v/research/kappa-rebuild/complex/rebuild_native.py create mode 100644 research/native-quotient-interface/v/research/missing-join-frame/PATCH.json create mode 100644 research/native-quotient-interface/v/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py create mode 100644 research/native-quotient-interface/verify.py diff --git a/research/native-quotient-interface/.gitattributes b/research/native-quotient-interface/.gitattributes new file mode 100644 index 0000000000..625449502b --- /dev/null +++ b/research/native-quotient-interface/.gitattributes @@ -0,0 +1 @@ +* -text diff --git a/research/native-quotient-interface/CONTENT-HASHES.json b/research/native-quotient-interface/CONTENT-HASHES.json new file mode 100644 index 0000000000..a2112cf4f9 --- /dev/null +++ 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"2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "VERIFY.json": "3cdc00b059d88c5934645ddacd7691896840ade3a3bf6299036d38f47049fdf6", + "verify.py": "ea3bf6242d830b933f42b9c9af86ff5a1835bbda7980d55f73fd4507a4b4e969" +} diff --git a/research/native-quotient-interface/FREE-GROUP-LIFT-REVIEW.md b/research/native-quotient-interface/FREE-GROUP-LIFT-REVIEW.md new file mode 100644 index 0000000000..1b9ad7bf63 --- /dev/null +++ b/research/native-quotient-interface/FREE-GROUP-LIFT-REVIEW.md @@ -0,0 +1,37 @@ +# Why the repaired local word holds at every fiber width + +Prepared for Dugongue with substantial OpenAI Codex assistance. Apache-2.0. + +## A universal finite certificate + +The exact row evaluator `verify_buffers.py` represents a row by a finite dictionary + + (independent_input_role, reduced_signed_generator_word) -> rational_coefficient. + +Its `warp` operation left-prepends the actual shared operator symbol, cancelling only an immediately adjacent inverse symbol. Its `add`, SCALE, COPY and owned CLEAR rules perform exact rational linear algebra on these dictionaries. Distinct backward operator symbols are also represented formally. It assumes no finite matrix identities among different generators. The second evaluator `native_extensions.literal_replay` invokes those same free-word arithmetic primitives while separately checking every physical frame incidence and all owned-buffer conventions. + +Thus a successful endpoint comparison is a finite coefficient-wise identity over the rational free group algebra Q[F_72], with distinct independent field labels. It is stronger than numerical agreement of 512-dimensional matrices. In particular the expected helper rows contain only their own input label and the empty word, while main rows contain the stated elementary shear and no unwanted helper input labels. The owned C row is identically zero. Those exact zero coefficients must remain explicit acceptance checks. + +## Evaluation theorem + +Assign any invertible operator K_j on a vector space A to each positive generator j and K_j^-1 to its negative occurrence. There is a unique rational algebra homomorphism + + ev : Q[F_72] -> End_Q(A) + +sending a reduced word to the ordered product of its assigned operators. Adjacent inverse cancellation is valid because each K_j is invertible. Exact addition, scalar multiplication and multiplication are preserved by linear extension. Consequently every formal endpoint identity remains true under this assignment, on every arbitrary independent input field. + +This handles sums correctly. It does NOT assert that tensor powers preserve addition. Instead it first proves a free-group-algebra identity, then evaluates each generator by K_j^(tensor f). Evaluation is an algebra homomorphism for every f separately, including f>1. + +## Physical frame restoration + +At a field in frame C_U, represent its physical data as C_U times its logical row. A paid frame transition applies exactly C_new C_old^-1, leaving the logical row unchanged. At a native warp, the physical operator C_new K_j C_old^-1 realizes logical multiplication by K_j. Scalar ADD/COPY operations use a common frame for their operands and therefore enact the exact field-level rational operations. Owned CLEAR produces zero at any declared frame. Exact monomial/Clifford normalizers must implement those stated physical operators, with their absolute phases, rather than only their projective tableaux. + +This is a direct induction over the chronological emitted program. Therefore the successful formal endpoint identity yields the actual physical endpoint C_final S C_start^-1, where S is the stated elementary main shear and independent helper identity. It also proves zero transfer from helper inputs to main outputs and zero final owned state. + +## Application to the repaired quotient + +The repaired construction supplies one invertible G_j for each of all 72 shared native operators and uses its inverse consistently at every negative occurrence. Its exact physical K_(G_j) are invertible monomials. Fresh literal free-word replay checks the complete emitted program in both orientations and every borrowed scalar-frame incidence. Hence the evaluation theorem applies to the repaired maps without retaining a new unknown all-fiber identity as an assumption. + +For f digit columns, choose K_j^(tensor f) and each canonical frame C_U^(tensor f), with the corresponding fixed coordinate ordering. The same physical-frame induction proves the endpoint with its actual tensorized address-operator blocks. Independent coefficient-block identities for the explicit main normalizers then give the stated type-A/type-B interface. The 2×2 FIELD matrix is never tensorized; only the ADDRESS operators assigned to its coefficients are lifted. Identity spectators add no Gaussian rank. + +This proves the all-fiber algebraic lift of the concrete repaired local word from an exact formal certificate and explicit Clifford/frame constructions. It does not establish a complete controller, recursive stock, finite compiler majorant, native precision/caller, or improved kappa. Those remain separate obligations. Credit the retained free-word row evaluator and its original authors, Cinna Davis's native/helper framework, Cao Yifan's shared-map interface, the repaired quotient construction, and all original notices. 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No claim to have reviewed every historical PR or proved novelty.", + "pulls": [ + { + "number": 4638, + "head": "385a4436a47ea8e80cc1503948fe7a36e1b1c5af", + "state": "open", + "title": "Sharpen chronological width to d+1 and extend batching to adaptive heights (no new kappa)" + }, + { + "number": 4637, + "head": "60d0b09f13a9f9ebdd93d98d83d16ce6907d70b6", + "state": "open", + "title": "Join the CRT scanner-owned mask to conditional sparse repair (no new kappa)" + }, + { + "number": 4610, + "head": "1eb8da6cfb35512c0cc2533413e5ca42f48e13c6", + "state": "open", + "title": "Conditional κ = 0.00302176 (+0.00000024): joint helper interfaces and Lean certificates" + }, + { + "number": 4643, + "head": "0c084991a7d3bcd18ef4426a5940516c0171ae74", + "state": "open", + "title": "Independently check #4628's m ≥ 4 projection bound: 2.99172, 2.97290, 2.9447 reproduce; tail proved for all k; two uncertified block-4 inputs isolated (no new κ)" + }, + { + "number": 4642, + "head": "d8c59e36a8efb301f0298871218cfe00f4e043f7", + "state": "open", + "title": "Independently check #4629's re-padding ledger and price: κ 0.015637149091 reproduces; re-pad is +1×187/+5×26, block-7 surplus −256, ninth axis reached only by padding (no new κ)" + }, + { + "number": 4641, + "head": "99007ce1bb6a3d2889ddeb763bbc7546724e1f52", + "state": "open", + "title": "Independently check #4635's native κ step: the +1.6099e-6 is #4610's paid profile, not the Word RAM transfer (no new κ)" + }, + { + "number": 4640, + "head": "2d64f3521bcfad893abf0aa8022914c7429abfbc", + "state": "open", + "title": "Independently check #4626's helper621 chart move: ΔP=H1+2H2−H3−H4, rank 9→7 and crossing reproduce; +2.9e-8 of the gain is the compiler-gap retune (no new κ)" + }, + { + "number": 4639, + "head": "ade9e6ab6ff3cb2c3328ef9601976eb599eb654c", + "state": "open", + "title": "Independently check #4623's monotone extension, decoder rank and idle-free controller; sharpen ceiling to C≥.005687/.006512 (no new κ)" + }, + { + "number": 4636, + "head": "b0a325a3e312b7c5ebceb420de4b8cb13181f43e", + "state": "open", + "title": "Audit #4633: full replay, native contract failures and verifier false positives" + }, + { + "number": 4596, + "head": "477232ced13ec75fa40e0451ad1377db54c9d385", + "state": "closed", + "title": "Conditional κ = 0.0034 (BIT-limited, +12.58%): complex supplier to 0.011417749 via the ambient quotient by span{511}" + }, + { + "number": 4629, + "head": "2cf7d081118f6f702aa317816d231b41ce073579", + "state": "closed", + "title": "No new kappa: complex supplier to 0.015637149 via the best ambient quotient (kernel 153 of 32 replay-valid directions)" + }, + { + "number": 4633, + "head": "b390d64abfcdba1a3816b86fc763cbc95d43c12c", + "state": "closed", + "title": "Conditional κ = 0.012401086416 (BIT-limited, +310.6%): BIT supplier to 0.012401086416 via the ambient quotient (kernel 150)" + }, + { + "number": 4634, + "head": "9f053f7051e5fc3327d4337bb4bd8ac52cf5fcd0", + "state": "open", + "title": "Prove optimal binary Schur sharpness dimension n = 3d for d >= 2" + }, + { + "number": 4635, + "head": "898b0c8e2ca23897c312230988515c2553154f30", + "state": "open", + "title": "Conditional Word RAM κ = 0.0030217754 (+0.0000016099 over #4630)" + }, + { + "number": 4631, + "head": "48aef2349dc761f6b3b6bf3e59c3ee8080dbbe7a", + "state": "open", + "title": "Fix sparse baseline preflight for selected explicit inventories" + } + ], + "credit_and_overlap": { + "4636": "Independent negative audit of quotient admission, native contract and verifier controls. Our package constructs replacement shared maps and typed positive interfaces; it does not repeat a full negative audit.", + "4604": "Predecessor main-endpoint objection remains valid; our output is a changed typed interface, not the old canonical main interface.", + "4629": "DaysSky kernel-153 supplier frames and profile retained, with native maps repaired here.", + "4610": "Cao Yifan joint helper/native-map search and supplier lineage.", + "4635": "Dugongue conditional native Word RAM consequence; no superior exponent established here.", + "4641": "lm1909 independent arithmetic audit confirms that #4635 numerical change comes from #4610 paid profile; native transfer is lossless and adds no numerical gain. Native/provider admission remains outside that audit.", + "4639": "Independent monotone/decoder/idle-free-controller audit of #4623, no new kappa; distinct from this repaired typed local supplier." + }, + "final_canonical_main": "b58ad9ef4d4e861b0eaa5dba41742bdc072dca51", + "main_delta": "Only docs/ci-verification.md, scripts/check_selected_ci_inputs.py and its tests changed; AGENTS.md, autoresearch.md, CONTRIBUTING.md, priority/card and selected record unchanged. Frozen mathematical source inputs retained." +} diff --git a/research/native-quotient-interface/PHASE-CUT.md b/research/native-quotient-interface/PHASE-CUT.md new file mode 100644 index 0000000000..cebae17d8b --- /dev/null +++ b/research/native-quotient-interface/PHASE-CUT.md @@ -0,0 +1,80 @@ +# Rank-one phase-flow optimization by a minimum cut + +Prepared for Dugongue with substantial OpenAI Codex assistance. Apache-2.0. + +This is a constructive extension of PHASE-FORM-GRAMMAR.md. It preserves the old subspaces, scalar chronological word, fixed logical native maps and exact main ABI. It permits and pays additional Gaussian children when a formerly monomial physical warp becomes nonmonomial. + +## Binary gauges + +Fix a nonzero ambient functional l on F2^n. At a contact node v with subspace U_v choose s_v in {0,1} and form + + b_v(x,u)=s_v (l·x)(l·u), x,u in U_v. + +An actual gauge is F_v=C_(U_v) D_(s_v ll^T), with the same inverse-image convention as the phase-form grammar. A scalar contact has one common gauge for all roles it touches. Fix all main endpoints to s=0. Initially also fix owned-center/non-G adapter boundaries to s=0, so those frozen instructions remain unchanged. Fix one endpoint of every helper to zero; allow its opposite endpoint to vary. Both choices, all helper entrances fixed or all helper exits fixed, are valid separate search problems. + +## Every physical edge has an exact rank invoice + +For an original paid edge U→V with I=U intersection V, its old rank is r=dimU+dimV-2dimI. The two rank-one forms restricted to I agree when both switches agree, so the added rank is one exactly when switches differ and l is nonzero on I. Its complete child cost at exponent t is (r+added_rank)^t, not an unpriced phase correction. + +For a fixed logical native warp K_G, the retained subspaces satisfy GU=V. The transported source form is the rank-one functional G^-T l restricted to V; the target form is l restricted to V. Write these restricted functionals as a and b. The physical operator is + + F_target K_G F_source^-1. + +Its Gaussian rank is exactly rank(s_source a a^T + s_target b b^T), hence one of 0,1,2. If a and b are equal nonzero, the rank table for switches (00,10,01,11) is (0,1,1,0). If they are distinct nonzero, the table is (0,1,1,2). If one vanishes, the table is (0,0,1,1) or (0,1,0,1); if both vanish every entry is zero. These cases are decided by exact binary linear algebra. + +The physical warp is emitted as its actual exact Clifford circuit. The retained Clifford normal form factors it into two explicit monomial adapters and one rank-one or rank-two Gaussian call, or only a monomial when the rank is zero. Thus a switch cannot make a formerly free native warp expensive without that expense appearing in the paid profile. All adapters, owned work and absolute phases remain covered by their explicit native construction and replay, rather than treated as cost-free semantic labels. + +## The binary edge costs are submodular + +Let f(r)=r^t for fixed 0= 0, + A=c10-c00-C, B=c01-c00-C. + +Thus C is a nonnegative cut-edge capacity, and A,B are unary contributions. Negative unaries are represented by a nonnegative terminal capacity plus a constant. There is no sign ambiguity or appeal to a floating optimization status in this reduction. + +## Productive rewards remain unary + +Suppose a helper has nested source/end subspaces U⊂V and original productive rank g=dimV-dimU. One endpoint switch is fixed zero. The relative helper's extra rank is s times rank((l|U)⊗²), hence zero or one. Its productive-moment reward is the unary quantity + + s * ((g+1)^t-g^t) + +when l is nonzero on U, and zero otherwise. The reward must be multiplied by every actual controller occurrence of that independent helper. Every helper remains a distinct arbitrary input and its true new Gaussian job is normalized explicitly. + +Consequently total added paid cost minus total added productive reward is a binary submodular energy and is reducible to an s–t minimum cut. The all-zero assignment is feasible with energy zero. Any negative-energy cut gives a strictly improved complete moment at exponent t. This conclusion requires the actual graph multiplicities, owned-center charges and controller invoice; it is not a local gain that can be added across overlapping windows. + +## Exact arithmetic and discovery + +At rational t the weights are algebraic powers, not generally rational numbers. A portable discovery implementation may solve min-cut problems for rational enclosures/approximations of these coefficients, then evaluate every selected cut with the retained outward-rational power engine. Only a strictly certified negative true energy is a mathematical improvement. Approximate optimality alone is not an exact ceiling. Because the graph has finitely many cuts, any strictly profitable true cut is eventually detected by sufficiently fine rational approximations; a bounded search that finds none gives no universal obstruction. + +All n-bit nonzero functionals l can be enumerated at the fixed local dimension n=9. This is 511 distinct rank-one phase families, not a claim to search arbitrary symmetric phases, simultaneous moving subspaces, or all native algorithms. + +## All-input semantic assembly and finite compiler + +The new physical edge for every old logical operation M is F_next M F_prev^-1. Adjacent gauges cancel exactly. At scalar contacts the same F acts on each operand, so the original scalar opcode and coefficient are retained. Main gauges are frozen to their original values. In the mode with all helper entrances frozen, the initial gauge is unchanged on every field, so every main endpoint is immediately unchanged on every arbitrary input. In the mode with varying helper entrances, additionally use the retained independent-helper direct-sum contract: the old global endpoint has zero blocks from helper inputs to main outputs. The original all-column certificate must check those zero blocks explicitly. Right-multiplying independent helper input blocks then cannot affect a main output. Thus both declared modes preserve the actual main ABI; freezing main gauges alone would not suffice for an arbitrary globally coupled operator. Helper endpoints change to the actual relative Gaussian/Clifford operators indicated by their gauges; they are not validated against an automatically redefined main contract. + +The original chronological word order is unchanged. Each new Gaussian child finishes before the suspended parent resumes. The exact normal form provides whole-job monomial adapters, so the retained direct mixed-target compiler can treat the additional rank-one/rank-two paid jobs and increased helper ranks as actual canonical Gaussian jobs. Owned erasure is not inferred from the moment: frozen owned instructions and their original all-column proof remain explicit. Actual all-column and absolute-phase replay must validate the emitted witness and helper normalizers. + +For every digit-column lift width f, tensor the actual one-column Clifford factorization independently over all f columns. Operator identities tensorize, active paid ranks multiply by f, and the helper rank gain becomes f. Identity spectators add no rank. This supplies an all-fiber algebraic extension of an admitted candidate; it is not a new unknown adapter hypothesis. + +After a negative cut is emitted and verified, the entire changed target/paid histograms must pass the critical-root mirror, funded majorant, finite uniform-word absorption, precision and native outer assembly checks. No new kappa follows from a min-cut objective alone. This theorem gives a sufficient exact candidate-generation and lowering mechanism; it does not assert a useful cut has been observed in the current word. + +Credit the classical submodular graph-cut reduction and symplectic/Clifford normal form; Cinna Davis's supplier/controller interfaces; Cao Yifan's actual round-three word; Dugongue's native phase-flow route and Word RAM assembly; zxv, Jacob Alan Sussman and all retained compiler/normalizer sources. The new role here is the source-convention-aware phase-flow energy that permits paid native warp changes while preserving the actual main ABI. + +## Extension: an arbitrary fixed symmetric ambient form + +The minimum-cut reduction is not restricted to rank-one Q=ll^T. Fix ANY symmetric ambient Q and choose b_v=s_v Q restricted to U_v. On a paid edge I=U intersection V, the extra rank is zero for equal switches and rank(Q|I) for unequal switches. Its incremental paid cost is a nonnegative Potts cut weight f(r+rank(Q|I))-f(r). + +For a formerly monomial logical warp G, pull both forms back to its source U. Put A=Q|U, B=(G^T Q G)|U, a=rankA, b=rankB and c=rank(A+B). The four paid costs are (0,f(a),f(b),f(c)). Rank subadditivity gives c<=a+b, and the increasing subadditive function f(k)=k^t gives f(c)<=f(a+b)<=f(a)+f(b). Thus this table is submodular too. A helper with one endpoint fixed has unary reward f(g+rank(Q|I))-f(g). All earlier source/normalizer/owned/main-ABI obligations remain unchanged. The actual diagonal Clifford D_Q is explicit and its phases must be carried literally. + +Consequently any chosen symmetric Q, including alternating rank-two and high-rank forms, supplies another exact min-cut discovery problem. Searching finitely many Q is bounded evidence; it does not exclude a useful form among the other 2^(n(n+1)/2) possibilities. diff --git a/research/native-quotient-interface/PHASE-FORM-GRAMMAR.md b/research/native-quotient-interface/PHASE-FORM-GRAMMAR.md new file mode 100644 index 0000000000..3e91b0b7e2 --- /dev/null +++ b/research/native-quotient-interface/PHASE-FORM-GRAMMAR.md @@ -0,0 +1,79 @@ +# Symmetric phase forms enlarge the native contact grammar + +Prepared for Dugongue with substantial OpenAI Codex assistance. Apache-2.0. + +## Exact model and conventions + +Let V=F2^n with the ordinary nondegenerate dot product. Write a Pauli exponent as (x,z), with symplectic pairing x·z'+z·x', and put y=x+z. Let L0={(0,z)}. The retained canonical frame C_U has involutive symplectic action and sends L0 to + + L_U={(x,z): x in U, x+z in U^perp}. + +A frame gauge F is assigned its INVERSE image chart L(F)=F^-1(L0). This orientation matters: a physical paid edge is F_next F_prev^-1. Its Fourier rank is n-dim(L(F_prev) intersection L(F_next)). For canonical C_U the inverse and forward symplectic images coincide; this coincidence must not be assumed for an arbitrary new gauge. + +For a subspace U and a symmetric bilinear form b:U×U→F2 define + + L(U,b)={(x,z): x in U, (x+z)·u=b(x,u) for every u in U}. + +The old canonical-frame grammar is precisely b=0. + +## Theorem 1: explicit gauges for every such chart + +L(U,b) is an n-dimensional Lagrangian. Every Lagrangian whose x-projection is U has this form for a unique symmetric b. + +Proof. For each x in U, the allowed y=x+z form an affine translate of U^perp, so total dimension is dimU+(n-dimU)=n. For two members (x,y),(u,t), the symplectic pairing is x·t+y·u=b(u,x)+b(x,u)=0. Conversely the vertical kernel of a Lagrangian with x-projection U is exactly U^perp; hence y·u is independent of the chosen y above x. It defines b, and isotropy proves symmetry. + +The construction is an exact Clifford circuit. Choose basis columns B of U, extend them to an invertible n×n matrix H, write S for the symmetric matrix of b on B, and put + + Q = H^-T blockdiag(S,0) H^-1. + +Then Q is symmetric and x^T Q u=b(x,u) on U. The retained diagonal Clifford D_Q acts symplectically as (x,z)→(x,z+Qx), equivalently (x,y)→(x,y+Qx). Choose + + F(U,b)=C_U D_Q. + +Because D_Q has involutive symplectic action and C_U^-1(L0)=L_U, its inverse-image chart is D_Q^-1 L_U=L(U,b). In the retained Op.then convention this circuit is `diag(Q).then(canonical_frame(U))`: D_Q acts first. The diagonal's Z4 linear coefficients have parity equal to diag(Q), as in the retained exact implementation. This fixes an actual circuit and absolute phase, not just a projective tableau. Different extensions of b may give different gauges with the same chart; their relative operator is monomial and is not silently identified as an exact circuit. + +## Theorem 2: complete paid rank formula + +For charts (U,b),(W,c), put I=U intersection W and let D be the symmetric form (b+c) restricted to I. The exact Fourier rank of F(W,c) F(U,b)^-1 is + + r = dimU+dimW-2dimI + rank(D). + +Proof. A vector in the intersection of the two Lagrangians has x in I. Its prescribed y-functional on U+W exists precisely when b(x,v)=c(x,v) for every v in I, that is, x lies in the radical of D. This radical has dimension dimI-rank(D). For each such x, allowed y form an affine space of dimension n-dim(U+W). Thus the intersection dimension is n-dimU-dimW+2dimI-rank(D). The B-block rank equals n minus this dimension, by applying F(W,c) to the inverse-image intersection. This proves the formula. + +In particular, every old paid rank is preserved exactly if the two forms agree on I. These are linear equations over F2, not nonlinear rank constraints. Once a candidate is emitted, the retained exact Clifford normal form constructs and checks its two monomial adapters and rank-r Gaussian child, with absolute phase. Every adapter has the native volume-linear implementation already charged by the source-bound provider theorem. This is a sufficient physical realization of the proposed rank, not free nonmonomial motion. + +## Theorem 3: native warp constraints are linear + +For the retained monomial K_G, Q_G=I+G^-T G^-1 gives + + (x,y)→(Gx,G^-T y). + +Therefore K_G sends L(U,b) to L(GU,b'), where + + b'(Gx,Gu)=b(x,u). + +The physical fixed-logical-warp edge F_next K_G F_prev^-1 is monomial exactly when K_G L_prev=L_next. With the retained subspaces already satisfying GU=W, this is exactly the displayed bilinear transport equality. It is linear in the local form coefficients. Its exact monomial and absolute phase are emitted from the full retained Clifford circuit, rather than inferred from the chart alone. + +## A sufficient positive profile mechanism + +Keep the actual scalar chronological word, original subspaces and logical warp maps fixed. Assign one form to each shared scalar-contact gauge and to all role endpoints. Impose: + +1. zero forms at all frozen main input/output endpoints; +2. equality of forms on every paid-edge intersection; +3. the bilinear transport equations for every fixed logical native warp; +4. one common actual gauge at each scalar contact; +5. zero forms at frozen owned-center and non-G adapter boundaries, unless their exact symplectic constraints are separately implemented. + +Every equation is homogeneous over F2. Solve it exactly. For a helper entrance (U,b) and exit (W,c), its productive Gaussian rank becomes its old rank plus rank((b+c)|I). It remains an arbitrary independent input; no initialized storage or redundant productive credit has been introduced. If ANY helper difference is nonzero on I, its productive rank strictly increases while every paid rank is unchanged. All other helper ranks weakly increase. Hence the complete productive moment increases for every positive exponent, with the entire paid invoice unchanged. The controller's multiplicity must be retained when rebuilding its whole moment. + +This is a genuine sufficient route to a changed supplier invoice. A numerical exponent additionally requires all-column endpoint reconstruction, absolute-phase lowering, actual whole-job adapters, exact critical-root/majorant and finite-compiler admission. The homogeneous equations alone are not a new multiplication theorem, and existence of a useful nonzero solution is not assumed. + +The all-column semantic proof is ordinary gauge telescoping: replacing each logical operation M_j by F_j M_j F_(j-1)^-1 gives total F_final(M_s…M_1)F_initial^-1. Main gauges are frozen, scalar contacts use a common gauge, and helper relative endpoints are updated honestly. If helper entrance gauges vary, the retained independent-helper direct-sum endpoint contract is also used: helper input blocks have zero transfer to main outputs. This must be checked in the old all-column certificate. Under that explicit source fact, the old main ABI is preserved exactly; frozen main endpoint gauges alone do not imply it for an arbitrary globally coupled operator. No quotiented or missing main chart is substituted. + +## Minimal exact coordinates for the solver + +If U has basis B=(u1,…,ud), use d(d+1)/2 variables S_ij with i<=j. Express x=B a and u=B c. 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Substantial OpenAI assistance. These are fresh constructions with +explicit arbitrary-input endpoints. An embedded cache output is not claimed +as an independent clean helper output until a whole caller erases its defect. +""" +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +import argparse +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import rebuild_native as N +import power_two_balance as B + +B_SHA = '76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424' + + +def common_frame_h(geo, offset, frame): + """H = diag(I,-I) S_L S_-K S_L, with all shear ADDs having coefficient ±1. + + Balancing only the eight selected coordinates avoids scaling104 ordinary + coordinates. No private field and no recursive transport are introduced. + Precondition: ALL112 physical fields share the stated actual frame gauge. + """ + A = geo['selected'] + out = [['phase', 'fresh_common_frame_H']] + def scale(n, d): + out.extend(N.scalar(['scale', ['L', offset+a], n, d], frame) for a in A) + def left(): + for k, a in enumerate(A): + for u, value in sorted(geo['L'][k].items()): + coefficient = 2*value + N.need(abs(coefficient) == 1, 'Balanced unit L coefficients') + out.append(N.scalar(['add', ['L', offset+a], ['L', offset+u], int(coefficient), 1], frame)) + scale(2, 1); left(); scale(1, 4) + for k, a in enumerate(A): + for u, value in sorted(geo['L'][k].items()): + coefficient = -2*value + out.append(N.scalar(['add', ['L', offset+u], ['L', offset+a], int(coefficient), 1], frame)) + scale(4, 1); left(); scale(-1, 2) + N.need(B.scalar_sum(out) == 10096, 'Exact common-frame H scalar allowance') + return out + + +def embedded_cache_roles(canonical): + roles = [i for i in range(224, 632) if canonical['start'][i] == 0 and canonical['final'][i] == 1] + N.need(len(roles) == 213, '213 genuinely cold, full-ended native helper roles') + return roles[:8] + + +def embedded_logger_suffix(canonical, geo, roles=None): + roles = embedded_cache_roles(canonical) if roles is None else list(roles) + N.need(len(roles) == len(set(roles)) == 8, 'Eight distinct embedded caches') + N.need(all(224 <= i < 632 and canonical['start'][i] == 0 and canonical['final'][i] == 1 for i in roles), + 'Embedded logger only uses cold full-ended physical helper references') + out = [['phase', 'fresh_embedded_dirty_logger']] + for k, a in enumerate(geo['selected']): + r = roles[k] + out += [N.scalar(['scale', ['L', r], 2, 1], 1), + N.scalar(['add', ['L', r], ['L', a], 2, 1], 1)] + out += [N.scalar(['add', ['L', r], ['L', u], int(2*q), 1], 1) + for u, q in sorted(geo['L'][k].items())] + out.append(N.scalar(['scale', ['L', r], 1, 2], 1)) + N.need(B.scalar_sum(out) == 3440, 'Embedded logger exact scalar bill') + return out + + +def make_embedded_logger(canonical, base_word, geo): + word = B.make_balanced_h(canonical, base_word, geo)['forward'] + return word+embedded_logger_suffix(canonical, geo) + + +def make_wrapped_h(canonical, base_word, geo): + words = B.make_balanced_h(canonical, base_word, geo) + return {direction: common_frame_h(geo, 112, 0)+word+common_frame_h(geo, 0, 1) + for direction, word in words.items()} + + +def literal_replay(v, c, program, backward=False): + """Second literal evaluator for new endpoints; all632 inputs arbitrary. + + This checker has no endpoint-specific shortcut. It applies every scalar + and free-warp event and checks each contact's frame before comparing rows. + """ + rows = {('L', i): v.identity(('L', i)) for i in range(632)} + rows['C', 0] = v.identity(('C', 0)) + current = {('L', i): f for i, f in enumerate(c['start'])}; current['C', 0] = None + spaces = [v.span(frame) for frame in c['frames']] + profile = Counter(); cost = 0; max_l1 = Q(1); witness = None; max_denominator = 1 + for j, event in enumerate(program): + kind = event[0]; touched = None + if kind == 'scalar': + g, frame = event[1:]; target = tuple(g[1]); touched = target + cost += N.primitive_allowance(g) + if g[0] == 'clear': + N.need(target == ('C', 0), 'Only owned C0 can be cleared') + rows[target] = {}; current[target] = frame + else: + N.need(current[target] == frame, 'Exact scalar target frame') + if g[0] in ('add', 'copy'): + source = tuple(g[2]); N.need(current[source] == frame, 'Exact scalar source frame') + if g[0] == 'copy': + N.need(target == ('C', 0), 'Only owned field overwritten by copy') + rows[target] = dict(rows[source]) + else: + N.need(target != source, 'Distinct reversible ADD arguments') + v.add(rows[target], rows[source], Q(g[3], g[4])) + else: + N.need(g[0] == 'scale', 'Known scalar action') + q = Q(g[2], g[3]); rows[target] = {i: q*x for i, x in rows[target].items()} + elif kind == 'warp': + _, r, op, old, new = event; target = tuple(r); touched = target + N.need(current[target] == old, 'Warp input frame') + rows[target] = v.warp(rows[target], op, backward); current[target] = new + elif kind in ('climb', 'center'): + if kind == 'climb': + _, part, i, old, new, rank = event; target = ('L', i) + N.need(spaces[old] < spaces[new], 'Ascending borrowed climb') + else: + _, i, old, new, rank = event; target = ('C', i) + N.need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested center transport') + N.need(current[target] == old and rank == abs(len(c['frames'][new])-len(c['frames'][old])), 'Paid rank and source frame') + current[target] = new; profile[rank] += 1 + else: + N.need(kind in ('phase', 'adapter', 'residual_adapter'), 'Known inert native marker') + if touched is not None: + norm = sum(map(abs, rows[touched].values()), Q(0)) + if norm > max_l1: + max_l1 = norm; witness = dict(event=j, role=list(touched)) + max_denominator = max(max_denominator, max((x.denominator for x in rows[touched].values()), default=1)) + N.need([current['L', i] for i in range(632)] == c['final'], 'Final native frames') + N.need(not rows['C', 0], 'Owned C0 cleared at return') + return rows, dict(independent_persistent_columns=632, independent_owned_entry_columns=1, + scalar_frames_checked=True, arbitrary_owned_C0_cleared=True, + paid_profile=dict(sorted(profile.items())), paid_rank_mass=sum(k*x for k, x in profile.items()), + real_scalar_allowance=cost, max_formal_prefix_l1=str(max_l1), max_denominator=max_denominator, + l1_witness=witness) + + +def check_rows(v, rows, geo, kind, backward=False, cache_roles=()): + mismatch = [] + for r in range(632): + actual = rows['L', r] + if kind == 'wrapped' and r < 224: + port = r % 112; wanted = {} + for j, q in geo['H'][port].items(): + v.add(wanted, v.identity(('L', (112 if r >= 112 else 0)+j)), q) + if backward and r < 112: + v.add(wanted, v.identity(('L', 112+j)), -q) + if not backward and r >= 112: + v.add(wanted, v.identity(('L', j)), q) + else: + wanted = v.identity(('L', r)) + if 112 <= r < 224: + for j, q in geo['H'][r-112].items(): + v.add(wanted, v.identity(('L', j)), q) + if r in cache_roles: + k = list(cache_roles).index(r) + for j, q in {geo['selected'][k]: Q(1), **geo['L'][k]}.items(): + v.add(wanted, v.identity(('L', j)), q) + if actual != wanted: + mismatch.append(r) + N.need(not mismatch, 'Fresh exact endpoint mismatch '+repr(mismatch[:5])) + + +def check_scalar_h(v, geo): + """Independent112-column execution without native body or Clifford data.""" + rows = {i: {i: Q(1)} for i in range(112)} + program = common_frame_h(geo, 0, 0) + for event in program: + if event[0] != 'scalar': + continue + g = event[1]; target = g[1][1] + if g[0] == 'scale': + q = Q(g[2], g[3]); rows[target] = {i: q*x for i, x in rows[target].items()} + else: + v.add(rows[target], rows[g[2][1]], Q(g[3], g[4])) + N.need(all(rows[i] == geo['H'][i] for i in range(112)), 'Three balanced shears exactly equal H') + return dict(all_columns=112, real_scalar_allowance=B.scalar_sum(program), + additions=sum(e[0] == 'scalar' and e[1][0] == 'add' for e in program), + unit_add_coefficients=True, owned_fields=0, new_recursive_children=0, + required_physical_precondition='All112 fields occupy one actual common frame reference.') + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--out', type=Path, default=HERE/'extension-certificates') + args = ap.parse_args(); args.out.mkdir(parents=True, exist_ok=True) + N.need(N.digest(HERE/'rebuild_native.py') == B.N_SHA and N.digest(HERE/'power_two_balance.py') == B_SHA, + 'Authenticated fresh prerequisite sources') + p, v, ce, receipt, inherited = N.authenticated(); geo = N.geometry(v.PACKET) + result = dict(schema='fresh-native-helper-log-and-common-frame-conjugation/1', + source_sha256=N.digest(Path(__file__)), reconstruction_source_sha256=B.N_SHA, + balance_source_sha256=B_SHA, scalar_H=check_scalar_h(v, geo), providers={}, no_new_kappa_claimed=True) + for tag in N.TAGS: + c = N.read(N.BASE/(tag+'-CANONICAL.json.gz')); word = N.read(N.BASE/(tag+'-NATIVE-WORD.json.gz')) + base_scalar = B.scalar_sum(word['forward']) + roles = embedded_cache_roles(c); embedded = make_embedded_logger(c, word, geo) + rows, embedded_check = literal_replay(v, c, embedded) + check_rows(v, rows, geo, 'embedded', cache_roles=roles) + N.need(embedded_check['real_scalar_allowance'] == base_scalar+3504+3440, 'Embedded complete scalar invoice') + wrapped = make_wrapped_h(c, word, geo); wrapped_checks = {} + for direction, program in wrapped.items(): + back = direction == 'backward' + rows, checked = literal_replay(v, c, program, back) + check_rows(v, rows, geo, 'wrapped', back) + N.need(checked['real_scalar_allowance'] == base_scalar+3504+2*10096, 'Wrapped H complete scalar invoice') + wrapped_checks[direction] = checked + ep = args.out/(tag+'-EMBEDDED-LOGGER.json.gz'); wp = args.out/(tag+'-SCALAR-WRAPPED-H.json.gz') + result['providers'][tag] = dict( + embedded_logger=dict(artifact=ep.name, sha256=N.save(ep, embedded), check=embedded_check, + cache_roles=roles, exactly_400_other_helpers_restored=True, + cache_output='d_k + X_A[k] + L[k] X_U', extra_children=0, + extra_persistent_fields=0, extra_owned_fields=0, extra_scalar_allowance=3440, + independent_clean_output_credit_for_eight_caches=False), + scalar_wrapped_H=dict(artifact=wp.name, sha256=N.save(wp, wrapped), checks=wrapped_checks, + endpoint='diag(H,H) times the corresponding identity shear in local logical coordinates', + new_recursive_children_beyond_H=0, extra_scalar_allowance=20192, + all_408_helpers_restored=True, + outer_intercall_frame_identification_certified=False)) + N.save(args.out/'RESULT.json', result) + print('PASS extensions', tag, 'embedded0 extra children; wrapped H20192 extra scalars', flush=True) + result['status'] = 'PASS_LOCAL_NATIVE_ENDPOINTS_WITH_EXPLICIT_OUTER_FRAME_OBLIGATION' + N.save(args.out/'RESULT.json', result) + + +if __name__ == '__main__': + main() diff --git a/research/native-quotient-interface/v/research/kappa-rebuild/complex/power_two_balance.py b/research/native-quotient-interface/v/research/kappa-rebuild/complex/power_two_balance.py new file mode 100644 index 0000000000..a55ae0ce78 --- /dev/null +++ b/research/native-quotient-interface/v/research/kappa-rebuild/complex/power_two_balance.py @@ -0,0 +1,130 @@ +#!/usr/bin/env python3 +"""Exact power-of-two balancing of the reconstructed H112 and dirty logger. + +Apache-2.0. Substantial OpenAI assistance. This changes only explicit local +coefficient streams and dyadic unit scales; every recursive child is retained. +The exact arbitrary-input verifier and endpoint-gauge phase receipts are reused +from the separately source-bound reconstruction in rebuild_native.py. +""" +from collections import Counter +from copy import deepcopy +from pathlib import Path +import argparse +import json +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import rebuild_native as N + +N_SHA = 'f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5' + + +def make_balanced_h(c, word, geo, exponent=1): + """Assemble 2^e v, transport it, deliver 12/2^e times that field.""" + N.need(isinstance(exponent, int) and -8 <= exponent <= 8, 'Bounded integral balancing exponent') + q = N.Q(2)**exponent + result = N.make_h_word(c, word, geo) + for direction, program in result.items(): + out = []; completion = False + for event in program: + if event[0] == 'phase': + completion = event[1] == 'fresh_H112_completion' + if not completion or event[0] != 'scalar': + out.append(event); continue + op, frame = event[1:] + if op[0] == 'copy' and op[1] == ['C', 0]: + out.append(event) + if q != 1: + out.append(N.scalar(['scale', ['C', 0], q.numerator, q.denominator], frame)) + elif op[0] == 'add': + factor = q if op[1] == ['C', 0] else 1/q + amount = N.Q(op[3], op[4])*factor + out.append(N.scalar(op[:3]+[amount.numerator, amount.denominator], frame)) + else: + out.append(event) + result[direction] = out + return result + + +def make_balanced_logger(c, word, geo, exponent=1): + """Scale arbitrary P by 2^e, add 2^e v, scale back; dirty P is preserved.""" + N.need(isinstance(exponent, int) and -8 <= exponent <= 8, 'Bounded integral balancing exponent') + q = N.Q(2)**exponent + suffix = [['phase', 'fresh_balanced_forward_dirty_logger']] + for k, a in enumerate(geo['selected']): + suffix.append(['cache_child', k, 0, 1, 9]) + if q != 1: + suffix.append(N.scalar(['scale', ['P', k], q.numerator, q.denominator], 1)) + suffix.append(N.scalar(['add', ['P', k], ['L', a], q.numerator, q.denominator], 1)) + for p, coefficient in sorted(geo['L'][k].items()): + x = q*coefficient + suffix.append(N.scalar(['add', ['P', k], ['L', p], x.numerator, x.denominator], 1)) + if q != 1: + suffix.append(N.scalar(['scale', ['P', k], q.denominator, q.numerator], 1)) + return word['forward']+suffix + + +def scalar_sum(program): + return sum(N.primitive_allowance(e[1]) for e in program if e[0] == 'scalar') + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--out', type=Path, default=HERE/'balanced-certificates') + args = ap.parse_args(); args.out.mkdir(parents=True, exist_ok=True) + N.need(N.digest(HERE/'rebuild_native.py') == N_SHA, 'Pinned fresh reconstruction source') + p, v, ce, receipt, inherited = N.authenticated(); geo = N.geometry(v.PACKET) + result = dict(schema='fresh-native-power-two-balancing/1', source_sha256=N.digest(Path(__file__)), + reconstruction_source_sha256=N_SHA, no_new_kappa_claimed=True, providers={}, + scope='Finite native all-column and phase certificates; full outer recurrence and rounded induction remain separate.') + for tag in N.TAGS: + c = N.read(N.BASE/(tag+'-CANONICAL.json.gz')); word = N.read(N.BASE/(tag+'-NATIVE-WORD.json.gz')) + base_scalar = scalar_sum(word['forward']) + scan = [] + for exponent in range(-4, 5): + hw = make_balanced_h(c, word, geo, exponent) + lw = make_balanced_logger(c, word, geo, exponent) + scan.append(dict(exponent=exponent, H_increment=scalar_sum(hw['forward'])-base_scalar, + logger_increment=scalar_sum(lw)-base_scalar)) + N.need(min(scan, key=lambda r: r['H_increment'])['exponent'] == 1, 'H minimum in scanned power-two family') + N.need(min(scan, key=lambda r: r['logger_increment'])['exponent'] == 1, 'Logger minimum in scanned power-two family') + hw = make_balanced_h(c, word, geo) + hp = Counter({int(k): n for k, n in c['local_profile'].items()}); hp[1] += 8 + checks = {d: N.replay_extended(v, hw[d], c, geo, d == 'backward', expected_profile=hp) + for d in ('forward', 'backward')} + N.need(all(check['real_scalar_allowance']-base_scalar == 3504 for check in checks.values()), 'H increment3504') + phases = N.h_child_recipes(p, ce, c, hw) + lw = make_balanced_logger(c, word, geo) + lp = Counter({int(k): n for k, n in c['local_profile'].items()}); lp[9] += 8 + logger_check = N.replay_extended(v, lw, c, geo, endpoint='logger', cache_count=8, expected_profile=lp) + N.need(logger_check['real_scalar_allowance']-base_scalar == 3440, 'Logger increment3440') + wrong = deepcopy(lw) + omitted = next(i for i, e in enumerate(wrong) if e[0] == 'scalar' and e[1] == ['scale', ['P', 0], 1, 2]) + wrong.pop(omitted) + control = N.replay_extended(v, wrong, c, geo, endpoint='logger', cache_count=8, allow_mismatch=True) + dirty_gain = N.Q(1) + for event in wrong: + if event[0] == 'scalar' and event[1][:2] == ['scale', ['P', 0]]: + dirty_gain *= N.Q(event[1][2], event[1][3]) + N.need(not control['exact_endpoint'] and dirty_gain == 2 and + any(x['role'] == ['P', 0] for x in control['mismatch_examples']), + 'Missing final dirty-cache rescale exposes arbitrary P coefficient error') + hpfile = args.out/(tag+'-BALANCED-H112-NATIVE.json.gz') + lpfile = args.out/(tag+'-BALANCED-FORWARD-LOGGER.json.gz') + result['providers'][tag] = dict(power_two_scan=scan, + H=dict(artifact=hpfile.name, sha256=N.save(hpfile, hw), checks=checks, new_child_recipes=phases, + increment=dict(profile={'1': 8}, real_scalar_allowance=3504, owned_C_fields=1), saved_scalar_allowance=832), + logger=dict(artifact=lpfile.name, sha256=N.save(lpfile, lw), check=logger_check, + increment=dict(profile={'9': 8}, real_scalar_allowance=3440, arbitrary_P_fields=8), saved_scalar_allowance=784, + missing_final_rescale_negative_control=dict(dirty_P0_coefficient=str(dirty_gain), + mismatches=control['mismatch_examples']))) + N.save(args.out/'RESULT.json', result) + print('PASS balanced', tag, 'H8H1+3504; logger8H9+3440', flush=True) + result['status'] = 'PASS_BALANCED_H_BOTH_DIRECTIONS_AND_FORWARD_LOGGER_ALL_FOUR_PROVIDERS' + N.save(args.out/'RESULT.json', result) + + +if __name__ == '__main__': + main() diff --git a/research/native-quotient-interface/v/research/kappa-rebuild/complex/rebuild_native.py b/research/native-quotient-interface/v/research/kappa-rebuild/complex/rebuild_native.py new file mode 100644 index 0000000000..78a7b1b0e6 --- /dev/null +++ b/research/native-quotient-interface/v/research/kappa-rebuild/complex/rebuild_native.py @@ -0,0 +1,453 @@ +#!/usr/bin/env python3 +"""Fresh reconstruction of H112, its dirty logger and helper boundary factors. + +Apache-2.0. Substantial OpenAI assistance. This is newly generated evidence; +it does not recreate or assert the identity of files lost in an earlier session. +The immutable predecessor is the attributed function-composition clean-J word. +Logical sparse replay extends the independently pinned verify_buffers grammar. +Physical lowering uses the attributed exact Clifford compiler and independently +decodes each new recipe, comparing tableau AND the exact zero-state phase. +""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import platform +import sys +import time + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +P_PATH = ROOT/'research/kappa-function-composition/complex/prune_native.py' +BASE = P_PATH.parent/'pruned-native' +P_SHA = 'f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257' +RECEIPT_SHA = 'b62c6c123f43a697802a336ee7178942040c0249c64ebc19cd6aad7ba2728ae7' +CE_SHA = '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962' +TAGS = ('THREE-base', 'THREE-extra', 'FOUR-base', 'FOUR-extra') +SELECTED = (0, 7, 20, 27, 36, 46, 57, 111) + + +def need(ok, why): + if not ok: + raise ValueError(why) + + +def digest(path): + return sha256(Path(path).read_bytes()).hexdigest() + + +def read(path): + path = Path(path) + raw = path.read_bytes() + return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw) + + +def save(path, value): + path = Path(path) + data = json.dumps(value, sort_keys=True, separators=(',', ':')).encode() + path.write_bytes(gzip.compress(data, mtime=0) if path.suffix == '.gz' else data+b'\n') + return digest(path) + + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, path) + obj = importlib.util.module_from_spec(spec) + sys.modules[name] = obj + spec.loader.exec_module(obj) + return obj + + +def authenticated(): + need(digest(P_PATH) == P_SHA, 'Pinned clean-J reconstruction utility') + need(digest(BASE/'RESULT.json') == RECEIPT_SHA, 'Pinned clean-J receipt') + p = load(P_PATH, 'fresh_h112_prune') + need(digest(p.CHECKER) == p.CHECKER_SHA, 'Pinned independent native interpreter') + need(digest(p.CLIFFORD) == CE_SHA, 'Pinned phase compiler') + v = load(p.CHECKER, 'fresh_h112_independent') + inherited = v.authenticate() + ce = load(p.CLIFFORD, 'fresh_h112_clifford') + receipt = read(BASE/'RESULT.json') + for tag in TAGS: + for filename, expected in receipt['providers'][tag]['artifacts'].items(): + need(digest(BASE/filename) == expected, 'Pinned predecessor artifact '+filename) + return p, v, ce, receipt, inherited + + +def geometry(packet): + """Return exact sparse R, L and the freshly checked 112 by 112 H.""" + packet = read(packet) if isinstance(packet, (str, Path)) else packet + R = [{int(k): Q(x) for k, x in row.items()} for row in packet['R_rows']] + ordinary = tuple(i for i in range(112) if i not in SELECTED) + need(len(R) == 8, 'Eight query rows') + dot = lambda a, b: sum((x*b.get(j, Q(0)) for j, x in a.items()), Q(0)) + need(all(dot(a, b) == 56*int(i == j) for i, a in enumerate(R) for j, b in enumerate(R)), 'R R^t = 56 I') + need(all(sum((r.get(a, 0)*r.get(b, 0) for r in R), Q(0)) == 4*int(a == b) + for a in SELECTED for b in SELECTED), 'Selected Gram matrix 4 I') + L = [{p: q for p in ordinary if (q := sum((r.get(a, 0)*r.get(p, 0) for r in R), Q(0))/4)} + for a in SELECTED] + need(all(len(row) == 52 and set(map(abs, row.values())) == {Q(1, 2)} for row in L), '416 half-integral L entries') + need(all(dot(a, b) == 13*int(i == j) for i, a in enumerate(L) for j, b in enumerate(L)), 'L L^t = 13 I') + J = [] + H = [] + for i in range(112): + row = {j: q for j in range(112) + if (q := Q(i == j)-sum((r.get(i, 0)*r.get(j, 0) for r in R), Q(0))/4)} + J.append(row) + changed = dict(row) + if i in SELECTED: + k = SELECTED.index(i) + for j, x in {i: Q(1), **L[k]}.items(): + changed[j] = changed.get(j, Q(0))+12*x + if not changed[j]: + del changed[j] + H.append(changed) + need(all(sum((x*H[k].get(j, 0) for k, x in H[i].items()), Q(0)) == int(i == j) + for i in range(112) for j in range(112)), 'Exact H squared equals identity') + need(any(H[i].get(j, 0) != H[j].get(i, 0) for i in range(112) for j in range(112)), 'H is not symmetric') + return dict(selected=SELECTED, ordinary=ordinary, R=R, L=L, J=J, H=H) + + +def kernel_h(packet): + return geometry(packet)['H'] + + +def scalar(op, frame): + return ['scalar', op, frame] + + +def make_h_word(canonical, base_word, geo): + """Forward suffix and separate backward prefix; H is NOT self-transpose.""" + out = deepcopy(base_word) + for backward in (False, True): + correction = [['phase', 'fresh_H112_completion']] + common = 0 if backward else 1 + source_offset = 112 if backward else 0 + target_offset = 0 if backward else 112 + for k, a in enumerate(geo['selected']): + target_frame = canonical['start'][a] if backward else canonical['final'][112+a] + correction += [scalar(['clear', ['C', 0]], common), + scalar(['copy', ['C', 0], ['L', source_offset+a]], common)] + correction += [scalar(['add', ['C', 0], ['L', source_offset+p], q.numerator, q.denominator], common) + for p, q in sorted(geo['L'][k].items())] + correction += [['center', 0, common, target_frame, 1], + scalar(['add', ['L', target_offset+a], ['C', 0], -12 if backward else 12, 1], target_frame), + scalar(['clear', ['C', 0]], target_frame)] + name = 'backward' if backward else 'forward' + out[name] = correction+out[name] if backward else out[name]+correction + return out + + +def make_logger_word(canonical, base_word, geo): + """Eight arbitrary cache fields; the caller owns their dirty baselines.""" + suffix = [['phase', 'fresh_forward_dirty_query_logger']] + for k, a in enumerate(geo['selected']): + suffix += [['cache_child', k, 0, 1, 9], scalar(['add', ['P', k], ['L', a], 1, 1], 1)] + suffix += [scalar(['add', ['P', k], ['L', p], q.numerator, q.denominator], 1) + for p, q in sorted(geo['L'][k].items())] + return base_word['forward']+suffix + + +def primitive_allowance(op): + if op[0] in ('clear', 'copy'): + return 2 + q = Q(op[3], op[4]) if op[0] == 'add' else Q(op[2], op[3]) + n, d = abs(q.numerator), q.denominator + need(n and not d & (d-1), 'Nonzero dyadic scalar') + if op[0] == 'scale': + need(not n & (n-1), 'Dyadic unit SCALE') + return 2*(abs(n.bit_length()-d.bit_length())+int(q < 0)) + need(op[0] == 'add', 'Known scalar macro') + return 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1) + + +def replay_extended(v, program, canonical, geo, backward=False, endpoint='H', cache_count=0, + expected_profile=None, allow_mismatch=False): + """Literal exact all-column native replay, including arbitrary C at entry. + + Transports change canonical coordinate tags and retain logical row values; + separate phase receipts implement the exact physical coordinate change. + Warp words remain free noncommuting symbols, including dual orientation. + """ + need(endpoint in ('H', 'J', 'logger'), 'Known endpoint') + n = len(canonical['start']) + need(n == 632, '632 persistent predecessor roles') + rows = {('L', i): v.identity(('L', i)) for i in range(n)} + current = {('L', i): f for i, f in enumerate(canonical['start'])} + centers = {e[1] for e in program if e[0] == 'center'} + centers |= {r[1] for e in program if e[0] == 'scalar' + for r in (e[1][1:3] if e[1][0] in ('add', 'copy') else e[1][1:2]) + if r[0] == 'C'} + need(centers <= {0}, 'Only one owned completion field') + for i in centers: + rows['C', i] = v.identity(('C', i)); current['C', i] = None + for i in range(cache_count): + rows['P', i] = v.identity(('P', i)); current['P', i] = 0 + spaces = [v.span(vectors) for vectors in canonical['frames']] + dimensions = [len(s).bit_length()-1 for s in spaces] + profile = Counter(); counts = Counter(); scalar_cost = 0 + max_l1 = Q(1); max_coefficient = Q(1); max_numerator = 1; max_denominator = 1 + witness = {'event': -1, 'role': ['L', 0]} + for i, e in enumerate(program): + kind = e[0]; counts[kind] += 1; touched = None + if kind in ('climb', 'center', 'cache_child'): + if kind == 'climb': + _, part, j, old, new, rank = e; role = ('L', j) + need(spaces[old] < spaces[new], 'Strict ascending borrowed climb') + else: + _, j, old, new, rank = e + role = ('C' if kind == 'center' else 'P', j) + need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested transport') + need(current[role] == old and rank == abs(dimensions[new]-dimensions[old]), 'Transport frame and exact rank') + current[role] = new; profile[rank] += 1 + elif kind == 'warp': + _, r, op, old, new = e; role = tuple(r) + need(current[role] == old, 'Warp source frame') + rows[role] = v.warp(rows[role], op, backward); current[role] = new; touched = role + elif kind == 'scalar': + op, frame = e[1:]; role = tuple(op[1]); touched = role + scalar_cost += primitive_allowance(op) + if op[0] == 'clear': + need(role[0] == 'C', 'No clearing arbitrary persistent inputs') + rows[role] = {}; current[role] = frame + else: + need(current[role] == frame, 'Scalar target frame at event '+str(i)) + if op[0] in ('add', 'copy'): + source = tuple(op[2]); need(current[source] == frame, 'Scalar source frame at event '+str(i)) + if op[0] == 'copy': + need(role[0] == 'C', 'Copy targets owned field') + rows[role] = dict(rows[source]) + else: + need(role != source, 'Reversible ADD distinct registers') + v.add(rows[role], rows[source], Q(op[3], op[4])) + else: + q = Q(op[2], op[3]); rows[role] = {k: q*x for k, x in rows[role].items()} + else: + need(kind in ('phase', 'adapter', 'residual_adapter'), 'Unsupported event '+kind) + if touched is not None: + values = [abs(x) for x in rows[touched].values()] + norm = sum(values, Q(0)) + if norm > max_l1: + max_l1 = norm; witness = {'event': i, 'role': list(touched)} + if values: + max_coefficient = max(max_coefficient, max(values)) + max_numerator = max(max_numerator, max(x.numerator for x in values)) + max_denominator = max(max_denominator, max(x.denominator for x in values)) + need([current['L', i] for i in range(n)] == canonical['final'], 'Exact final native frames') + need(all(current['P', i] == 1 for i in range(cache_count)), 'Logger cache terminal frame') + if expected_profile is not None: + need(dict(profile) == {int(k): x for k, x in expected_profile.items()}, 'Complete profile binding') + mismatch = [] + matrix = geo['H'] if endpoint == 'H' else geo['J'] + for role, actual in rows.items(): + wanted = {} if role[0] == 'C' else v.identity(role) + if role[0] == 'L': + port = role[1] if backward else role[1]-112 + if 0 <= port < 112: + offset, sign = (112, -1) if backward else (0, 1) + for j, q in matrix[port].items(): + v.add(wanted, v.identity(('L', offset+j)), sign*q) + elif role[0] == 'P': + need(endpoint == 'logger' and not backward, 'Only forward logger cache contract') + k = role[1] + for j, q in {geo['selected'][k]: Q(1), **geo['L'][k]}.items(): + v.add(wanted, v.identity(('L', j)), q) + if actual != wanted: + differences = {k: actual.get(k, Q(0))-wanted.get(k, Q(0)) for k in actual.keys() | wanted.keys()} + differences = {k: x for k, x in differences.items() if x} + first = min(differences) + mismatch.append({'role': list(role), 'unequal_coefficients': len(differences), + 'first_input': list(first[0]), 'first_word': list(first[1]), + 'first_coefficient': str(differences[first])}) + if not allow_mismatch: + need(not mismatch, 'Endpoint mismatch: '+repr(mismatch[:3])) + return dict(direction='backward' if backward else 'forward', endpoint=endpoint, + independent_persistent_input_fields=n+cache_count, + independently_initialized_owned_C_fields=len(centers), owned_C_fields_zero_at_exit=all(not rows['C', i] for i in centers), + all_408_helpers_exactly_restored_in_logical_coordinates=all(rows['L', i] == v.identity(('L', i)) for i in range(224, 632)), + all_scalar_frames_checked=True, all_new_coefficients_dyadic=True, + event_counts=dict(counts), paid_profile=dict(sorted(profile.items())), + paid_rank_mass=sum(k*x for k, x in profile.items()), real_scalar_allowance=scalar_cost, + prefix=dict(max_formal_row_l1=str(max_l1), max_abs_coefficient=str(max_coefficient), + max_abs_numerator=max_numerator, max_denominator=max_denominator, l1_witness=witness, + scope='Exact logical ideal prefixes; no rounded recursive error bound.'), + exact_endpoint=not mismatch, mismatch_examples=mismatch[:3]) + + +def lower_exact(p, ce, op): + recipe, _ = ce.lower_child(op) + left = p.monomial(ce, recipe['left'], op.n) + if recipe['rank']: + right = p.monomial(ce, recipe['right'], op.n) + decoded = right.then(ce.fourier(op.n, range(recipe['rank']))).then(left) + else: + decoded = left + need(decoded.tab == op.tab and decoded.zero_state() == op.zero_state(), 'Independent recipe decode including absolute phase') + return recipe + + +def normal_form(p, ce, op, rank): + recipe = lower_exact(p, ce, op) + need(recipe['rank'] == rank, 'Physical rank equals promised helper width') + left = p.monomial(ce, recipe['left'], 9) + right = p.monomial(ce, recipe['right'], 9) + pre = right.adjoint(); post = left.adjoint() + pre_recipe = lower_exact(p, ce, pre); post_recipe = lower_exact(p, ce, post) + need(pre_recipe['rank'] == post_recipe['rank'] == 0, 'Free boundary wrappers') + wrapped = pre.then(op).then(post); target = ce.fourier(9, range(rank)) + need(wrapped.tab == target.tab and wrapped.zero_state() == target.zero_state(), 'Helper boundary is exact standard Fourier including phase') + return dict(rank=rank, factorization=recipe, outer_pre_monomial=pre_recipe['left'], + outer_post_monomial=post_recipe['left'], exact_tableau_and_global_phase=True) + + +def helper_normal_forms(p, ce, canonical, cache=None): + """Certify every helper, with explicit inherited and fresh outer wrappers. + + Bare residual is F_end F_start^-1. The retained residual_adapter convention + already maps it to C_width in forward, and conjugate(C_width) in backward. + New outer normalizers below act at the WHOLE invocation boundaries. They + require no change to internal frames, helper reads, or scalar event order. + """ + cache = {} if cache is None else cache + rows = []; widths = Counter() + for role in range(224, 632): + start, end = canonical['start'][role], canonical['final'][role] + A, B = canonical['frames'][start], canonical['frames'][end] + rank = len(B)-len(A) + need(0 < rank <= 9, 'Positive productive helper width') + key = (tuple(A), tuple(B)) + if key not in cache: + physical = ce.canonical_frame(9, A).adjoint().then(ce.canonical_frame(9, B)) + inherited = lower_exact(p, ce, physical) + need(inherited['rank'] == rank, 'Native helper residual rank') + lm = p.monomial(ce, inherited['left'], 9) + rm = p.monomial(ce, inherited['right'], 9) + directions = {} + for backward in (False, True): + name = 'backward' if backward else 'forward' + op = p.conjugate(ce, physical) if backward else physical + l = p.conjugate(ce, lm) if backward else lm + r = p.conjugate(ce, rm) if backward else rm + native = r.adjoint().then(op).then(l.adjoint()) + target = ce.fourier(9, range(rank)) + if backward: + target = p.conjugate(ce, target) + need(native.tab == target.tab and native.zero_state() == target.zero_state(), 'Inherited oriented native helper boundary') + directions[name] = dict(bare_residual_normal_form=normal_form(p, ce, op, rank), + inherited_native_target='conjugate(C_width)' if backward else 'C_width', + existing_native_boundary_normal_form=normal_form(p, ce, native, rank)) + cache[key] = dict(start_basis=A, end_basis=B, inherited_forward_factorization=inherited, directions=directions) + rows.append(dict(role=role, start_frame=start, end_frame=end, width=rank, certificate=cache[key])) + widths[rank] += 1 + expected = {5: 28, 6: 18, 7: 56, 8: 93, 9: 213} if widths[7] == 56 else {5: 28, 6: 18, 7: 57, 8: 92, 9: 213} + need(dict(widths) == expected, 'Exact all-helper productive width profile') + return dict(status='PASS_ALL_408_HELPERS_BOTH_ORIENTATIONS_WITH_ABSOLUTE_PHASE', + count=len(rows), widths=dict(sorted(widths.items())), total_width=sum(k*x for k, x in widths.items()), + recipes=rows, unique_frame_pairs=len({(r['start_frame'], r['end_frame']) for r in rows}), + scope='Native ideal helper block and free boundary adapters only; productive outer ownership and full recursive bill are separate obligations.') + + +def h_child_recipes(p, ce, canonical, words): + result = {} + for direction, program in words.items(): + rows = [] + for i, e in enumerate(program): + if e[0] != 'center': + continue + _, role, old, new, rank = e + # These corrections occur OUTSIDE the inherited data adapters. + # The physical endpoint references are the original port gates, + # not the monomial-equivalent canonical representatives. Using a + # bare canonical_frame here would leave an uncharged/missing phase + # adapter on the scalar contact despite a correct logical replay. + k = len(rows); port_index = SELECTED[k]; q = canonical['ports'][port_index] + if direction == 'forward': + source = ce.fourier(9) + target = ce.cgate(9, q).adjoint().then(ce.fourier(9)) + else: + source = ce.ident(9) + target = p.conjugate(ce, ce.cgate(9, q)) + op = source.adjoint().then(target) + recipe = lower_exact(p, ce, op) + need(recipe['rank'] == rank == 1, 'Completion child rank one') + direct = ce.cgate(9, q).adjoint() + need(op.tab == direct.tab and op.zero_state() == direct.zero_state(), 'External completion is exact inverse port gate') + rows.append(dict(event=i, selected_port=port_index, port_vector=q, + source_frame=old, target_frame=new, recipe=recipe, + physical_reference='original external endpoint gauge; inherited adapters already outside the contact', + exact_inverse_port_gate_including_phase=True)) + need(len(rows) == 8, 'Exactly eight completion children') + result[direction] = rows + return result + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--out', type=Path, default=HERE/'fresh-certificates') + ap.add_argument('--stage', choices=('helpers', 'H', 'logger', 'all'), default='all') + ap.add_argument('--tags', nargs='+', choices=TAGS, default=list(TAGS)) + args = ap.parse_args(); args.out.mkdir(parents=True, exist_ok=True) + p, v, ce, receipt, inherited = authenticated() + geo = geometry(v.PACKET) + run = dict(schema='fresh-native-H112-reconstruction/1', reconstructed_after_loss=True, + source_sha256=digest(Path(__file__)), predecessor_receipt_sha256=RECEIPT_SHA, + predecessor_generator_sha256=P_SHA, independent_interpreter_sha256=p.CHECKER_SHA, + clifford_compiler_sha256=CE_SHA, packet_sha256=digest(v.PACKET), + geometry=dict(selected=list(SELECTED), ordinary_count=104, L_nonzeros=416, H_squared_identity=True, + H_not_symmetric=True, divisions_by_odd_numbers=0), + environment=dict(python=sys.version, platform=platform.platform()), + no_new_kappa_claimed=True, providers={}) + phase_cache = {} + for tag in args.tags: + started = time.monotonic() + c = read(BASE/(tag+'-CANONICAL.json.gz')); word = read(BASE/(tag+'-NATIVE-WORD.json.gz')) + row = dict(predecessor_artifacts=receipt['providers'][tag]['artifacts']) + if args.stage in ('helpers', 'all'): + helpers = helper_normal_forms(p, ce, c, phase_cache) + path = args.out/(tag+'-HELPER-BOUNDARIES.json.gz') + row['helper_boundaries'] = dict(artifact=path.name, sha256=save(path, helpers), widths=helpers['widths'], + total_width=helpers['total_width'], count=408) + print('PASS helpers', tag, helpers['widths'], flush=True) + if args.stage in ('H', 'all'): + hw = make_h_word(c, word, geo); expected_profile = Counter({int(k): x for k, x in c['local_profile'].items()}); expected_profile[1] += 8 + checks = {d: replay_extended(v, hw[d], c, geo, d == 'backward', expected_profile=expected_profile) for d in ('forward', 'backward')} + phases = h_child_recipes(p, ce, c, hw) + baseline_scalar = receipt['providers'][tag]['checks']['forward']['independent_literal_replay']['conservative_real_scalar_primitive_allowance'] + need(all(check['real_scalar_allowance']-baseline_scalar == 4336 for check in checks.values()), 'Exact 4336 scalar increment') + broken = deepcopy(hw['forward']) + omitted = next(i for i, e in enumerate(broken) if e[0] == 'scalar' and e[1][:2] == ['add', ['L', 112+SELECTED[0]]] and e[1][2] == ['C', 0]) + broken.pop(omitted) + negative = replay_extended(v, broken, c, geo, allow_mismatch=True) + need(not negative['exact_endpoint'], 'Missing completion negative control rejected') + path = args.out/(tag+'-H112-NATIVE.json.gz') + row['H112'] = dict(artifact=path.name, sha256=save(path, hw), checks=checks, new_child_recipes=phases, + increment=dict(profile={'1': 8}, real_scalar_allowance=4336, owned_C_fields=1, persistent_fields=0), + omitted_completion_negative_control=negative['mismatch_examples']) + print('PASS H112', tag, '8 H1 + 4336; both directions', flush=True) + if args.stage in ('logger', 'all'): + lw = make_logger_word(c, word, geo) + profile = Counter({int(k): x for k, x in c['local_profile'].items()}); profile[9] += 8 + check = replay_extended(v, lw, c, geo, endpoint='logger', cache_count=8, expected_profile=profile) + baseline_scalar = receipt['providers'][tag]['checks']['forward']['independent_literal_replay']['conservative_real_scalar_primitive_allowance'] + need(check['real_scalar_allowance']-baseline_scalar == 4224, 'Exact 4224 scalar logger increment') + op = ce.canonical_frame(9, c['frames'][0]).adjoint().then(ce.canonical_frame(9, c['frames'][1])) + recipe = lower_exact(p, ce, op); need(recipe['rank'] == 9, 'Logger paid rank nine') + path = args.out/(tag+'-FORWARD-LOGGER.json.gz') + row['logger'] = dict(artifact=path.name, sha256=save(path, lw), check=check, cache_child_recipe=recipe, + increment=dict(profile={'9': 8}, real_scalar_allowance=4224, owned_C_fields=0, arbitrary_cache_fields=8), + cache_restored=False, productive_cache_credit_claimed=False) + print('PASS logger', tag, '8 H9 + 4224', flush=True) + row['seconds'] = time.monotonic()-started + run['providers'][tag] = row + save(args.out/('RESULT-'+args.stage+'.json'), run) + run['status'] = 'PASS_FRESH_RECONSTRUCTION_REQUESTED_STAGES' + save(args.out/('RESULT-'+args.stage+'.json'), run) + + +if __name__ == '__main__': + main() diff --git a/research/native-quotient-interface/v/research/missing-join-frame/PATCH.json b/research/native-quotient-interface/v/research/missing-join-frame/PATCH.json new file mode 100644 index 0000000000..f96d295d40 --- /dev/null +++ b/research/native-quotient-interface/v/research/missing-join-frame/PATCH.json @@ -0,0 +1,24 @@ +{ + "phase": "B", + "ordinal": 480, + "old_frame": 732, + "new_basis": [ + 168, + 336, + 45 + ], + "old_basis": [ + 258, + 133, + 82, + 45 + ], + "incoming_frames": [ + 364, + 360 + ], + "outgoing_frames": [ + 736, + 692 + ] +} diff --git a/research/native-quotient-interface/v/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py b/research/native-quotient-interface/v/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/native-quotient-interface/v/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<

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zm7B*8_ka5J&p(|0`T6PemmmNBw;%s{`p1X!!|D0M`Sf`I>*wdw+xzF!{g>01^Ybfc zeK_4ceSSRMKi^!4Jl;OP`|#$==U<-Qoi8)Jy#talg!6WOS4+CRt>^c(ZI=f%zCXX+ z-+p2m>#4gX4rAgUFHm7m;_nyb(Q%C#l_c*sxx{ts84Qqyfq008_=vy}h< literal 0 HcmV?d00001 diff --git a/research/native-quotient-interface/README.md b/research/native-quotient-interface/README.md new file mode 100644 index 0000000000..ebef976905 --- /dev/null +++ b/research/native-quotient-interface/README.md @@ -0,0 +1,49 @@ +# A repaired native quotient with an exact typed seven-axis interface + +Prepared for Dugongue with substantial OpenAI Codex assistance; Apache-2.0. + +This package constructs a usable local supplier from the kernel-153 complex quotient: one consistent replacement for each of its 72 shared native address maps, exact monomial realizations of every actual warp, and explicit monomial wrappers giving the complete two-bank main operator. It proves the arbitrary-input identity at every fiber width by evaluation of an exact free-group-algebra certificate. It establishes no new multiplication exponent or improved kappa. + +The main theorem is constructive. There are 56 main pairs of type A, `diag(D,D) S_y(Q^-1)`, and 56 of type B, `diag(D,QD) S_y(Q^-1)`, where D is a seven-axis Gaussian and Q is a separate one-axis central Gaussian. The extra Q in type B acts on physical Y. The backward word realizes the corresponding inverse transpose. The 408 helpers remain arbitrary independent inputs, with target census `{3:2,6:7,7:47,8:139,9:213}`; the complete local paid census is `{1:2177,2:424,3:389,4:147,5:50,8:8}`. + +Read [TYPED-QUOTIENT-INTERFACE.md](TYPED-QUOTIENT-INTERFACE.md) for the construction, explicit wrappers, all-width proof and exact contract. [FREE-GROUP-LIFT-REVIEW.md](FREE-GROUP-LIFT-REVIEW.md) independently checks the crucial universal evaluation argument. This is a sufficient local operator theorem: it does not ask a future worker to invent the maps or recover an unspecified endpoint. + +## Why this is needed + +The large quotient numbers in PRs #4596, #4629 and #4633 price changed supplier endpoints. A lower local moment does not by itself yield a valid old-controller invoice. PR #4604 identified the main-endpoint problem, and the newer independent PR #4636 records concrete native-contract and verifier failures. Those findings are predecessor work, not discoveries claimed here. All three numerical-claim PRs were closed without merging at the observed checkpoint; closure is not a mathematical proof. + +Our contribution is a positive repair. The replacement maps satisfy every shared occurrence together, rather than choosing different maps for different uses. The actual main operator is explicitly normalized to the two types above. The former common eight-axis interface is not asserted. The repaired native maps, typed interfaces and universal evaluation proof are new artifacts relative to those frozen source submissions; no general novelty priority is claimed for the classical symplectic or group-algebra facts used. + +## Proof and verification + +The retained logical interpreter works over the free group algebra on 72 named generators with exact rational coefficients. Both orientations reduce every one of 632 final input-field rows to its specified endpoint with no nonempty generator words left. Evaluation in any invertible matrix representation preserves this finite formal identity. It therefore applies to tensor-power address maps at every width. This argument evaluates a formal algebra identity; it does not assume tensor powers preserve sums. + +The independent Clifford lowering checks every one of 180 warp classes in both orientations, including absolute phase. It also checks all 448 main input/output monomial wrappers and 336 block-operator identities using tableaux and exact zero states. The all-width interface follows by tensoring each address-operator block identity separately. All scalar contacts, eight paid centers, helper repadding and monomial wrappers remain part of the real construction. A later consumer must charge the fixed native work of these wrappers; they are not zero-cost machine instructions. + +Reproduce with Python 3.12 or later, using only its standard library, on Windows or Linux: + +```sh +python3 -I -O -B research/native-quotient-interface/verify.py +``` + +The verifier authenticates every file, copies the package into a temporary directory, runs assertion-enabled isolated reconstruction subprocesses, compares regenerated mathematical payloads, and rejects independent source and artifact mutations. It does not require Git, SciPy, a GPU, Lean, the author's drives or a network connection. `-O` does not disable the retained source assertions because the child processes explicitly run without optimization. Fresh execution timings are not compared to frozen timing fields. An exact Laurent-polynomial check verifies the raw backward inverse transposes and their explicit even-power monomial conjugations, and rejects both formulas with the conjugation omitted. + +The supplementary [phase-form grammar](PHASE-FORM-GRAMMAR.md) proves an exact symmetric-form extension of subspace-only chart search, with a complete relative-rank formula and explicit Clifford realization. [PHASE-CUT.md](PHASE-CUT.md) gives sufficient binary minimum-cut models including the real rank-one/rank-two costs of formerly free warps. Its finite check exhausts all 153 Lagrangians in dimensions 1 through 3 and all 18,459 ordered pairs, with sampled exact phase lowering. The proof, rather than these small cases, establishes the general formula. + +## Bound status and practical use + +The old retained controller does not become profitable merely by inserting these two port types. Exact central parity accounting must cover chronological local calls, both scalar boundary programs, query shears, ordinary additions and final productive rank. The tested full parity model did not improve the invoice. Bounded phase searches also found no profitable certificate. These failures are search observations, not universal impossibility theorems and not the research result. + +There is no new best kappa in this package. PR #4635's conditional native Word RAM value remains a separate predecessor result with its own assumptions; this package does not re-audit or promote it. The independent arithmetic audit #4641 confirms that its numerical increase comes from #4610's paid profile, while the native transfer adds no numerical gain and provider admission remains separate. A useful next implementation can consume the supplied actual typed operator, or use the phase grammar, without repeating the map reconstruction or mistaking a changed frame for the old ABI. Nothing here uses a Turing-machine simulator or an unbounded-word arithmetic primitive. + +## Sources, overlap and credit + +The precise implementation closure and input hashes are in `SOURCE-CLOSURE.json`; all package bytes are bound by `CONTENT-HASHES.json`. The source snapshot is `f626db5c3a3d781d8f7695038776c621651f75e1`; quotient inputs originate from `b2998bacd50d57c301fe67c5392054440c42398c`, with the unchanged complex component of #4629. The source closure is vendored unchanged with its notices. `SOURCES.json` also pins the canonical-main provenance and task card. `OVERLAP.json` records the refreshed PR coverage and relevant heads; that coverage is not a claim of exhaustive historical review. + +Credit DaysSky for the quotient construction and local numerical exploration; Cao Yifan for #4610's joint helper/native-map search; Ryanson Jonathan for #4604's endpoint objection; Cinna Davis and the DreamingOfClouds/eumemic, PR589 and PR4470 supplier/controller lineage; Rohan Arun and the #4636 authors for concurrent contract review; Dugongue for the native Word RAM and transported-frame work; lm1909 for the independent #4641 arithmetic audit; Dillon for the exponent engine; zxv, Jacob Alan Sussman and all authors named in the retained Clifford and whole-job compiler sources. No independent human review or general mathematical novelty is claimed. The source notices retain more detailed predecessor attribution. + +## Open next questions + +1. Build a profitable controller for the exact A/B pair types. First reconstruct the complete central-gauge chronology, including both scalar boundaries and all paid corrections, then derive its full target/paid moment. A better local profile alone does not settle this task. +2. Find a profitable node-dependent symmetric phase schedule. First preserve the fixed main endpoint gauges, generate every physical bridge and warp, and recompute the full invoice from their exact lowerings. +3. If either route gives a positive moment, prove the complete native compiler and outer all-size admission with a funded strict exponent gap. 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b/research/native-quotient-interface/SOURCE-CLOSURE.json @@ -0,0 +1,64 @@ +{ + "schema": "typed-quotient-source-closure/1", + "source_commit": "f626db5c3a3d781d8f7695038776c621651f75e1", + "quotient_commit": "b2998bacd50d57c301fe67c5392054440c42398c", + "files": [ + { + "path": "research/joint-helper-lattice/native_joint.py", + "sha256": "50869b1bcad7493e6b4cb2a4cd5d2fd9a193a5921100483fa2c3f2c999ddfd46" + }, + { + "path": "research/joint-helper-lattice/PATCH.json", + "sha256": "296d0e8c58cc70febe042c681ef30d6bb469818c0835fbcaac8aa8d330f5b727" + }, + { + "path": "research/fresh-helper-boundary/native.py", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29" + }, + { + "path": "research/fresh-helper-boundary/CHANGES.json", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "sha256": 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"schema_version": 1, + "base_commit": "fbc9ea0249746acca4f504d4fda2b84e0e36cf0d", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395", + "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + } + ] +} diff --git a/research/native-quotient-interface/TASK.json b/research/native-quotient-interface/TASK.json new file mode 100644 index 0000000000..d4733c0463 --- /dev/null +++ b/research/native-quotient-interface/TASK.json @@ -0,0 +1,80 @@ +{ + "schema_version": 1, + "task_id": "uniform-transfer-audit", + "priority_revision": 7, + "base_commit": "fbc9ea0249746acca4f504d4fda2b84e0e36cf0d", + "original_card": { + "id": "uniform-transfer-audit", + "question": "Does one quantified step of the proposed #4100 all-size construction hold at its actual caller?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Prove one missing implication with explicit quantified hypotheses.", + "Find an exact counterexample at the claimed interface boundary." + ], + "acceptance_gate": "Identify the proposition and what would change downstream; do not equate a finite replay with a universal proof.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read PROOF.md and AUDIT.md in #4100. Select one distinct obligation: CRT total repair, native/free-algebra lifting, precision/conditioning, or complete fixed-tape cost. This is an author-submitted proof, not an accepted unconditional theorem.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Check live handoffs; name one proposition, its caller, quantified domain and dependency closure. Independently prove the implication or exhibit a precise gap/counterexample. Prioritize CRT.md total repair or COMPLEX.md free-algebra lift only if unclaimed. Stop at the chosen obligation; do not substitute finite samples or root arithmetic for an all-size proof, or launch the complete package by default.", + "bottleneck_link": "Finite supplier improvements are useful only under the retained transfer obligations.", + "allowed_variations": [ + "One CRT repair, native lift, precision/conditioning or tape-cost proposition, with its exact caller." + ], + "scope_change_triggers": [ + "Replacing a quantified obligation with another finite smoke test.", + "Treating archive intake, an author PASS receipt or a finite composed fixture as discharge of the universal hypotheses." + ], + "overlap_terms": [ + "uniform transfer", + "all-size", + "precision", + "4100", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #4100: proposed unconditional construction and finite checks, without independent acceptance.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Independent proof audit of one caller-bound all-size implication; all other premises remain explicit.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Construct native shared-warp repair and exact typed interfaces for the kernel-153 complex quotient, with a universal group-algebra evaluation proof and phase-chart extension theorem.", + "scope_change_reason": "User assigned investigation of unusually large quotient kappa claims and a superior native bound; actual endpoint contracts must be repaired before a bound can be claimed.", + "bottleneck_link": "The quotient profiles cannot be consumed by the retained controller until actual shared maps and full two-bank main operators are established.", + "budget_minutes": 60, + "stop_rule": "One bounded session; certify source bytes, all shared-map constraints, exact phases, typed interfaces and universal assembly statement. Do not claim a profitable controller without a complete invoice.", + "outcome": "completed", + "evidence": "TYPED-QUOTIENT-INTERFACE.md, FREE-GROUP-LIFT-REVIEW.md and verify.py provide the explicit constructive proof and exact source-bound replay.", + "author": "Dugongue", + "ai_assistance": "Prepared for Dugongue with substantial OpenAI Codex assistance; one coordinating worker and three parallel workers.", + "open_questions": [ + { + "question": "Can a controller consume the two certified port types profitably?", + "why_it_matters": "Would turn the improved local supplier into a genuine native bound.", + "first_step": "Use exact type A/B block matrices, carry central gauges through both scalar boundaries, and regenerate the full productive/paid invoice.", + "blocked_by": "No profitable complete controller certificate established here." + }, + { + "question": "Can nonzero symmetric phase forms improve the repaired supplier invoice?", + "why_it_matters": "The phase-form grammar adds chart freedoms absent from subspace-only retiming.", + "first_step": "Optimize node-dependent forms, then lower every actual paid bridge and native warp.", + "blocked_by": "A profitable complete phase schedule is not supplied." + } + ] +} diff --git a/research/native-quotient-interface/TYPED-PAIR-NORMALIZERS.json.gz b/research/native-quotient-interface/TYPED-PAIR-NORMALIZERS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..22cc543bf61456bc608ecb7a096cae09624efa27 GIT binary patch literal 7735 zcmV-79?0PziwFP!000023e{cPlG`|v{g-;?1MUR+ZTBmtcVfa((OsT)Ot48c0kKyH)x6j|--aq``+b`e0yubWp-}>_QpVwc$fB5y& z>p#DIe*OK!-(G(D{{G`__4hyD|NXb$-d^ABhrWIM`01BVcGUTwKfb^I@n&KC`SS78 zG@hnpn0~XPP%4I(Z{J_vzq@~9^K1JrI_xtPD zuW#>u&`+Pg{_y|t&zIldK7RMlpFTS*|0C>oCj%MyK!)Yne&;`4zrTO_&xiLf|8{3b z8GClbV83}dJv2HyUp{{P_7*<#>u;~$-u$co{qg$i`|I~lzsw_y$_{LYQPO|RIQq}A z*xz42|I7cE_fP-)%?|VV$M3(}zYdUp&VfueAxn?g%-2(vA-4a`k53V}Uw(WCPqD+w z?#6n=3r)Zouv`GMEx@B6d<^F$JmHX&rq`F0Wp*{-?;V3zkj*_E3i(Uz zjA+GQIxv6?&;*2E42hRPp+RX&1{RE)?4{1T%>%h$+F86tB?)5MO)TPAaa@W1JGkGOOUVa#PgNW_FQedUNaHU4uZmc#F#A~?VLwxM(*>-%40F^hjt+0f zTL)){e zohpiOhDEgqGfaeC)VnSY?S+>tfwbq07QkDmI6NC&Z%9g`2}&B(5tegFDi<0bEG$q~HOELDE z!`NFI-DT0j3_Xv%XTZ&6FA&oOre7`<{20>_9))T|;fn!>cr3gLv)Eh;;Bglx*u*qO zv#}^S!is*baI|Oeg~HLnA_c?Iz$DBJM|(TkjU%GZIW!!tf*oBEj&5Z~GorG?(W<)? 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Apache-2.0. + +This note is a sufficient consumer construction after the quotient word's ACTUAL typed normal forms and monomial wrappers have been independently established. It does not infer those types from frame dimensions. Use the corrected physical-row convention: X is the first 112-role bank and Y the second. A type-B extra central transform is on physical Y, in both orientations. + +Let Q be the retained symmetric one-axis central Gaussian operator, Q^T=Q, with Q^2 an explicitly known monomial, and D_s a symmetric seven-axis Gaussian on disjoint fresh axes, D_s^T=D_s and D_s² monomial. Hence Q commutes with every D_s. Forward typed local operators are + + A_s = diag(D_s,D_s) S_y(Q^-1), + B_s = diag(D_s,Q D_s) S_y(Q^-1). + +Their retained backward-dual forms are + + A_s^dual = diag(D_s^-T,D_s^-T) S_x(-Q^-1), + B_s^dual = diag(D_s^-T,Q^-1 D_s^-T) S_x(-Q^-1). + +These are the raw inverse transposes, using Q^T=Q. To obtain the retained controller shear S_x(-Q), explicitly apply input-Y Q² and output-Y Q^-2; then apply D_s² on both output rows to convert D_s^-T=D_s^-1 into D_s. These are paid volume-linear monomial wrappers, checked with absolute phases. Explicitly set R=diag(I,Q²), L=diag(I,Q^-2), and P=diag(D_s²,D_s²). Direct block multiplication gives + + P L A_s^dual R = diag(D_s,D_s) S_x(-Q), + P L B_s^dual R = diag(D_s,Q^-1 D_s) S_x(-Q). + +The rightmost input wrapper R acts first; the leftmost output wrapper P acts last. Both equations retain their exact even powers and phases. The inverse exponent in B_s^dual does not change the parity flip: it is still physical Y. These formulas are subject to the exact typed normal-form certificate. A previous provisional X/Y assignment was incorrect and must not be used as evidence. + +## Row gauges and their exact meaning + +Put Q^a on a controller row, a an integer. For a logical shear that adds epsilon Q^k times source row j into target row i, conjugation by row gauges gives physical coefficient + + epsilon Q^(k+a_i-a_j). + +This is an exact operator equation. Reduce exponents modulo two only for the Fourier-rank invoice; retain every even exponent as its explicit monomial Q^(2m). Signs and those monomial wrappers remain in the actual circuit. An odd central exponent costs one rank-one Gaussian job; an even exponent is monomial. No exact statement Q^2=I is assumed. + +Therefore: + +- a plain ADD, k=0, is scalar/monomial when row parities agree and costs a rank-one job when they differ; +- a QUERY shear, k odd, is scalar/monomial when row parities differ and costs a rank-one job when they agree; +- a signed swap carries row gauges along with its swapped rows; a swap is not permission to relabel a physical Y extra as an X extra. + +A paid rank-one shear coefficient can be implemented with one owned temporary: COPY the source, apply the central Q or Q^-1 Gaussian job with its exact even-power monomial, add the result to the target, then CLEAR the owned temporary. All four stages are charged by the native implementation. The original source remains intact. This uses the admitted owned-erasure convention; it cannot be applied to dirty borrowed storage. + +## Local type incidence constraints + +To consume A_s or B_s as the retained logical A_s under row gauges without an additional corrective Gaussian, require equal input parities on X and Y. Type A carries both parities through unchanged. Type B carries X through unchanged and flips Y. The same incidence rule holds in the controller-compatible backward orientation only after the explicit monomial wrappers above, with its actual S_x shear and inverse central exponent. The raw inverse transpose alone has shear -Q^-1 and must not be relabelled -Q. + +These constraints follow by conjugating the complete two-row operator, not by observing a changed main chart. If the two input parities disagree, either an explicitly priced central gauge change or an explicitly priced corrective shear is needed. A consumer may optimize those choices, but may not impose the free incidence rule and silently ignore incompatible events. + +## Productive target credit + +For a diagonal output row whose retained logical endpoint is + + Q^m product_s D_s^(e_s), + +the actual endpoint with final row gauge Q^a is Q^(m+a) product_s D_s^(e_s). If the e_s are the retained 0/1 fresh-slot exponents, its exact Gaussian rank is + + 7 sum_s e_s + ((m+a) mod 2). + +All signs, inverse orientations and even powers belong to explicit monomial normalizers. A final parity bit alone is not a productive credit. In particular when m is odd, final parity one REMOVES the central productive rank; it does not add one. Initial main gauges are fixed to preserve the requested input ABI. If an optimizer changes helper entrance gauges, the independent-helper zero cross-block condition must be retained as in the phase-flow theorem. + +## Complete admission + +A candidate parity schedule must reconstruct every chronological LOCAL, IDLE, ADD, QUERY and signed swap, include every extra central child and every final productive central rank, then check the resulting exact matrix endpoints. The ambient block is seven, not eight: an unused local coordinate does not earn an eight-axis ladder or diagonal credit. Any extra central primitive, transport, owned copy and monomial wrapper is actually emitted and paid. The full target/paid moment, compiler, precision and outer native assembly must then be certified anew. + +This is a constructive sufficient consumer interface and a precise optimizer specification. It reports no profitable parity schedule, no admission of a malformed quotient warp, and no new kappa. Credit the actual typed quotient normalizer, Cinna Davis's local supplier/controller lineage, the query-thinned controller authors, Dugongue's native Word RAM/phase-gauge construction, and the retained Gaussian/Clifford/whole-job compiler sources. + +## Equivalent type-B factorization + +The corrected forward type B also has the exact identity + + diag(1,Q) S_y(Q^-1) = S_y(1) diag(1,Q). + +Both sides send (X,Y) to (X,X+QY). Thus the extra central Q may be viewed as an input-Y transform followed by a plain scalar ADD. This is an operator identity including signs and inverse powers as written, not a free replacement of Q by I. It may help a new controller derivation, but the complete chronological controller polynomial and all output central exponents still have to be recomputed. diff --git a/research/native-quotient-interface/TYPED-QUOTIENT-INTERFACE.md b/research/native-quotient-interface/TYPED-QUOTIENT-INTERFACE.md new file mode 100644 index 0000000000..bf4ff1af66 --- /dev/null +++ b/research/native-quotient-interface/TYPED-QUOTIENT-INTERFACE.md @@ -0,0 +1,136 @@ +# A physically realized mixed seven-axis quotient supplier + +Prepared for Dugongue with substantial OpenAI Codex assistance. Apache-2.0. + +## Sufficient constructive statement + +Starting with the credited kernel-153 complex quotient word, there is an explicit replacement of its 72 shared native address maps and explicit monomial input/output normalizers on every main port such that: + +- Every actual shared native warp has rank zero and an exact monomial realization, including its absolute phase and inverse-transpose orientation. +- The complete local paid profile is unchanged: + + P={1:2177,2:424,3:389,4:147,5:50,8:8}. + +- All 408 arbitrary independent helpers retain their actual whole-job target census: + + H={3:2,6:7,7:47,8:139,9:213}. + +- Of the 112 independent main pairs, exactly 56 realize + + F_A=D S_y(Q⁻¹), + + and exactly 56 realize + + F_B=diag(D,QD) S_y(Q⁻¹). + +Here D is the Gaussian transform on seven fresh address axes, Q is the Gaussian transform on a separate central axis, and the ninth axis is a spectator. In the field ordering X=roles 0 through 111 and Y=roles 112 through 223, the extra central Q in type B acts on Y, the target of the forward shear. The backward interface is the inverse transpose of the corresponding forward matrix. These statements hold at every digit-column fiber width f, with D and Q replaced by their f-column counterparts. + +This is a sufficient typed local interface. It establishes neither the old common rank-eight interface nor a completed improved multiplication bound. Its main purpose is to give a controller an actual proved operator to consume, instead of pricing changed output charts as though they were unchanged. + +## 1. Repair all shared native maps constructively + +Let H₈ denote the image of the nine-dimensional ambient under the kernel-153 quotient. Before spectator padding it is the coordinate eight-plane. Every native operator has a shared contract H₈→H₈ and one additional equal-dimensional pair A→B. Twelve operators also have a nonzero line a→b. In the submitted finite word the line belongs to A if and only if b belongs to B. These incidences are checked explicitly, not inferred from dimensions alone. + +For a two-subspace contract, choose bases of A and B and extend each to H₈. Mapping corresponding basis vectors gives an invertible map on H₈. For a line plus subspace, put a and b first in their respective bases if they belong to A and B; otherwise first choose bases of A and B, then append a and b. Extend both lists to bases of H₈. Map the corresponding bases, and fix the unused ninth coordinate. This constructs one invertible G for every operator, satisfying all occurrences of that operator simultaneously. Negative occurrences use its inverse. + +Use the native monomial K_G specified by the retained source. Every actual physical warp is + + C_input.adjoint().then(K_G).then(C_output), + +or uses K_G⁻¹ for a negative occurrence. The canonical-frame Lagrangian formula implies its Fourier rank is zero whenever G maps the input subspace onto the output subspace. The exact Clifford lowering constructs the monomial and checks its tableau and absolute phase. Shared-map consistency is essential: separately choosing a map at each occurrence would not preserve the arbitrary-input symbolic identity. + +The exact emitted word passes both retained literal interpreters on all 632 arbitrary-input fields in both orientations. Therefore replacing the shared operators preserves the source's formal all-column identity, with no initialized-helper assumption. All 180 actual warp classes were freshly lowered in both orientations and had exact rank zero, including absolute phases. No Fourier call is hidden inside a supposed free warp. The eight paid center operations and every helper-final repadding call are included in P. + +## 2. The exact two-field endpoint before normalization + +At every main pair, X starts in the central line c and ends in H₈. Y starts at ground and ends in a subspace A. Writing C_H, C_c and C_A for the exact canonical frame operators, the forward physical block matrix is + + [ C_H C_c⁻¹ 0 ] + M = [ C_A C_c⁻¹ C_A ]. + +There are precisely two cases: + +- Type A: dim A=7, A⊂H₈, and c∉A, so A⊕c=H₈. +- Type B: A=H₈. + +Both cases occur 56 times. These are properties of the literal source frames, independently checked for each port. The distinction is why a uniform common rank-eight replacement was invalid. + +## 3. Explicit monomial normalizers + +Choose standard central axis e₀ and standard seven-plane E=span(e₁,…,e₇). Put Q=C_e₀ and D=C_E. They act on disjoint axes, so they commute. + +In type A, choose an invertible binary map G sending e₀ to c and E to A. It consequently sends span(e₀,E) to H₈. In type B, choose G sending e₀ to c and span(e₀,E) to H₈. Extend it on the spectator coordinate. Let N=K_G, an explicit native monomial. Define + + T_Y=D in type A, + T_Y=QD in type B, + + M_Y=N, + M_X=C_c N Q⁻¹, + O_X=D Q N⁻¹ C_H⁻¹, + O_Y=T_Y N⁻¹ C_A⁻¹. + +All products use ordinary matrix multiplication, with the rightmost factor applied first. + +Each of the four M_X,M_Y,O_X,O_Y is monomial. To see this without assuming an oracle, use + + L_U=C_U(L₀)={(x,z):x∈U, x+z∈U⊥}. + +The monomial K_G sends L_U to L_GU. Every canonical frame is involutory at the symplectic level. Therefore M_X sends L₀ to L₀ because N sends L_e₀ to L_c. Likewise O_X sends L₀ to L₀ because N sends L_span(e₀,E) to L_H₈. In type A, O_Y is monomial because N sends L_E to L_A; in type B use L_span(e₀,E) instead. A Clifford preserving L₀ is monomial. Exact lowering resolves its affine permutation, quadratic phase and absolute scalar phase. + +Direct multiplication, without approximation, gives + + O_X (C_H C_c⁻¹) M_X = D, + O_Y C_A M_Y = T_Y, + O_Y (C_A C_c⁻¹) M_X = T_Y Q⁻¹. + +Thus diag(O_X,O_Y) M diag(M_X,M_Y) is exactly F_A or F_B as claimed. No independently chosen column is credited twice; the wrappers act on the original two independent main inputs and their actual outputs. Helpers remain independent and unchanged by these external main-only wrappers. + +The monomial wrappers are explicit finite nonrecursive operations. They must be counted in any subsequent finite-template route/scalar allowance; they are not zero-cost machine instructions. Their degree, coordinate dimension and coefficients are fixed, so they contribute fixed linear per-record work under the native lowering. All their phases have modulus one, so the wrappers do not introduce a growing conditioning loss. + +## 4. Inverse transpose and every fiber width + +The actual backward source word uses the inverse-transpose logical identity and the corresponding conjugated frame operators. If F=O M N is the forward identity, then + + F⁻ᵀ=O⁻ᵀ M⁻ᵀ N⁻ᵀ. + +The inverse transpose of a monomial is monomial. Hence the normalized backward type is exactly F_A⁻ᵀ or F_B⁻ᵀ, rather than an independently guessed orientation. The extra central Q is on physical Y before taking this dual; its exponent changes sign under inverse transpose. + +For fiber width f, tensor each ADDRESS-OPERATOR block identity f times. For example, from O_X A_X M_X=D one obtains O_X^(⊗f) A_X^(⊗f) M_X^(⊗f)=D^(⊗f). Apply the same argument separately to the Y diagonal and the off-diagonal coefficient. This preserves the two-field block shape and scalar coefficient 1. It does not tensor the entire 2×2 field matrix, which would create additional field rows. Monomial tensor powers remain explicit monomials, and the chronological arbitrary-input identity at every fiber width follows from the independent free-group-algebra argument below. + +## 5. A universal free-group-algebra evaluation proof + +The logical endpoint is not inferred by tensoring a numerical one-column field matrix. The retained literal interpreter computes a stronger symbolic identity. + +Let F be the free group on 72 named generators g₁,…,g₇₂ and R=Q[F] its group algebra. A row is a finitely supported map from pairs (initial field, reduced group word) to rational coefficients. Initialize each of the 632 persistent fields as its own basis vector. The owned C field is also represented symbolically until it is explicitly cleared. Process every record as follows: + +- A native warp with signed operator i multiplies each coefficient on the LEFT by g_|i| or its inverse. The implementation prepends the signed symbol and removes it only when it cancels the adjacent inverse symbol. +- ADD and SCALE perform exact rational module arithmetic. COPY duplicates the source expression only into permitted owned storage. CLEAR sets only permitted owned storage to zero. +- A paid frame change is the identity on logical values; its physical conjugating frame operators are accounted separately. Phase and adapter markers do not modify the logical row. + +These are precisely module operations in the free R-module on the initial field symbols. Induction on the record index therefore proves that the interpreter's row is the corresponding formal logical expression, before any native operator has been assigned a numerical matrix. In particular, no relation such as commutation, finite order, dimension, a chosen binary G map, or a one-column coincidence is used. + +At termination, the checked forward rows are X_i↦X_i, Y_i↦Y_i+X_i and h_j↦h_j; the backward rows are X_i↦X_i−Y_i, Y_i↦Y_i and h_j↦h_j. Every surviving coefficient has the EMPTY group word. The owned C row is zero. The fresh receipt records 632 persistent rows, 744 exact terms and zero nonempty group words in each orientation. Changing one occurrence to a new unshared generator produces a nonzero endpoint difference and is explicitly rejected. + +Now take any vector space V over Q or C and assign ANY invertible linear operator T_i∈GL(V) to each shared generator. Send a reduced word to the ordered product of those operators and extend Q-linearly. This is a well-defined algebra homomorphism R→End(V): the only reduction used, g_i g_i⁻¹=1, is valid because T_i is invertible. Extending it componentwise to module rows sends every step of the formal computation to the actual vector-valued operation. Hence the final formal identity proves the same endpoint for arbitrary independent V-valued inputs. + +Apply this evaluation independently at every fiber width f, assigning the explicitly constructed shared K_G,f and their inverses. The same operator must be used at every occurrence of its name; this is why the simultaneous shared-map construction in section 1 was required. The 72 new maps satisfy that condition. The backward interpreter uses a separately named set of generators, so the result also applies to the inverse-transpose assignments. This proves the changed word's universal logical all-fiber endpoint directly. The only tensor arguments needed are for individual frame/normalizer operator identities, where tensor powers do preserve composition; no assertion that tensor powers preserve sums is made. + +This evaluation theorem is completely separate from a contraction or a complete multiplication algorithm. It proves the arbitrary-input operator identity and does not supply a favorable paid invoice by itself. + +## 6. Controller relevance and paid obligations + +The type-B identity has a useful exact rewriting: + + diag(1,Q) S_y(Q⁻¹)=S_y(1) diag(1,Q). + +Also Q² is monomial. This permits central-parity row gauges that can change whether a query coefficient requires a rank-one Gaussian call. It does not make all queries free: an ADD across different central gauges can itself require a paid rank-one call. A complete controller must charge every such bridge and derive its final central target parities from the actual diagonal operator. The seven-axis target ranks cannot be priced with the old eight-axis invoice. + +The receipt intentionally states only a typed local supplier. A full contraction, compiler, native caller and larger κ must be proved using the resulting complete paid and productive profiles. + +## Evidence, source status and credit + +`repair_shared_warps.py` constructs the repaired 72 shared maps, resynthesizes the word, performs two-interpreter arbitrary-input replay and lowers all actual warp classes in both orientations. Its word payload SHA-256 is `599da9a45213bc4cd98d897d6bd00e5e4bc2af8160e90ec50aec467e0c6236eb`. + +`typed_pair_normalizers.py` constructs all 448 monomial wrappers, lowers them with absolute phases and checks all 336 block identities by exact tableaux and exact zero-state vectors. Its normalizer payload SHA-256 is `7617a2893f7cb117beb35c499a02feac3d2b0a6b3e60bdd4aa198a680a26ab54`. The check takes about 18 seconds with CPython 3.12. These are exact finite certificates plus the all-fiber argument above, not Lean verification or an independent human review. + +Credit DaysSky for the kernel quotient and helper repadding in #4596/#4629/#4633; Nick Petalas for the quotient family classification in #4627; Ryanson Jonathan for the endpoint-frame audit in #4604; Cinna Davis and the PR #4470 native/helper word; Cao Yifan for the shared-generator interface work in #4610; Dugongue for the transported/arbitrary-frame and native Word RAM work; zxv and Jacob Alan Sussman for retained native and compiler/matching results; and all original source notices. The new contribution here is the explicit shared-map repair, universal free-group-algebra evaluation argument, and exact typed mixed seven-axis normal form, not an assertion that the original quotient already supplied the old operator. diff --git a/research/native-quotient-interface/VERIFY.json b/research/native-quotient-interface/VERIFY.json new file mode 100644 index 0000000000..9fb097f8d3 --- /dev/null +++ b/research/native-quotient-interface/VERIFY.json @@ -0,0 +1,59 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/native-quotient-interface/.gitattributes", + "research/native-quotient-interface/CONTENT-HASHES.json", + "research/native-quotient-interface/FREE-GROUP-LIFT-REVIEW.md", + "research/native-quotient-interface/LICENSE", + "research/native-quotient-interface/OVERLAP.json", + "research/native-quotient-interface/PHASE-CUT.md", + "research/native-quotient-interface/PHASE-FORM-GRAMMAR.md", + "research/native-quotient-interface/phase_form_check.py", + "research/native-quotient-interface/QUOTIENT-PROGRAMS.json.gz", + "research/native-quotient-interface/QUOTIENT-WORD.json.gz", + "research/native-quotient-interface/README.md", + "research/native-quotient-interface/repair_shared_warps.py", + "research/native-quotient-interface/REPAIRED-WARP-PHASES.json.gz", + "research/native-quotient-interface/REPAIRED-WARP-RECEIPT.json", + "research/native-quotient-interface/REPAIRED-WARP-WORD.json.gz", + "research/native-quotient-interface/SOURCE-CLOSURE.json", + "research/native-quotient-interface/SOURCES.json", + "research/native-quotient-interface/TASK.json", + "research/native-quotient-interface/TYPED-PAIR-NORMALIZERS.json.gz", + "research/native-quotient-interface/TYPED-PAIR-RECEIPT.json", + "research/native-quotient-interface/TYPED-PARITY-CONSUMER.md", + "research/native-quotient-interface/TYPED-QUOTIENT-INTERFACE.md", + "research/native-quotient-interface/typed_pair_normalizers.py", + "research/native-quotient-interface/v/research/fresh-helper-boundary/CHANGES.json", + "research/native-quotient-interface/v/research/fresh-helper-boundary/native.py", + "research/native-quotient-interface/v/research/joint-helper-lattice/native_joint.py", + "research/native-quotient-interface/v/research/joint-helper-lattice/PATCH.json", + "research/native-quotient-interface/v/research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "research/native-quotient-interface/v/research/kappa-function-composition/complex/prune_native.py", + "research/native-quotient-interface/v/research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/native-quotient-interface/v/research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/native-quotient-interface/v/research/kappa-rebuild/complex/native_extensions.py", + "research/native-quotient-interface/v/research/kappa-rebuild/complex/power_two_balance.py", + "research/native-quotient-interface/v/research/kappa-rebuild/complex/rebuild_native.py", + "research/native-quotient-interface/v/research/missing-join-frame/PATCH.json", + "research/native-quotient-interface/v/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "research/native-quotient-interface/VERIFY.json", + "research/native-quotient-interface/verify.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 240, + "checks": "Authenticate all frozen bytes; reconstruct 72 shared native maps, both formal arbitrary-input identities, 360 warp orientations and phases, 448 main wrappers and 336 exact block identities; enumerate 153 small Lagrangian charts and 18,459 pair ranks; reject source mutations. Verify raw backward inverse transposes and explicit monomial conjugations, rejecting both missing-conjugation controls." + } + ] +} diff --git a/research/native-quotient-interface/phase_form_check.py b/research/native-quotient-interface/phase_form_check.py new file mode 100644 index 0000000000..9f45862a50 --- /dev/null +++ b/research/native-quotient-interface/phase_form_check.py @@ -0,0 +1,78 @@ +"""Exact small-space phase-form checks; Apache-2.0. +Dugongue with substantial OpenAI Codex assistance. +The Clifford implementation is a caller-specified frozen source input. +""" +from pathlib import Path +import importlib.util,sys,argparse,json,hashlib + +def rank(vs): + piv={} + for v in vs: + while v: + i=v.bit_length()-1 + if i not in piv:piv[i]=v;break + v^=piv[i] + return len(piv) + +def basis(s): + out=[] + for x in sorted(s): + if rank(out+[x])>len(out):out.append(x) + return out + +def span(vs): + s={0} + for v in vs:s|={x^v for x in tuple(s)} + return s + +def spaces(n): + return [s for mask in range(1<<(1<>i&1}] + if all(x^y in s for x in s for y in s)] + +def check(path): + p=Path(path);sp=importlib.util.spec_from_file_location('phase_form_ce',p) + ce=importlib.util.module_from_spec(sp);sys.modules[sp.name]=ce;sp.loader.exec_module(ce) + def mul(A,B,n): + cols=ce.transpose(B,n) + return tuple(sum(((row&col).bit_count()%2)<>k&1:S[i]^=1< len(B): + B.append(x) +Gs = {} +checks = [] +for op, ps in sorted(pairs.items()): + ps = sorted(ps, key=lambda ab: len(spaces[ab[0]])) + small = [ab for ab in ps if len(spaces[ab[0]]) < 256] + if not len(small) in (1, 2): + raise ValueError('Exact check failed at original source line 39') + if len(small) == 2: + (a, b), (A, B) = small + if not len(spaces[a]) == len(spaces[b]) == 2: + raise ValueError('Exact check failed at original source line 41') + av = next(iter(spaces[a] - {0})) + bv = next(iter(spaces[b] - {0})) + ain = av in spaces[A] + if not ain == (bv in spaces[B]): + raise ValueError('Exact check failed at original source line 42') + if ain: + ib = [av] + ob = [bv] + else: + ib = [] + ob = [] + for x in basis(spaces[A]): + independent_append(ib, x) + for x in basis(spaces[B]): + independent_append(ob, x) + if not ain: + ib.append(av) + ob.append(bv) + else: + a, b = small[0] + ib = basis(spaces[a]) + ob = basis(spaces[b]) + if not len(ib) == len(ob): + raise ValueError('Exact check failed at original source line 50') + for i in range(8): + independent_append(ib, 1 << i) + independent_append(ob, 1 << i) + if not len(ib) == len(ob) == 8: + raise ValueError('Exact check failed at original source line 52') + ib.append(256) + ob.append(256) + image = {0: 0} + for a, b in zip(ib, ob): + image.update({x ^ a: y ^ b for x, y in tuple(image.items())}) + if not len(image) == len(set(image.values())) == 512: + raise ValueError('Exact check failed at original source line 55') + for a, b in ps: + if not frozenset((image[x] for x in spaces[a])) == spaces[b]: + raise ValueError('Exact check failed at original source line 56') + Gs[op] = [image[1 << i] for i in range(9)] + checks.append(dict(operator=op, declared_pairs=len(ps), all_512_columns_bijective=True, all_shared_frame_pairs=True)) +if not set(Gs) == set(range(1, 73)): + raise ValueError('Exact check failed at original source line 59') +for w in c['warps']: + w['G_columns'] = Gs[w['op']] +programs = {d: F.synthesize(c, p) for d, p in rawprograms.items()} +profiles = {} +literal = {} +formal = {} +for d, p in programs.items(): + rows, rec = X.literal_replay(V, c, p, d == 'backward') + if not all((rows['L', r] == V.expected(('L', r), [], d == 'backward', False) for r in range(632))): + raise ValueError('Exact check failed at original source line 63') + profiles[d] = {int(k): n for k, n in rec['paid_profile'].items()} + rebound = deepcopy(c) + rebound['local_profile'] = profiles[d] + V.replay(p, rebound, [], d == 'backward', False) + literal[d] = rec + rows_items = [(r, rows['L', r]) for r in range(632)] + nonempty = sum((bool(word) for r, row in rows_items for variable, word in row)) + if not nonempty == 0: + raise ValueError('Exact check failed at original source line 66') + formal[d] = dict(persistent_rows=632, exact_formal_terms=sum((len(row) for r, row in rows_items)), nonempty_warp_words=nonempty, owned_C_terms=len(rows['C', 0]), coefficient_ring='Q', operator_ring='free group algebra on shared native symbols; no matrix substitution', endpoint='identity on 408 helpers and original signed identity shear on 224 main logical fields') +if not profiles['forward'] == profiles['backward'] == {1: 2177, 2: 424, 3: 389, 4: 147, 5: 50, 8: 8}: + raise ValueError('Exact check failed at original source line 68') +bad = deepcopy(programs['forward']) +next((e for e in bad if e[0] == 'warp'))[2] = 999 +_badrows, _ = X.literal_replay(V, c, bad, False) +if not any((_badrows['L', r] != V.expected(('L', r), [], False, False) for r in range(632))): + raise ValueError('Exact check failed at original source line 71') +formal['shared_symbol_negative_control'] = dict(changed_one_occurrence_to_fresh_symbol=True, rejected_by_nonzero_exact_endpoint_difference=True) +framecache = {} +K = {} + +def frame(a): + if a not in framecache: + framecache[a] = ce.canonical_frame(9, c['frames'][a]) + return framecache[a] +for op, cols in Gs.items(): + G = ce.transpose(tuple(cols), 9) + gi = ce.inv(G, 9) + tr = ce.transpose(gi, 9) + Q = tuple((1 << i ^ sum((ce.parity(a & b) << j for j, b in enumerate(tr))) for i, a in enumerate(tr))) + K[op] = ce.perm(9, G).then(ce.diag(9, Q)) +classes = sorted({tuple(e[2:5]) for e in programs['forward'] if e[0] == 'warp'}) +phase = [] +st = time.monotonic() +for i, (op, a, b) in enumerate(classes): + body = K[abs(op)] if op > 0 else K[abs(op)].adjoint() + actual = frame(a).adjoint().then(body).then(frame(b)) + ds = {} + for d in ('forward', 'backward'): + physical = P.conjugate(ce, actual) if d == 'backward' else actual + rec = X.N.lower_exact(P, ce, physical) + if not (rec['rank'] == 0 and rec['right'] is None): + raise ValueError('Exact check failed at original source line 84') + ds[d] = rec + phase.append(dict(operator=op, input=a, output=b, recipes=ds)) + if i % 30 == 0: + print('PHASE', i + 1, '/', len(classes), flush=True) +payload = {'canonical': c, 'programs': programs} +data = (json.dumps(payload, sort_keys=True, separators=(',', ':')) + '\n').encode() +(H / 'REPAIRED-WARP-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0)) +out = dict(status='PASS_SHARED_MAP_QUOTIENT_WARPS_ONLY_CANONICAL_MAIN_STILL_OPEN', paid=profiles, shared_maps=checks, actual_warp_classes=len(classes), both_orientation_absolute_phase=True, canonical_payload_sha256=sha256(data).hexdigest(), phase_seconds=time.monotonic() - st, formal_cancellation=formal, scope='Changed supplier main charts retained; not a canonical supplier or kappa certificate') +(H / 'REPAIRED-WARP-RECEIPT.json').write_text(json.dumps(out, indent=2)) +(H / 'REPAIRED-WARP-PHASES.json.gz').write_bytes(gzip.compress(json.dumps(phase, sort_keys=True).encode(), mtime=0)) +print(json.dumps({k: v for k, v in out.items() if k != 'shared_maps'}, indent=2)) diff --git a/research/native-quotient-interface/typed_pair_normalizers.py b/research/native-quotient-interface/typed_pair_normalizers.py new file mode 100644 index 0000000000..63a755dc0e --- /dev/null +++ b/research/native-quotient-interface/typed_pair_normalizers.py @@ -0,0 +1,123 @@ +"""Portable exact typed quotient checker. Apache-2.0; substantial AI assistance.""" +from pathlib import Path +from collections import Counter +from hashlib import sha256 +import json, gzip, sys, time +import argparse +_parser = argparse.ArgumentParser() +_parser.add_argument('--source-root', required=True, type=Path) +_args = _parser.parse_args() +H = Path(__file__).resolve().parent +R = _args.source_root.resolve() +_manifest = json.loads((H / 'SOURCE-CLOSURE.json').read_text(encoding='utf-8')) +for _row in _manifest['files']: + if not sha256((R / _row['path']).read_bytes()).hexdigest() == _row['sha256']: + raise ValueError('Changed source: ' + _row['path']) +for _name, _hash in _manifest['owned_inputs'].items(): + if not sha256((H / _name).read_bytes()).hexdigest() == _hash: + raise ValueError('Changed quotient artifact: ' + _name) +sys.path.insert(0, str(R / 'research/joint-helper-lattice')) +import native_joint as J +F = J.F +ce = F.load(R / 'research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py', 'typed_nf_ce') +P = F.load(R / 'research/kappa-function-composition/complex/prune_native.py', 'typed_nf_decode') +X = F.load(R / 'research/kappa-rebuild/complex/native_extensions.py', 'typed_nf_lower') +_repaired_raw = gzip.decompress((H / 'REPAIRED-WARP-WORD.json.gz').read_bytes()) +if not sha256(_repaired_raw).hexdigest() == _manifest['repaired_payload_sha256']: + raise ValueError('Exact check failed at original source line 20') +z = json.loads(_repaired_raw) +c = z['canonical'] +cache = {} + +def frame(i): + if i not in cache: + cache[i] = ce.canonical_frame(9, c['frames'][i]) + return cache[i] + +def sp(b): + s = {0} + for v in b: + s |= {x ^ v for x in tuple(s)} + return frozenset(s) + +def basis(s): + b = [] + cur = {0} + for v in sorted(s): + if v not in cur: + b.append(v) + cur |= {x ^ v for x in tuple(cur)} + return b + +def extend(B, more): + for v in more: + if ce.rank(B + [v]) > len(B): + B.append(v) + return B + +def Kop(cols): + G = ce.transpose(tuple(cols), 9) + gi = ce.inv(G, 9) + tr = ce.transpose(gi, 9) + quad = tuple((1 << i ^ sum((ce.parity(a & b) << j for j, b in enumerate(tr))) for i, a in enumerate(tr))) + return ce.perm(9, G).then(ce.diag(9, quad)) + +def equal(a, b): + return a.tab == b.tab and a.zero_state() == b.zero_state() +D = ce.fourier(9, range(1, 8)) +Q = ce.cgate(9, 1) +out = [] +st = time.monotonic() +kinds = Counter() +for port in range(112): + sx, sy = (c['start'][port], c['start'][112 + port]) + hy, ax = (c['final'][port], c['final'][112 + port]) + if not (not c['frames'][sy] and len(c['frames'][sx]) == 1): + raise ValueError('Exact check failed at original source line 43') + cvec = c['frames'][sx][0] + AA = sp(c['frames'][ax]) + HH = sp(c['frames'][hy]) + if not (len(HH) == 256 and cvec in HH): + raise ValueError('Exact check failed at original source line 44') + if len(AA) == 128: + kind = 'A' + if not (cvec not in AA and AA < HH): + raise ValueError('Exact check failed at original source line 46') + cols = [cvec] + basis(AA) + TY = D + else: + kind = 'B' + if not AA == HH: + raise ValueError('Exact check failed at original source line 48') + cols = extend([cvec], basis(HH)) + TY = D.then(Q) + cols = extend(cols, [1 << i for i in range(9)]) + if not len(cols) == 9: + raise ValueError('Exact check failed at original source line 49') + MY = Kop(cols) + Cc, CA, CH = (frame(sx), frame(ax), frame(hy)) + AX = Cc.adjoint().then(CH) + MX = Q.adjoint().then(MY).then(Cc) + OX = CH.adjoint().then(MY.adjoint()).then(Q).then(D) + OY = CA.adjoint().then(MY.adjoint()).then(TY) + wrappers = {} + for name, op in [('input_X', MX), ('input_Y', MY), ('output_X', OX), ('output_Y', OY)]: + rec = X.N.lower_exact(P, ce, op) + if not (rec['rank'] == 0 and rec['right'] is None): + raise ValueError('Exact check failed at original source line 56') + wrappers[name] = rec + if not equal(MX.then(AX).then(OX), D): + raise ValueError('Exact check failed at original source line 57') + if not equal(MY.then(CA).then(OY), TY): + raise ValueError('Exact check failed at original source line 58') + if not equal(MX.then(Cc.adjoint()).then(CA).then(OY), Q.adjoint().then(TY)): + raise ValueError('Exact check failed at original source line 59') + kinds[kind] += 1 + out.append(dict(port=port, kind=kind, center_vector=cvec, frames=dict(start_X=sx, start_Y=sy, final_X=hy, final_Y=ax), address_map_columns=cols, wrappers=wrappers, exact_diagonal_X=True, exact_diagonal_Y=True, exact_shear_coefficient=True)) + if port % 16 == 0: + print('PAIR', port, '/', 112, flush=True) +payload = json.dumps(out, sort_keys=True, separators=(',', ':')).encode() +(H / 'TYPED-PAIR-NORMALIZERS.json.gz').write_bytes(gzip.compress(payload, mtime=0)) +receipt = dict(status='PASS_EXACT_TYPED_QUOTIENT_PAIR_NORMAL_FORM', port_types=dict(kinds), ports=112, exact_monomial_normalizers=448, exact_block_identities=336, absolute_phases=True, source_word_payload_sha256=sha256(gzip.decompress((H / 'REPAIRED-WARP-WORD.json.gz').read_bytes())).hexdigest(), normalizers_payload_sha256=sha256(payload).hexdigest(), seconds=time.monotonic() - st, forward_type_A='D S_y(Q^-1)', forward_type_B='diag(D,QD) S_y(Q^-1)', D_rank=7, Q_rank=1, Q_squared='monomial', scope='Typed local supplier, not old rank-eight interface or a completed multiplication theorem') +(H / 'TYPED-PAIR-RECEIPT.json').write_text(json.dumps(receipt, indent=2)) +print(json.dumps(receipt, indent=2)) diff --git a/research/native-quotient-interface/v/research/fresh-helper-boundary/CHANGES.json b/research/native-quotient-interface/v/research/fresh-helper-boundary/CHANGES.json new file mode 100644 index 0000000000..45744fedd0 --- /dev/null +++ b/research/native-quotient-interface/v/research/fresh-helper-boundary/CHANGES.json @@ -0,0 +1,562 @@ +{ + "entrances": [ + [448, 114, 0], + [449, 114, 0], + [450, 115, 0], + [451, 115, 0], + [452, 115, 0], + [453, 115, 0], + [454, 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a/research/native-quotient-interface/v/research/fresh-helper-boundary/native.py b/research/native-quotient-interface/v/research/fresh-helper-boundary/native.py new file mode 100644 index 0000000000..1b36f6cb5f --- /dev/null +++ b/research/native-quotient-interface/v/research/fresh-helper-boundary/native.py @@ -0,0 +1,183 @@ +"""Retiming of the pinned full-identity word; Apache-2.0, OpenAI Codex assistance. + +The scalar order and free-operator words stay fixed. Every changed transport +is independently lowered as an exact Clifford, including its absolute phase. +""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +import gzip +import importlib.util +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +BASE = ROOT/'research/kappa-rebuild/complex/full-identity-certificates' + +def need(ok, why): + if not ok: + raise ValueError(why) + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, path) + m = importlib.util.module_from_spec(spec) + sys.modules[name] = m + spec.loader.exec_module(m) + return m + +def read(path): + data = Path(path).read_bytes() + return json.loads(gzip.decompress(data) if str(path).endswith('.gz') else data) + +def span(basis): + out = {0} + for x in basis: + out |= {v ^ x for v in tuple(out)} + return frozenset(out) + +def gates(program): + phase = None + counters = Counter() + result = {} + for i, e in enumerate(program): + if e[0] == 'phase': + phase = e[1] + if e[0] == 'scalar': + g = e[1] + roles = g[1:3] if g[0] in ('add', 'copy') else g[1:2] + if all(r[0] == 'L' for r in roles): + key = (phase, counters[phase]) + result[key] = i + counters[phase] += 1 + return result + +def dual(g): + g = deepcopy(g) + if g[0] == 'add': + g[1], g[2] = g[2], g[1] + g[3] *= -1 + else: + need(g[0] == 'scale', 'Reversible persistent scalar') + g[2], g[3] = g[3], g[2] + return g + +def synthesize(c, program): + current = c['start'][:] + out = [] + def climb(r, f): + old = current[r] + if old == f: + return + need(span(c['frames'][old]) < span(c['frames'][f]), 'Nested positive retimed transport') + out.append(['climb', 'retimed', r, old, f, len(c['frames'][f])-len(c['frames'][old])]) + current[r] = f + i = 0 + while i < len(program): + e = deepcopy(program[i]); i += 1 + if e[0] == 'climb': + continue + if e[0] == 'center': + second = program[i] + need(second[0] == 'center' and e[1] == second[1] == 0 and e[3] == second[2], 'Original center split') + need(sorted((e[4], second[4])) == [3, 5], 'Original 3+5 center') + e = ['center', 0, e[2], second[3], 8]; i += 1 + if e[0] == 'scalar': + g = e[1] + roles = g[1:3] if g[0] in ('add', 'copy') else g[1:2] + for r in roles: + if r[0] == 'L': + climb(r[1], e[2]) + elif e[0] == 'warp': + need(e[1][0] == 'L', 'Persistent source warp') + climb(e[1][1], e[3]); current[e[1][1]] = e[4] + elif e[0] in ('adapter', 'residual_adapter'): + # Helper wrappers are recomputed on the new whole-job boundaries. + role = e[2] if e[0] == 'adapter' else e[2] + if role >= 224: + continue + out.append(e) + for r, f in enumerate(c['final']): + climb(r, f) + return out + +def run(changes=None, phase_check=True): + c = read(BASE/'THREE-base-FULL-IDENTITY-CANONICAL.json.gz') + original = read(BASE/'THREE-base-FULL-IDENTITY-NATIVE.json.gz') + changes = read(HERE/'CHANGES.json') if changes is None else changes + for key, frame_key in (('entrances', 'start'), ('exits', 'final')): + seen = set() + for role, old, new in changes[key]: + need(role not in seen and 224 <= role < 632 and c[frame_key][role] == old, 'Bound unique helper boundary') + seen.add(role); c[frame_key][role] = new + maps = {d: gates(p) for d, p in original.items()} + need(set(maps['forward']) == set(maps['backward']), 'Both scalar orientations have the same contact inventory') + for key in maps['forward']: + f = original['forward'][maps['forward'][key]] + b = original['backward'][maps['backward'][key]] + need(b[1] == dual(f[1]) and b[2] == f[2], 'Actual inverse-transpose scalar correspondence') + changed = deepcopy(original) + seen = set() + for phase, ordinal, old, new in changes['gates']: + key = (phase, ordinal) + need(key not in seen and key in maps['forward'], 'Bound unique retimed scalar contact') + seen.add(key) + for d in changed: + e = changed[d][maps[d][key]] + need(e[2] == old, 'Original scalar frame pin') + e[2] = new + programs = {d: synthesize(c, p) for d, p in changed.items()} + V = load(ROOT/'research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'fresh_boundary_rows') + X = load(ROOT/'research/kappa-rebuild/complex/native_extensions.py', 'fresh_boundary_literal') + checks = {} + profiles = {} + for d, p in programs.items(): + rows, receipt = X.literal_replay(V, c, p, d == 'backward') + for r in range(632): + need(rows['L', r] == V.expected(('L', r), [], d == 'backward', False), 'Every actual arbitrary-input endpoint, role '+str(r)) + profiles[d] = Counter({int(k): v for k, v in receipt['paid_profile'].items()}) + rebound = deepcopy(c) + rebound['local_profile'] = dict(profiles[d]) + receipt['second_literal'] = V.replay(p, rebound, [], d == 'backward', False) + checks[d] = receipt + need(profiles['forward'] == profiles['backward'], 'Same complete native tariff in both orientations') + H = Counter() + for r in range(224, 632): + a, b = c['start'][r], c['final'][r] + need(span(c['frames'][a]) <= span(c['frames'][b]), 'Nested productive helper boundary') + width = len(c['frames'][b])-len(c['frames'][a]) + need(width > 0, 'Every declared helper is independently productive') + H[width] += 1 + physical = [] + if phase_check: + ce = load(ROOT/'research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py', 'fresh_boundary_clifford') + P = load(ROOT/'research/kappa-function-composition/complex/prune_native.py', 'fresh_boundary_lowering') + N = X.N + old_edges = {(e[3], e[4]) for e in original['forward'] if e[0] == 'climb'} + new_edges = {(e[3], e[4]) for e in programs['forward'] if e[0] == 'climb'} + helper_edges = {(c['start'][r], c['final'][r]) for r in range(224, 632)} + for a, b in sorted((new_edges-old_edges) | helper_edges): + op = ce.canonical_frame(9, c['frames'][a]).adjoint().then(ce.canonical_frame(9, c['frames'][b])) + want = len(c['frames'][b])-len(c['frames'][a]) + directions = {} + for d in ('forward', 'backward'): + actual = P.conjugate(ce, op) if d == 'backward' else op + rec = N.lower_exact(P, ce, actual) + need(rec['rank'] == want, 'New physical Fourier rank including phase') + directions[d] = rec + physical.append({'old': a, 'new': b, 'rank': want, 'recipes': directions}) + return {'status': 'PASS_RETIMED_BOTH_ORIENTATIONS_ALL_632_COLUMNS', + 'helpers': dict(sorted(H.items())), 'paid': dict(sorted(profiles['forward'].items())), + 'changed_entrances': len(changes['entrances']), 'changed_exits': len(changes['exits']), + 'changed_scalar_frames': len(changes['gates']), 'native': checks, + 'new_physical_edges_and_boundaries': physical}, c, programs + +if __name__ == '__main__': + import argparse + p = argparse.ArgumentParser(); p.add_argument('--skip-phase', action='store_true'); p.add_argument('--write-result', action='store_true'); args = p.parse_args() + result, _, _ = run(phase_check=not args.skip_phase) + if args.write_result: + need(not args.skip_phase, 'Do not replace a complete phase receipt with a diagnostic') + 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Substantial OpenAI assistance. Uses the credited native retiming +implementation of PR4441 and preserves PR4447's missing-span predecessor. +""" +from collections import Counter +from copy import deepcopy +from pathlib import Path +import json,gzip,sys +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +sys.path.insert(0,str(ROOT/'research/fresh-helper-boundary')) +import native as F +need=F.need + +def construct(patch=None): + c=F.read(F.BASE/'THREE-base-FULL-IDENTITY-CANONICAL.json.gz') + original=F.read(F.BASE/'THREE-base-FULL-IDENTITY-NATIVE.json.gz') + parent=F.read(F.HERE/'CHANGES.json') + maps={d:F.gates(p) for d,p in original.items()} + need(set(maps['forward'])==set(maps['backward']),'Same scalar contact inventory') + for key in maps['forward']: + f=original['forward'][maps['forward'][key]];b=original['backward'][maps['backward'][key]] + need(b[1]==F.dual(f[1]) and b[2]==f[2],'Retained exact dual scalar words') + for key,field in [('entrances','start'),('exits','final')]: + for r,old,new in parent[key]: + need(c[field][r]==old,'Parent boundary pin');c[field][r]=new + for phase,ordinal,old,new in parent['gates']: + for d,p in original.items(): + i=maps[d][phase,ordinal];need(p[i][2]==old,'Parent scalar pin');p[i][2]=new + prior=F.read(ROOT/'research/missing-join-frame/PATCH.json') + need(prior['phase']=='B' and prior['ordinal']==480,'Exact prior contact') + prior_frame=len(c['frames']);c['frames'].append(prior['new_basis']) + for d,p in original.items(): + i=maps[d]['B',480];need(p[i][2]==prior['old_frame'],'Missing-span parent pin');p[i][2]=prior_frame + baseline=deepcopy(c) + before={d:F.synthesize(c,p) for d,p in original.items()} + patch=F.read(HERE/'PATCH.json') if patch is None else patch + need(patch['source_head']=='322e0ec764aa7ef7801383feb1f656e460dd8bed','Pinned candidate head') + labels={frozenset(F.span(b)):i for i,b in enumerate(c['frames'])} + def label(b): + s=frozenset(F.span(b));need(len(s)==2**len(b),'Independent binary basis') + if s not in labels:labels[s]=len(c['frames']);c['frames'].append(b) + return labels[s] + seen=set();counts=Counter() + for move in patch['changes']: + phase,r=move['phase'],move['ordinal'];key=(phase,r) + need(key not in seen,'No duplicate changed boundary/contact');seen.add(key) + a,b=F.span(move['old']),F.span(move['new']);need(a!=b,'No unchanged patch entry') + f=label(move['new']);counts[phase]+=1 + if phase in ('entrance','exit'): + need(224<=r<632,'Only independent helper boundaries may change') + field='start' if phase=='entrance' else 'final' + need(F.span(c['frames'][c[field][r]])==a,'Current helper source pin') + c[field][r]=f + else: + for d,p in original.items(): + i=maps[d][key];need(F.span(c['frames'][p[i][2]])==a,'Current scalar source pin');p[i][2]=f + programs={d:F.synthesize(c,p) for d,p in original.items()} + return c,programs,baseline,before,counts + +def run(phase_check=True): + c,programs,baseline,before,counts=construct() + V=F.load(ROOT/'research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py','joint_rows') + X=F.load(ROOT/'research/kappa-rebuild/complex/native_extensions.py','joint_literal') + checks={};profiles={} + for d,p in programs.items(): + rows,rec=X.literal_replay(V,c,p,d=='backward') + for r in range(632):need(rows['L',r]==V.expected(('L',r),[],d=='backward',False),'All 632 arbitrary-input endpoints') + profiles[d]=Counter({int(k):v for k,v in rec['paid_profile'].items()}) + rebound=deepcopy(c);rebound['local_profile']=dict(profiles[d]) + rec['second_literal']=V.replay(p,rebound,[],d=='backward',False);checks[d]=rec + need(profiles['forward']==profiles['backward'],'Both complete native rank tariffs') + H=Counter() + for r in range(224,632): + a,b=c['start'][r],c['final'][r] + need(F.span(c['frames'][a]) 0 else -1) * (abs(operator) + (10**6 if backward else 0)) + out = {} + for (variable, word), coefficient in row.items(): + moved = word[1:] if word and word[0] == -symbol else (symbol,) + word + key = variable, moved + out[key] = out.get(key, Q(0)) + coefficient + return {k: v for k, v in out.items() if v} + + +def expected(role, R, backward, clean): + out = identity(role) + name, i = role + if name != "L": + return out + target = i < 112 if backward else 112 <= i < 224 + if not target: + return out + port = i if backward else i - 112 + source_offset = 112 if backward else 0 + sign = -1 if backward else 1 + add(out, identity(("L", source_offset + port)), Q(sign)) + if clean: + for query in R: + if port in query: + for j, value in query.items(): + add(out, identity(("L", source_offset + j)), -sign * query[port] * value / 4) + return out + + +def replay(program, canonical, R, backward, clean, omit_cleanup_last=False): + """All L inputs and all Z inputs are independent, including dirty outputs.""" + n = 2 * canonical["v"] + canonical["R"] + need(n == 632, "Retained compact width") + rows = {("L", i): identity(("L", i)) for i in range(n)} + current = {("L", i): frame for i, frame in enumerate(canonical["start"])} + center_indices = set() + for event in program: + if event[0] == "scalar": + op = event[1] + for register in op[1:3] if op[0] in ("add", "copy") else op[1:2]: + if register[0] == "C": + center_indices.add(register[1]) + elif event[0] == "center": + center_indices.add(event[1]) + need(center_indices <= set(range(8)), "Known center workspace indices") + for i in center_indices: + rows["C", i] = identity(("C", i)) + current["C", i] = None + spaces = [span(vectors) for vectors in canonical["frames"]] + dimensions = [len(s).bit_length() - 1 for s in spaces] + need(dimensions[1] == 9, "Cleanup uses the full native frame") + live = set() + profile = Counter() + counts = Counter() + scalar_primitives = 0 + cleanup_start = next(i for i, event in enumerate(program) if event == ["phase", "full_frame_cleanup"]) + last_scalar = max(i for i, event in enumerate(program) if event[0] == "scalar" and i > cleanup_start) + for position, event in enumerate(program): + kind = event[0] + counts[kind] += 1 + if kind in ("climb", "center"): + if kind == "climb": + _, part, index, old, new, rank = event + role = "L", index + need(spaces[old] < spaces[new], "Non-nested or empty paid climb") + else: + _, index, old, new, rank = event + role = "C", index + need(spaces[old] < spaces[new] or spaces[new] < spaces[old], "Center residual is not nested") + need(current[role] == old and rank == abs(dimensions[new] - dimensions[old]), "Paid edge source/rank") + current[role] = new + profile[rank] += 1 + elif kind == "zero_buffer": + _, action, index = event + role = "Z", index + if action == "alloc": + need(role not in rows and role not in live, "Cleanup buffer duplicate") + rows[role] = identity(role) + current[role] = 1 + live.add(role) + else: + need(action == "free" and role in live and current[role] == 1, "Cleanup buffer retirement") + live.remove(role) + elif kind == "warp": + _, role, operator, old, new = event + role = tuple(role) + need(current[role] == old, "Warp entrance frame") + rows[role] = warp(rows[role], operator, backward) + current[role] = new + elif kind == "scalar": + op, frame = event[1:] + target = tuple(op[1]) + if op[0] == "clear": + need(target[0] == "C", "A borrowed input was cleared") + rows[target] = {} + current[target] = frame + scalar_primitives += 1 + continue + need(current[target] == frame, "Scalar target frame") + if op[0] in ("add", "copy"): + source = tuple(op[2]) + need(current[source] == frame, "Scalar source frame") + if op[0] == "copy": + need(target[0] == "C", "Copy overwrites borrowed state") + rows[target] = dict(rows[source]) + scalar_primitives += 1 + continue + coefficient = Q(op[3], op[4]) + need(target != source, "Self-ADD is not a reversible shear") + numerator, denominator = abs(coefficient.numerator), coefficient.denominator + need(numerator and denominator & (denominator - 1) == 0, "Non-dyadic ADD") + scalar_primitives += 3 + numerator.bit_length() - 1 + numerator.bit_count() + denominator.bit_length() - 1 + if not (omit_cleanup_last and position == last_scalar): + add(rows[target], rows[source], coefficient) + else: + need(op[0] == "scale", "Unknown scalar event") + coefficient = Q(op[2], op[3]) + numerator, denominator = abs(coefficient.numerator), coefficient.denominator + need(numerator and numerator & (numerator - 1) == 0 and denominator & (denominator - 1) == 0, + "Nonunit dyadic SCALE") + scalar_primitives += abs(numerator.bit_length() - denominator.bit_length()) + int(coefficient < 0) + if not (omit_cleanup_last and position == last_scalar): + rows[target] = {k: coefficient * v for k, v in rows[target].items()} + else: + need(kind in ("phase", "adapter", "residual_adapter"), "Unknown native event") + need(not live and [current["L", i] for i in range(n)] == canonical["final"], "Retired fields/final frames") + need(dict(profile) == {int(k): v for k, v in canonical["local_profile"].items()}, "Complete paid profile") + mismatches = [] + for role, actual in rows.items(): + wanted = {} if role[0] == "C" else expected(role, R, backward, clean) + if actual != wanted: + mismatches.append({"role": list(role), "unequal_coefficients": sum(actual.get(k, 0) != wanted.get(k, 0) for k in set(actual) | set(wanted))}) + if not omit_cleanup_last: + need(not mismatches, "Native dirty-buffer operator mismatch: " + repr(mismatches[:3])) + else: + need(mismatches, "Missing-cleanup negative control unexpectedly accepted") + buffer_count = sum(role[0] == "Z" for role in rows) + return dict(direction="backward" if backward else "forward", clean_J=clean, + independent_borrowed_input_fields=632+buffer_count, original_data_fields=224, + expected_restored_helpers=408, expected_restored_arbitrary_cleanup_buffers=buffer_count, + explicitly_owned_C_fields_cleared=len(center_indices), event_counts=dict(counts), + paid_profile=dict(sorted(profile.items())), paid_rank_mass=sum(k*v for k,v in profile.items()), + conservative_real_scalar_primitive_allowance=2*scalar_primitives, + all_scalar_frames_checked=True, dyadic_coefficients_and_unit_scales_checked=True, + free_warp_operator_endpoint_matches=not mismatches, + negative_control_omitted_last_cleanup_scalar=omit_cleanup_last, + mismatch_examples=mismatches[:3]) + + +def liveness(canonical): + times = defaultdict(list) + for i, event in enumerate(canonical["cleanup"]): + for role in event[1:3] if event[0] == "add" else event[1:2]: + role = tuple(role) if isinstance(role, list) else ("L", role) + times[role].append(i) + full = [i for i, f in enumerate(canonical["final"]) if f == 1] + candidates = [] + for z in canonical["zero_buffers"]: + begin, end = min(times["Z", z]), max(times["Z", z]) + possible = [i for i in range(112) if all(t < begin or t > end for t in times["L", i])] + candidates.append(dict(buffer=z, first_use=begin, last_use=end, + noninterfering_same_call_X_candidates=possible, + noninterfering_full_frame_L_candidates=[i for i in full if all(t < begin or t > end for t in times["L", i])])) + return dict(full_frame_live_roles=len(full), full_frame_roles_unused_in_cleanup=[i for i in full if not times["L", i]], + same_call_X_outputs_touched=sum(bool(times["L", i]) for i in range(112)), + buffers_with_no_noninterfering_same_call_X=sum(not row["noninterfering_same_call_X_candidates"] for row in candidates), + buffers_with_no_noninterfering_full_frame_L=sum(not row["noninterfering_full_frame_L_candidates"] for row in candidates), + intervals=candidates, + conclusion="Arbitrary-buffer restoration does not establish a legal same-call completed-output alias.", + external_same_frame_bank_requirement=91, + external_bank_hosting_constructed=False) + + +def find_aliases(canonical): + """Injective lifetime-safe matching; no native L access during its Z span.""" + options = {row["buffer"]: row["noninterfering_full_frame_L_candidates"] + for row in liveness(canonical)["intervals"]} + owner = {} + + def augment(z, seen): + for role in options[z]: + if role in seen: + continue + seen.add(role) + if role not in owner or augment(owner[role], seen): + owner[role] = z + return True + return False + + for z in sorted(options, key=lambda z: (len(options[z]), z)): + augment(z, set()) + bindings = {z: role for role, z in owner.items()} + need(len(set(bindings.values())) == len(bindings), "Alias must be injective") + need(all(role in options[z] for z, role in bindings.items()), "Interfering alias") + return bindings + + +def alias_program(program, bindings): + """Replace only Z register operands, retaining every native/scalar event.""" + out = [] + + def mapped(role): + return ["L", bindings[role[1]]] if role[0] == "Z" and role[1] in bindings else list(role) + + for event in program: + if event[0] == "zero_buffer" and event[2] in bindings: + continue + if event[0] == "scalar": + op = event[1].copy() + op[1] = mapped(op[1]) + if op[0] in ("add", "copy"): + op[2] = mapped(op[2]) + out.append(["scalar", op, event[2]]) + elif event[0] == "warp": + out.append([event[0], mapped(event[1]), *event[2:]]) + else: + out.append(event) + return out + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--output", type=Path, default=HERE / "RESULT.json") + args = parser.parse_args() + pins = authenticate() + R = [{int(k): Q(v) for k, v in row.items()} for row in read(PACKET)["R_rows"]] + providers = {} + for tag in TAGS: + providers[tag] = {} + for clean in (False, True): + folder = "converted" if clean else "sources" + canonical = read(CORE / folder / (tag + "-CANONICAL.json.gz")) + programs = read(CORE / folder / (tag + "-NATIVE-WORD.json.gz")) if clean else emit_original(canonical) + checks = [replay(programs[direction], canonical, R, direction == "backward", clean) + for direction in ("forward", "backward")] + bindings = find_aliases(canonical) + aliases = {direction: alias_program(program, bindings) for direction, program in programs.items()} + aliased_checks = [replay(aliases[direction], canonical, R, direction == "backward", clean) + for direction in ("forward", "backward")] + need(len(bindings) == 53, "Expected source-bound 53-field lifetime match") + for original, aliased in zip(checks, aliased_checks): + need(original["paid_profile"] == aliased["paid_profile"] and + original["conservative_real_scalar_primitive_allowance"] == aliased["conservative_real_scalar_primitive_allowance"], + "Aliasing changes the charged operation list") + providers[tag]["clean_J" if clean else "ordinary"] = dict(checks=checks, liveness=liveness(canonical), + lifetime_alias_bindings={str(z): role for z, role in sorted(bindings.items())}, + aliased_checks=aliased_checks, + eliminated_cleanup_fields=len(bindings), remaining_cleanup_fields=91-len(bindings), + aliased_word_sha256={direction: sha256(json.dumps(program, sort_keys=True, separators=(",", ":")).encode()).hexdigest() + for direction, program in aliases.items()}) + print("PASS all arbitrary cleanup inputs", tag, flush=True) + canonical = read(CORE / "converted/THREE-base-CANONICAL.json.gz") + programs = read(CORE / "converted/THREE-base-NATIVE-WORD.json.gz") + controls = [replay(programs[direction], canonical, R, direction == "backward", True, True) + for direction in ("forward", "backward")] + result = dict(schema="literal-native-dirty-buffers/1", status="PASS_NATIVE_ARBITRARY_DIRTY_BUFFER_REPLAY", + new_multiplication_kappa=False, physical_phase_generation_rerun=False, + phase_evidence="Pinned inherited exact native phase receipts; unchanged native edges.", + source_hashes=pins, verifier_sha256=digest(Path(__file__)), providers=providers, + negative_controls=controls, + lifetime_safe_local_full_frame_aliases_per_word=53, + remaining_external_bank_fields_per_word=38, + all_91_local_output_alias_claim=False, external_bank_placement_and_cost_closed=False) + args.output.parent.mkdir(parents=True, exist_ok=True) + args.output.write_text(json.dumps(result, indent=2) + "\n") + print(result["status"], flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/native-quotient-interface/v/research/kappa-function-composition/complex/prune_native.py b/research/native-quotient-interface/v/research/kappa-function-composition/complex/prune_native.py new file mode 100644 index 0000000000..8c3e11b240 --- /dev/null +++ b/research/native-quotient-interface/v/research/kappa-function-composition/complex/prune_native.py @@ -0,0 +1,253 @@ +#!/usr/bin/env python3 +"""Delete exact unconsumed centre-assembly/inverse pairs, including dirty state. + +Apache-2.0; substantial OpenAI assistance. The native writer and final verifier +are reused with attribution from the frozen causal-continuation package. The +new search checks literal rational perturbations, never numerical similarity. +""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import sys +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +RESEARCH = HERE.parents[1] +BASE = RESEARCH / 'kappa-global-routing/integrated-complex' +CHECKER = RESEARCH / 'kappa-causal-continuation/buffer-borrowing/verify_buffers.py' +CHECKER_SHA = '106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7' +CLIFFORD = RESEARCH / 't74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py' +TAGS = ('THREE-base', 'THREE-extra', 'FOUR-base', 'FOUR-extra') + + +def need(ok, why): + if not ok: raise ValueError(why) + + +def digest(path): return sha256(path.read_bytes()).hexdigest() + + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + + +def save(path, value): + data = json.dumps(value, sort_keys=True, separators=(',', ':')).encode() + path.write_bytes(gzip.compress(data, mtime=0)) + + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, path) + obj = importlib.util.module_from_spec(spec) + sys.modules[name] = obj + spec.loader.exec_module(obj) + return obj + + +def apply(v, rows, event, backward=False): + if event[0] == 'warp': + r = tuple(event[1]); rows[r] = v.warp(rows[r], event[2], backward) + elif event[0] == 'scalar': + g = event[1]; r = tuple(g[1]) + if g[0] == 'add': v.add(rows[r], rows[tuple(g[2])], Q(g[3], g[4])) + else: + need(g[0] == 'scale', 'No owned field in the clean-J baseline') + rows[r] = {k: Q(g[2], g[3])*x for k, x in rows[r].items()} + + +def index_sections(program): + phase = None; result = {'A': [], 'full_frame_cleanup': []} + for i, e in enumerate(program): + if e[0] == 'phase': phase = e[1] + if phase in result and e[0] in ('scalar', 'warp'): result[phase].append(i) + return result + + +def exact_candidate_screen(v, canonical, program, R): + """Test the final 48 assembly gates, with their actual scheduled inverses.""" + indices = index_sections(program) + need(len(indices['A']) == len(canonical['A']), 'Native A gate correspondence') + need(len(indices['full_frame_cleanup']) == len(canonical['cleanup']), 'Cleanup gate correspondence') + options = []; unmatched = [] + for j in range(len(canonical['A']) - 48, len(canonical['A'])): + g = canonical['A'][j] + need(g[0] == 'add' and len(canonical['frames'][g[-1]]) in (7, 8), 'Final centre-assembly grammar') + inverse = g[:]; inverse[3] *= -1; inverse[-1] = 1 + hits = [i for i, h in enumerate(canonical['cleanup']) if h == inverse] + if len(hits) == 1: + cj = hits[0] + options.append((j, cj, indices['A'][j], indices['full_frame_cleanup'][cj])) + else: unmatched.append({'A_index': j, 'gate': g, 'matching_inverse_occurrences': hits}) + sites = {k for option in options for k in option[2:]} + effects = {}; rows = {('L', i): v.identity(('L', i)) for i in range(632)} + for i, e in enumerate(program): + if i in sites: + g = e[1] + effects[i] = (tuple(g[1]), {k: -Q(g[3], g[4])*x for k, x in rows[tuple(g[2])].items()}) + apply(v, rows, e) + need(all(row == v.expected(r, R, False, True) for r, row in rows.items()), 'Pinned baseline endpoint') + accepted = []; rejected = [] + for aj, cj, ai, ci in options: + delta = {('L', i): {} for i in range(632)} + live_data_effect = False + for i in range(ai, len(program)): + if i in (ai, ci): + target, effect = effects[i]; v.add(delta[target], effect, Q(1)) + else: apply(v, delta, program[i]) + if i < indices['full_frame_cleanup'][0]: + e = program[i] + if e[0] == 'scalar' and e[1][0] in ('add', 'scale'): + r = tuple(e[1][1]) + if r[0] == 'L' and 112 <= r[1] < 224 and delta[r]: live_data_effect = True + bad = [(r, row) for r, row in delta.items() if row] + item = {'A_index': aj, 'cleanup_index': cj, 'A_gate': canonical['A'][aj], + 'cleanup_gate': canonical['cleanup'][cj], + 'native_scalar_sites': [ai, ci], 'Y_difference_before_cleanup': live_data_effect} + if not bad: + item['all_632_arbitrary_input_columns_exactly_preserved'] = True + accepted.append(item) + else: + r, row = bad[0]; key, value = next(iter(sorted(row.items()))) + item['first_exact_nonzero_residual'] = {'output': list(r), 'input': list(key[0]), + 'operator_word': list(key[1]), 'coefficient': str(value)} + item['changed_output_fields'] = len(bad) + rejected.append(item) + need(all(not a['Y_difference_before_cleanup'] for a in accepted), 'No changed data consumer before cleanup') + return accepted, rejected, unmatched + + +def prefix_growth(v, program, backward): + rows = {('L', i): v.identity(('L', i)) for i in range(632)} + maximum_l1 = Q(1); max_coefficient = Q(1); max_numerator = 1; max_denominator = 1 + witness = {'event': -1, 'register': ['L', 0]} + for i, event in enumerate(program): + apply(v, rows, event, backward) + if event[0] not in ('scalar', 'warp'): continue + role = tuple(event[1] if event[0] == 'warp' else event[1][1]) + values = [abs(x) for x in rows[role].values()] + norm = sum(values, Q(0)) + if norm > maximum_l1: + maximum_l1 = norm; witness = {'event': i, 'register': list(role)} + if values: + max_coefficient = max(max_coefficient, max(values)) + max_numerator = max(max_numerator, max(x.numerator for x in values)) + max_denominator = max(max_denominator, max(x.denominator for x in values)) + return {'max_formal_row_l1': str(maximum_l1), 'max_abs_coefficient': str(max_coefficient), + 'max_abs_numerator': max_numerator, 'max_denominator': max_denominator, + 'l1_witness': witness, 'independent_input_columns': 632, + 'scope': 'Exact logical scalar/monomial prefixes over arbitrary inputs; no rounded child error bound.'} + + +def monomial(ce, recipe, n): + result = ce.diag(n, tuple(recipe['quadratic_rows']), tuple(recipe['linear_Z4'])) + result = result.then(ce.perm(n, tuple(recipe['matrix_rows']))).then(ce.xgate(n, recipe['offset'])) + return result.then(ce.Op(n, ce.identity(n), [('phase', recipe['phase'])])) + + +def conjugate(ce, op): + n = op.n; result = ce.ident(n) + for g in op.circuit: + if g[0] == 'P': part = ce.perm(n, g[1]) + elif g[0] == 'X': part = ce.xgate(n, g[1]) + elif g[0] == 'C': part = ce.cgate(n, g[1], -g[2]) + elif g[0] == 'D': part = ce.diag(n, g[1], tuple(-x % 4 for x in g[2])) + else: + need(g[0] == 'phase', 'Known Clifford primitive') + part = ce.Op(n, ce.identity(n), [('phase', -g[1] % 4)]) + result = result.then(part) + return result + + +def check_new_edges(canonical, old_program, new_program, cache): + ce = load(CLIFFORD, 'function_composition_clifford') + old = {(e[3], e[4]) for e in old_program if e[0] == 'climb'} + new = {(e[3], e[4]) for e in new_program if e[0] == 'climb'} + reports = [] + for a, b in sorted(new - old): + A, B = canonical['frames'][a], canonical['frames'][b] + key = tuple(A), tuple(B) + if key not in cache: + source = ce.canonical_frame(9, A).adjoint().then(ce.canonical_frame(9, B)) + records = {} + for name, op in (('forward', source), ('inverse_transpose', conjugate(ce, source))): + recipe, _ = ce.lower_child(op) + need(recipe['rank'] == len(B)-len(A), 'Exact new physical child rank') + decoded = monomial(ce, recipe['right'], 9).then(ce.fourier(9, range(recipe['rank']))).then(monomial(ce, recipe['left'], 9)) + need(decoded.tab == op.tab and decoded.zero_state() == op.zero_state(), 'Decoded Clifford equality including global phase') + records[name] = recipe + cache[key] = records + reports.append({'old_frame': a, 'new_frame': b, 'old_basis': A, 'new_basis': B, + 'rank': len(B)-len(A), 'exact_physical_recipes': cache[key]}) + return reports + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--out', type=Path, default=HERE/'pruned-native') + args = parser.parse_args(); args.out.mkdir(parents=True, exist_ok=True) + need(digest(CHECKER) == CHECKER_SHA, 'Frozen independent checker') + v = load(CHECKER, 'function_composition_independent'); v.authenticate() + base_receipt = read(BASE/'RESULT.json') + R = [{int(k): Q(x) for k, x in row.items()} for row in v.read(v.PACKET)['R_rows']] + providers = {}; phase_cache = {} + for tag in TAGS: + path = BASE/(tag+'-CANONICAL.json.gz') + need(digest(path) == base_receipt['providers'][tag]['artifacts'][path.name], 'Pinned baseline canonical') + old = read(path); old_native = v.emit_original(old) + yes, no, unmatched = exact_candidate_screen(v, old, old_native['forward'], R) + candidate = deepcopy(old) + a_drop = {r['A_index'] for r in yes}; c_drop = {r['cleanup_index'] for r in yes} + candidate['A'] = [g for i, g in enumerate(old['A']) if i not in a_drop] + candidate['cleanup'] = [g for i, g in enumerate(old['cleanup']) if i not in c_drop] + native = v.emit_original(candidate) + histogram = Counter(e[5] for e in native['forward'] if e[0] == 'climb') + candidate['local_profile'] = {str(r): n for r, n in sorted(histogram.items())} + candidate['edges'] = [list(e) for e in sorted({(e[3], e[4]) for e in native['forward'] if e[0] == 'climb'})] + checks = {} + for name in ('forward', 'backward'): + checks[name] = {'independent_literal_replay': v.replay(native[name], candidate, R, name == 'backward', True), + 'baseline_prefix_growth': prefix_growth(v, old_native[name], name == 'backward'), + 'new_prefix_growth': prefix_growth(v, native[name], name == 'backward')} + phases = check_new_edges(candidate, old_native['forward'], native['forward'], phase_cache) + # Removing the computation while retaining its inverse must be rejected. + negative = deepcopy(candidate) + first = yes[0] + negative['cleanup'].insert(0, first['cleanup_gate']) + bad_program = v.emit_original(negative) + rejected_control = False + try: v.replay(bad_program['forward'], negative, R, False, True) + except ValueError as error: + rejected_control = 'operator mismatch' in str(error) + need(rejected_control, 'Unpaired deletion negative control') + cp = args.out/(tag+'-CANONICAL.json.gz'); np = args.out/(tag+'-NATIVE-WORD.json.gz') + save(cp, candidate); save(np, native) + providers[tag] = {'baseline_canonical_sha256': digest(path), 'candidate_pairs_tested': len(yes)+len(no), + 'accepted_pairs': yes, 'rejected_pairs': no, 'unmatched_pairs': unmatched, + 'old_paid_profile': old['local_profile'], 'new_paid_profile': candidate['local_profile'], + 'old_paid_rank_mass': sum(int(r)*n for r, n in old['local_profile'].items()), + 'new_paid_rank_mass': sum(int(r)*n for r, n in candidate['local_profile'].items()), + 'recursive_calls_removed': sum(old['local_profile'].values())-sum(histogram.values()), + 'scalar_ADDs_removed': 2*len(yes), 'checks': checks, + 'new_physical_edges': phases, 'unpaired_deletion_negative_control_rejected': True, + 'artifacts': {cp.name: digest(cp), np.name: digest(np)}} + print('PASS pruned native', tag, len(yes), 'pairs;', dict(sorted(histogram.items())), flush=True) + result = {'schema': 'consumer-driven-clean-J-native-pruning/1', + 'status': 'PASS_ALL_FOUR_BOTH_DIRECTIONS_632_ARBITRARY_FIELDS', + 'generator_sha256': digest(Path(__file__)), 'baseline_receipt_sha256': digest(BASE/'RESULT.json'), + 'independent_interpreter_sha256': CHECKER_SHA, 'phase_compiler_path': str(CLIFFORD.relative_to(RESEARCH.parent)), + 'phase_compiler_sha256': digest(CLIFFORD), 'providers': providers, + 'native_word_new_children_phase_lowered': True, 'local_data_and_helper_endpoints_unchanged': True, + 'same_632_field_inventory': True, 'zero_owned_fields': True, 'zero_external_cleanup_fields': True, + 'no_new_kappa_claimed': True, 'query_producer_contract_preserved': False, + 'scope': 'Exact ideal clean-J local endpoints only. Final historical query assemblies are partially removed because this local word has no centre consumers. A caller that reads those historical queries cannot substitute this word without reconstructing and pricing its producer interface. The full caller and rounded induction remain open.'} + (args.out/'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(result['status'], flush=True) + + +if __name__ == '__main__': main() diff --git a/research/native-quotient-interface/v/research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz b/research/native-quotient-interface/v/research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..4a8c4ed26e53a72362d571c972e65aff546be784 GIT binary patch literal 82793 zcmZs>1yG!Au&s*^?(Xi+5C}mBcbDL90fGnj;2KQvfnR%zrOA@`o6RZz0I8cZU>cD z*}v)eK0O*TxHF^0;KWv8`}u$Ua=X|>j4KME1*>(Z6-joy{`S1!`*1QhQ`W2b`zVDl z$M^N=x38%^U0V;6_VXUv*0)s*1((Hh^}|+nSG*U0N#8h_s*$-p1^;^gdp)8cRa-a& zvohq}0^_sc6>;D5*3C=39P_aCQhU04&{r2fw=Q1pzThgA^>4q_(sMVG489>$v<$Bx 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