From 1b2638a3b34ffb7cf6cb5b90e8fd14ca7f216127 Mon Sep 17 00:00:00 2001 From: ross Date: Mon, 19 Oct 2026 23:00:10 +1100 Subject: [PATCH 1/2] Verify fixed paired-helper kernel boundaries and conditional caller screen --- .../ADAPTATIONS.json | 140 + .../FROZEN-SHA256.json | 32 + .../bit-paired-helper-boundaries/ORIGINS.json | 182 + .../PROOF-CALLER.md | 316 + .../PROOF-NATIVE.md | 282 + .../bit-paired-helper-boundaries/README.md | 167 + .../REVIEW-CALLER.md | 106 + .../REVIEW-NATIVE.md | 140 + .../bit-paired-helper-boundaries/SOURCES.json | 60 + .../bit-paired-helper-boundaries/TASK.json | 67 + .../bit-paired-helper-boundaries/VERIFY.json | 110 + .../bit-paired-helper-boundaries/controls.py | 126 + .../bit-native-caller/GLOBAL-KERNEL-BOOST.md | 153 + .../GLOBAL-KERNEL-E2-GEOMETRY.json.gz | Bin 0 -> 43860 bytes .../GLOBAL-KERNEL-E2-WORD.json.gz | Bin 0 -> 112047 bytes .../bit-native-caller/GLOBAL-KERNEL-E2.json | 470462 ++++++++++++++ .../bit-native-caller/HYBRID-BUDGET.json | 253 + .../KERNEL-ENTRANCES-WORD.json.gz | Bin 0 -> 57854 bytes .../bit-native-caller/KERNEL-ENTRANCES.json | 410 + .../bit-native-caller/KERNEL-ENTRANCES.md | 48 + .../OLD-KERNEL-E2-GEOMETRY.json.gz | Bin 0 -> 43860 bytes .../OLD-KERNEL-E2-WORD.json.gz | Bin 0 -> 111871 bytes .../bit-native-caller/OLD-KERNEL-E2.json | 475090 +++++++++++++++ .../changed/bit-native-caller/cold_cosets.py | 129 + .../bit-native-caller/global_kernel_boost.py | 252 + .../bit-native-caller/helper_tail_retime.py | 124 + .../bit-native-caller/hybrid_budget.py | 59 + .../bit-native-caller/kernel_entrances.py | 149 + .../bit-native-caller/native_seed_binding.py | 258 + .../bit-native-caller/old_kernel_boost.py | 188 + .../bit-native-caller/physical_code.py | 226 + .../changed/budgets/PAIRED-HELPER-OWNERS.json | 641 + .../changed/budgets/PAIRED-HELPER-OWNERS.md | 107 + .../changed/budgets/paired_owner_fixture.py | 104 + .../BIT-FULL-COMPENSATION-WORD.json.gz | Bin 0 -> 57926 bytes .../bit-endpoint/BIT-FULL-COMPENSATION.json | 2218 + .../reviews/caller/INDEPENDENT-RESULT.json | 1010 + .../reviews/caller/independent_check.py | 281 + .../frozen/reviews/native/RESULT.json | 113164 ++++ .../reviews/native/independent_check.py | 454 + .../words/r438-t154.json.gz | Bin 0 -> 42305 bytes .../data/bit/bitE8-r865.json.gz | Bin 0 -> 33865 bytes .../bit-paired-helper-boundaries/verify.py | 163 + 43 files changed, 1067671 insertions(+) create mode 100644 research/bit-paired-helper-boundaries/ADAPTATIONS.json create mode 100644 research/bit-paired-helper-boundaries/FROZEN-SHA256.json create mode 100644 research/bit-paired-helper-boundaries/ORIGINS.json create mode 100644 research/bit-paired-helper-boundaries/PROOF-CALLER.md create mode 100644 research/bit-paired-helper-boundaries/PROOF-NATIVE.md create mode 100644 research/bit-paired-helper-boundaries/README.md create mode 100644 research/bit-paired-helper-boundaries/REVIEW-CALLER.md create mode 100644 research/bit-paired-helper-boundaries/REVIEW-NATIVE.md create mode 100644 research/bit-paired-helper-boundaries/SOURCES.json create mode 100644 research/bit-paired-helper-boundaries/TASK.json create mode 100644 research/bit-paired-helper-boundaries/VERIFY.json create mode 100644 research/bit-paired-helper-boundaries/controls.py create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/GLOBAL-KERNEL-BOOST.md create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/GLOBAL-KERNEL-E2-GEOMETRY.json.gz create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/GLOBAL-KERNEL-E2-WORD.json.gz create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/GLOBAL-KERNEL-E2.json create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/HYBRID-BUDGET.json create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/KERNEL-ENTRANCES-WORD.json.gz create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/KERNEL-ENTRANCES.json create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/KERNEL-ENTRANCES.md create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/OLD-KERNEL-E2-GEOMETRY.json.gz create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/OLD-KERNEL-E2-WORD.json.gz create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/OLD-KERNEL-E2.json create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/cold_cosets.py create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/global_kernel_boost.py create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/helper_tail_retime.py create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/hybrid_budget.py create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/kernel_entrances.py create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/native_seed_binding.py create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/old_kernel_boost.py create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/physical_code.py create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/budgets/PAIRED-HELPER-OWNERS.json create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/budgets/PAIRED-HELPER-OWNERS.md create mode 100644 research/bit-paired-helper-boundaries/frozen/changed/budgets/paired_owner_fixture.py create mode 100644 research/bit-paired-helper-boundaries/frozen/major/bit-endpoint/BIT-FULL-COMPENSATION-WORD.json.gz create mode 100644 research/bit-paired-helper-boundaries/frozen/major/bit-endpoint/BIT-FULL-COMPENSATION.json create mode 100644 research/bit-paired-helper-boundaries/frozen/reviews/caller/INDEPENDENT-RESULT.json create mode 100644 research/bit-paired-helper-boundaries/frozen/reviews/caller/independent_check.py create mode 100644 research/bit-paired-helper-boundaries/frozen/reviews/native/RESULT.json create mode 100644 research/bit-paired-helper-boundaries/frozen/reviews/native/independent_check.py create mode 100644 research/bit-paired-helper-boundaries/frozen/upstream/research/bit-r438-transport-rehost/words/r438-t154.json.gz create mode 100644 research/bit-paired-helper-boundaries/frozen/upstream/research/e8-bit-carrier-skeleton/data/bit/bitE8-r865.json.gz create mode 100644 research/bit-paired-helper-boundaries/verify.py diff --git a/research/bit-paired-helper-boundaries/ADAPTATIONS.json b/research/bit-paired-helper-boundaries/ADAPTATIONS.json new file mode 100644 index 0000000000..bd496c37f7 --- /dev/null +++ b/research/bit-paired-helper-boundaries/ADAPTATIONS.json @@ -0,0 +1,140 @@ +{ + "frozen/changed/bit-native-caller/cold_cosets.py": [ + { + "new": "BASE=PORTABLE.root/'frozen'", + "old": "BASE=Path('/Users/ross/git/math')" + }, + { + "new": "RAW=BASE/'upstream/research/bit-r438-transport-rehost/words/r438-t154.json.gz'", + "old": "RAW=BASE/'integer-mult-bounds/research/bit-r438-transport-rehost/words/r438-t154.json.gz'" + }, + { + "new": "FULL=BASE/'upstream/research/e8-bit-carrier-skeleton/data/bit/bitE8-r865.json.gz'", + "old": "FULL=BASE/'integer-mult-bounds/research/e8-bit-carrier-skeleton/data/bit/bitE8-r865.json.gz'" + }, + { + "new": "COMP=BASE/'major/bit-endpoint/BIT-FULL-COMPENSATION.json'", + "old": "COMP=BASE/'.research-automation/runs/kappa-major-20261018T1330Z/bit-endpoint/BIT-FULL-COMPENSATION.json'" + } + ], + "frozen/changed/bit-native-caller/global_kernel_boost.py": [ + { + "new": "PORTABLE.equal(p,out)", + "old": 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caller and owner statements for the fixed B10 +lane. Its exact finite checker reconstructs the seven coordinate-prefix +tariffs from raw geometry, the hybrid seed operators, and a complete dedicated +owner fixture. It does not replay the new local supplier words. Their full +dirty-column identities, integer cleanup, joined ADDRESS charts and literal +native cuts are owned by the separate construction review. + +The source lane is `kappa-changed-endpoints-20261019T0153Z`, at scientific pin +`20ecf2891d80b5acf18d980b2164fb44ea7faa90`. Exact source bytes are pinned in +`independent_check.py` and `INDEPENDENT-RESULT.json`. No producer code is +imported. No all-partition B11 result, improved supplier exponent or kappa is +claimed here. + +## 1. Arbitrary physical dirt at a paired boundary + +Use a legal exact ADDRESS field and nondegenerate frame projectors. Write + + D_P = [[I-P, P], [P, I-P]]. + +These are linear ADDRESS involutions and induce permutations of complete +VALUE arrays. Suppose a local word is verified on every independent logical +source, old-target and helper input. Assume helper h has entrance frame E, +terminal frame U, final logical helper row exactly h, and zero coefficient +in every required public output over the BIT VALUE field F2. This is a full +row/column contract, not merely a right eigenvector or a dimension count. + +For an arbitrary physical array u, define h=D_E^{-1}u in the proof. This is +a bijective change of variables, not an executed entrance operation. The +verified physical endpoint is then + + u -> D_U D_E^{-1}u, + +and all public outputs, **as F2 VALUE arrays**, are independent of u. Signed +integer target coefficients may remain nonzero and even; binary D*S=0 does +not assert their integer vanishing. Exact integer source/helper return and +the binary target shear are distinct obligations. Since the logical theorem holds +for every joint tuple, it also holds when different entering physical arrays +are correlated with each other or with public data. No probabilistic or +clean-input assumption is used. Executing an additional entrance query is +required only if a caller separately demands the predecessor's identification +h=u while changing E. That is a different boundary contract. + +If E is contained in U, the orthogonal projectors satisfy +P_E P_U=P_U P_E=P_E. Direct block multiplication gives + + D_U D_E^{-1} = D_(P_U-P_E), + (P_U-P_E)^2=P_U-P_E, + rank(P_U-P_E)=dim(U)-dim(E). + +Thus the residual is the interchange on U intersect E-perp. For U=FULL, +it has width 8-dim(E). This algebra does not establish that its adapter, +queries or tape implementation are free. It applies only where the exact +projectors and ADDRESS maps are defined. + +The ten rank-one precursor helpers consequently have candidate paired widths +seven, with 419 unchanged width-eight helpers. The stated local mass 5087 is +consistent with 10*7+419*8 helper mass and 111 source width-seven plus 111 +target width-eight paths. The common-E2 R429 word instead has candidate +inventory 318 width-six and 111 width-eight helpers. These are applications +conditional on the separately checked local identities; this review supplies +no public-window allocation for the ten-helper precursor. + +## 2. Dedicated cover-bank theorem + +Fix a finite cover group G acting through doubled charts diag(g,g). It must +contain every adapter used below. Public families and private work families +are separate from the ordinary helper banks. Let m contain each full local +footprint, including spectators, not just its residual rank. + +For each role j assigned to a particular bank, let T_j be its certified +paired physical residual. Choose disjoint coordinate blocks I_j and explicit +adapters Pi_j in G satisfying + + Pi_j T_j Pi_j^{-1} = D_(I_j). + +Within any one local invocation and bank, require all Pi_j to be distinct. +The physical family label is the complete pair (bank,g); disjoint coordinate +blocks alone do not excuse a repeated family in the same invocation. + +At cover invocation d, assign role j to g=d Pi_j^{-1}. For fixed j this is +a bijection of G. For distinct roles in one invocation, distinct Pi_j imply +distinct g, hence no simultaneous-family alias. At fixed physical owner g, +role j occurs at d=g Pi_j and acts by + + d T_j d^{-1} = g D_(I_j) g^{-1}. + +Every role therefore reaches that owner exactly once. The D_(I_j) commute +because their coordinate blocks are disjoint. Their product is the swap on +the union. Add and charge a padding query on the complementary coordinates. +The final owner action is g D_(I_m) g^{-1}=D_(I_m), because a full head/tail +swap commutes with every doubled chart diag(g,g). + +Execute each complete local call before the next, in an order preserving the +public source chronology. Intermediate helper states are not exposed to +another invocation. Each later invocation accepts the arbitrary array left +by the preceding ones. These premises make the argument chronological; they +do not construct pending windows for recycled public families. + +Unused local spectator axes may belong to a different role's later residual +block. The completed current endpoint is the identity on its spectators, and +the next role accepts arbitrary entering arrays. No permanently untouched +global spectator block is needed. Simultaneous reuse or a local theorem that +assumes those spectators clean would invalidate this conclusion. + +This is an algebraic finite-cover hosting theorem. Every adapter, source +access, controller, private buffer and native query still requires its paid +implementation. A rational GL chart is not automatically admitted by an +orthogonal or dyadic native alphabet. Centrality of the final full swap does +not authorize arbitrary non-diagonal ADDRESS charts. + +## 3. Complete m=36 fixture and integral E2 inventory + +For the actual coordinate E2={0,1}, U={0,...,7}, first use the fixed local +coordinate permutation + + [0,1,2,3,4,5,6,7] -> [6,7,0,1,2,3,4,5]. + +It makes the residual axes {0,...,5} and the two spectator/entrance axes +{6,7}. The original orthogonal cover contains such coordinate permutations; +the finite cyclic fixture starts after this canonical embedding. This fixed +permutation is not claimed to belong to the fixture's smaller cyclic group. + +In m=36 let Pi_j be the simultaneous shift by 6j on both ADDRESS halves, +0<=j<6. Its residual is I_j={6j,...,6j+5} modulo 36, and its spectators are +the first two axes of I_(j+1). The six adapters are distinct. With cyclic +cover classes d,g in Z/6, assign g=d-j. The six residual blocks fill m=36, +so there is no padding in this width-six fixture. + +The checker directly applies both paired endpoint operations to every one of +72 independent ADDRESS columns at every owner. All 6*72=432 columns become +the full swap; all 36 assignments match the retained fixture. It also checks +centrality of all six doubled charts on all columns. Ignoring the entrance +changes 144 columns; omitting the last role changes 72; duplicating one +adapter is rejected as a same-call family alias. A chart shifting only the +head half fails the required centrality test. + +For the fixed R429 E2 inventory, use 12 replicas. Enumerate width-six roles +by z=318*replica+helper, and assign bank=floor(z/6), slot=z mod 6. Enumerate +width-eight roles separately by z=111*replica+helper, with bank=floor(z/4), +slot=z mod 4. This assigns every role once and uses + + 12*318/6 = 636 width-six banks, + 12*111/4 = 333 width-eight banks. + +Each bank receives each slot exactly once, even when a width-eight bank +straddles replicas. Within one replica/call, each bank's slots are distinct. +For width eight, use four coordinate blocks [0,8),[8,16),[16,24),[24,32) +and distinct coordinate permutations exchanging the first block with the +chosen block; pay a rank-four query on [32,36). The abstract cover must +contain these permutations as well. The checker verifies all 5,148 actual +replica/helper role placements and their slot distinctness; it does not +enumerate this larger cover group. + +Per call/replica, helper stock and complete helper mass are + + W_h = 318/6 + 111/4 = 323/4, + Q_local = 318*6 + 111*8 = 2796, + Q_padding = (111/4)*4 = 111, + Q_local+Q_padding = 2907 = 36 W_h. + +At 12 replicas there are 969 banks and 333 rank-four padding queries: +12*2796+333*4=36*969=34884. This is only the helper-bank portion of an +invoice. It grants no public-bank dividend or missing native alphabet +admission. Counts for the R438 E2 inventory (327 width-six helpers plus +111 width-eight) are not silently substituted into this R429 fixture. +Omitting the actual rank-four padding from a width-eight bank leaves eight +of its 72 coordinate columns with the wrong endpoint. + +## 4. Exact hybrid seed and all-bank rank obstruction + +Fix one public port and one common nontrivial involution N. Work formally in +R=F2[N]/(N^2-I), or in a faithful actual representation of it. Set d=N+I; +then d^2=0 and d is nonzero. The checker uses the faithful binary matrices + + N = [[0,1],[1,0]], d = [[1,1],[1,1]]. + +The images of 0,I,N,I+N are all distinct. Thus checking the resulting +four-by-four binary block matrices verifies every coefficient of the +two-bank seed; no scalar substitution N=I can hide a coefficient defect. + +With epsilon indicating whether the actual target cap was lifted to FULL, +the normalized forward and backward operators are + + F0=[[I,0],[N,I]], B0=[[I,N],[0,I]], + F1=[[I,0],[I,N]], B1=[[N,I],[0,I]]. + +Exact multiplication gives + + F0 B0 F0 = [[0,N],[N,0]], + F1 B1 F1 = [[I+N,N],[I,I+N]], + (F1 B1 F1)^2 = diag(N,N). + +The six-call squared seed does not undo a FULL target lift already charged +inside each call. Omitting its actual middle B changes the operator. + +Write any of these four calls as A(I+dR_j), with A its invertible constant +matrix at N=I. The respective normalized derivatives are + + R_F0=E21, R_B0=E12, R_F1=E22, R_B1=E11, + +all rank one over F2. Embedding the call in any number b of banks preserves +this rank. Arbitrary interleaved **N-independent scalar** bank matrices in +GL_b(F2) may be granted free; they conjugate these derivatives and do not +increase their ranks. No port mixing or operator-valued adapter is admitted +by this statement. + +Move every constant factor to the left in a k-call product. Since scalar +bank matrices commute with d and d^2=0, the result is + + A_total [I+d (R'_1+...+R'_k)], + +where each R'_j is a conjugate of a rank-one matrix. If the normalized +required endpoint is N on n independent banks and I on any additional +restored banks, its d coefficient has rank n. Faithfulness forces equality +of coefficients. Rank subadditivity therefore gives + + n = rank(sum_j R'_j) <= sum_j rank(R'_j) = k. + +This proves the obstruction for every b,n,k, not only the checked two-bank +seed. A fixed nontrivial common N, independent bank inputs and the permitted +scalar adapter alphabet are essential. At N=I the representation is not +faithful. If distinct queries use different noncommuting involutions, the +products of their d terms need not vanish. N-dependent free adapters could +themselves supply the required endpoint. These changed models are excluded. + +## 5. Raw geometry and conditional deficit screen + +For the old R438 CLEAN word let E_d=span(e0,...,e_(d-1)), 1<=d<=7. Let K_p +be the actual final target cap. A port remains a cap port exactly when +E_d is contained in K_p. At retained-total helper h, let V_h be its actual +frame at the end of the A phase. The copied-total tariff is + + c_h = dim(V_h+E_d)-d. + +The checker reconstructs each V_h by reverse chronological inspection of +the raw A stream. The nine cut frames are 510,...,518. Independently of the +producer's rational basis code, it computes exact rational ranks by +fraction-free integer elimination and uses + + dim(K+E_d)=d+rank(project_(E_d-perp) K). + +This checks every cap membership and all 63 COPY tariffs directly from the +raw integer E8 geometry. The complete results are: + +| d | Remaining caps | FULL lifts F | Nine COPY ranks | Sum C | Caps-C | +| ---: | ---: | ---: | --- | ---: | ---: | +| 1 | 56 | 55 | 6,6,6,6,6,7,7,6,6 | 56 | 0 | +| 2 | 28 | 83 | 6,6,6,6,5,6,6,5,6 | 52 | -24 | +| 3 | 12 | 99 | 5,5,5,5,4,5,5,5,5 | 44 | -32 | +| 4 | 11 | 100 | 4,4,4,4,3,4,4,4,4 | 35 | -24 | +| 5 | 3 | 108 | 3,3,3,3,3,3,3,3,3 | 27 | -24 | +| 6 | 2 | 109 | 2,2,2,2,2,2,2,2,2 | 18 | -16 | +| 7 | 1 | 110 | 1,1,1,1,1,1,1,1,1 | 9 | -8 | + +The deficit conclusion additionally assumes the stated common-prefix +coverage model: n public banks retain all 111 independent ports, giving at +most 111n unpaid common-coordinate units; every one of k repeated calls is +charged F FULL lifts and all nine COPY tariffs totaling C; completed helper +banks, including padding, earn no additional deficit. All other work is +optimistically free or nonnegative. Under exactly these accounting premises, + + D <= 111n-k(F+C) <= k(111-F-C) = k(Caps-C) <= 0. + +The second inequality uses n<=k. No favorable chronological owner construction +can evade this necessary screen while preserving its coverage assumptions. +The rank theorem itself requires no helper-owner assignment; converting it +into a deficit inequality does require the explicit accounting premises above. + +For the R438 E2 example the full local mass decomposes as + + 327*6+111*8 + 2*111*7 + 83 + 52 = 4539. + +For the R429 FULL E2 word, all 111 targets already have the FULL extra +exposure and there are no copied totals: F=111,C=0, giving D<=111(n-k)<=0 +in the same common-prefix family. Its stated local mass is +318*6+111*8+111*7+111*8=4461. These consistency identities do not replace +the construction review's complete local-word replay. + +Deleting the actual first COPY tariff from d=1 changes Caps-C from zero +to +6. Deleting one actual FULL lift changes it to +1. The positive numbers +are deliberately defective invoices, not candidate suppliers. Mixed E +families, port-mixing codes/adapters, changed source cuts, different endpoint +credits, and different native alphabets require a new argument. The seven +leading coordinate prefixes are not the B11 census of 273 other partitions. + +## 6. Credit and unresolved implementation obligations + +The dedicated cover-bank assignment and arbitrary correlated-dirt reasoning +come from retained [PR386](https://github.com/CrocSwap/integer-mult-bounds/pull/386), +whose proof is stored at +`research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt`. Its attribution +credits Zhihao Chen for the compressed composition and Dylan Crow's PR370 +local BIT ancestry, with the upstream contributors retained there. This is +an application and clarification of that method, not a new general cover +banking theorem. + +Credit [PR2857](https://github.com/CrocSwap/integer-mult-bounds/pull/2857), +Yiyang Lu (`Lyy-iiis`), head `0b2e2537b368a0cade07ce3f71452ea018ebe394`, +for the compensation-kernel repacking lineage: a changed input basis must +change the actual compensation and be integrated with a new owner fill. +Credit [PR2908](https://github.com/CrocSwap/integer-mult-bounds/pull/2908), +Jeremy Diviney, head `51309592971e3b5be935599eed2a95404dc7781e`, for the +paired input/output extraction lineage and its full restoration/private-stock +obligations. Their historical complex constructions do not certify these +new BIT words; their original authors and predecessor credits remain intact. + +The fixed source R429/R438 word ancestry, joined frame projectors and actual +native routes remain credited to the immutable lane. This review leaves to +the construction reviewer the full local operator and integer identities. +It leaves open native alphabet admission of the rational GL charts, charged +adapter/scan implementation, public source windows, a complete caller ledger, +rounded precision, fixed-tape realization and all-size transfer. It proves +neither a supplier nor a new kappa. Substantial OpenAI Codex assistance; +Apache-2.0. No independent human or formal-kernel review is claimed. diff --git a/research/bit-paired-helper-boundaries/PROOF-NATIVE.md b/research/bit-paired-helper-boundaries/PROOF-NATIVE.md new file mode 100644 index 0000000000..15001059a3 --- /dev/null +++ b/research/bit-paired-helper-boundaries/PROOF-NATIVE.md @@ -0,0 +1,282 @@ +# Three fixed helper-kernel words and their paired native residuals + +This proof covers the frozen ten-entrance R429 word, the common coordinate-E2 +R429 word, and the common coordinate-E2 old CLEAN R438 word. It establishes +their literal local signed and binary maps, costs, and rational ADDRESS +identities. It does not supply a chronological owner construction, a compatible +all-size native compiler, rounded/tape admission or a new kappa bound. +Substantial OpenAI Codex assistance; Apache-2.0. + +## Domains and fixed inputs + +Every ordinary source, old target and helper has an independent entrance +column. The two R429 words have 651 arbitrary integer scalar inputs, comprising +111 sources, 111 targets and 429 helpers, with no private allocation. The R438 +word has 660 arbitrary integer inputs, comprising 111 sources, 111 targets and +438 helpers. It additionally uses one initially zero private cell, reused for +nine COPY/ERASE lifecycles. A zero frame is not a zero value. + +Signed scalar lifts are over the integers. Clean target behavior and the +native arbitrary-dirt interpretation below are over binary VALUE arrays. +ADDRESS matrices are rational; the two common-E2 constructions specialize to +fields of characteristic outside {2,3,5}. The ten rank-one paired residuals +are dyadic and specialize to odd characteristic. This distinction is material: +integer source/helper restoration is exact, but integer target helper +coefficients are generally nonzero and even. + +The inputs are the pinned R438 source, the pinned R429 FULL compensation word, +and the three emitted words and their saved geometry. The independent checker +does not import a producer utility. It reconstructs semantic dirty maps from +signed replay, consumes the emitted words directly, and derives projectors +from independent integer-root bases. Exact input pins are in `RESULT.json`. + +## Semantic dirty columns and the integer basis change + +Let D be the helper-to-target binary dirty map with the initial compensation +ADDs omitted. The independent calculation initializes every helper with a +separate integer column, executes the whole uncompensated word including +every old COPY/ERASE, and reduces its target coefficients modulo two. For the +R429 FULL word, D has size 111 by 429; for the old CLEAN word it has size +111 by 438. Both have binary rank 111. Every column agrees with its literal +original compensation column. Thus the construction uses the actual semantic +dirty map, not a count of syntactic incidences. + +For the global constructions, scan original helper columns in their fixed +order, retaining an independent column whenever possible. There are 111 +pivot helpers. Each dependent column j has a unique expansion in these +original pivot columns: + + D_j = sum_(i in I_j) D_i over F2. + +Low-pivot dense elimination independently reconstructs all selected pivots and +expansions, and matches every emitted helper-basis ADD. Set + + N = sum_(j dependent, i in I_j) E_(i,j), S=I+N. + +Every destination i is a pivot and every source j is dependent. These sets +are disjoint, so N^2=0 over the integers. The basis ADDs commute, S is +unimodular, and S^-1=I-N is realized by negating their coefficients. The +emitted inverse lists are checked literally. This identity also proves that +permuting commuting setup gates is an equivalent construction. + +Right multiplication by S leaves the pivot columns of D unchanged and kills +all selected dependent columns modulo two. The verifier checks every entry +of the new compensation against D S. All its ADDs are at ZERO and read only +helpers whose declared entrance frame is ZERO. The changed basis has + + R429 E2: 318 dependent helpers, 12,756 setup ADDs and 12,756 inverse ADDs; + R438 E2: 327 dependent helpers, 11,389 setup ADDs and 11,389 inverse ADDs. + +The integer kernel statement is N^2=0; the dirty cancellation D S is a +binary statement. No integer equation D S=0 is asserted. + +## Ten actual rank-one entrances + +The selected R429 helpers, in construction order, are + + 242,467,462,469,463,464,367,401,444,470. + +Their actual first frames are, respectively, + + 7,29,49,52,54,56,65,76,79,94. + +Seven have zero D column. The remaining three have the same D columns as +helpers 233,360,385, respectively; these columns have weights 19,17,18. +The setup gates are + + 233 += 242, 360 += 367, 385 += 401, + +each at the genuine common first frame for that pair. The three companion +first MOVEs are advanced and retained. The selected ten helpers are instead +supplied at their rank-one frames, so their ten ZERO-to-rank-one MOVEs are +deleted. The complete initial compensation is D S modulo two. The three +inverse basis ADDs occur at actual FULL common frames after cleanup. + +The checker verifies the entire inherited scalar sequence, its common frames, +the changed starts, and the exact multiset of MOVEs: it is the original +multiset with precisely those ten rank-one queries removed. Source and target +cuts remain unchanged. The six basis ADDs are included in the word; no new +recursive query or private cell is used. + +## The two global E2 words and the old snapshots + +Let E=span(e0,e1). Dependent helpers enter at E, pivot helpers enter at ZERO, +and all helpers end at FULL. Initial compensation uses only pivot helpers at +ZERO. All helpers are then brought to the genuine common E setup cut, and S +is executed. Every later original scalar frame f is replaced by span(f,E). +All forced public climbs are emitted and paid. Finally S^-1 is executed at +FULL. The independent checker matches every inherited ADD's operands, sign, +chronological position and joined frame; it also matches every inherited +COPY/ERASE to its joined source/private frames and every declared final frame +to the old final frame joined with E. + +The R429 FULL variant retains its original source rank-one entrances, source +FULL exits, target ZERO entrances and target FULL exits. In the old R438 word, +the target exits change from K_p to K_p+E. Exactly 83 become FULL and 28 remain +at their original rank-seven cap. All 222 public frame paths, including every +rank along them, are checked against the saved paths. + +The old word still pays for all nine copied totals. Their helper sources are +471 through 479. A copied source at U+E is read into the one fresh zero private +field at E, with tariff dim(U+E)-2. The source cannot be modified while its +snapshot is live. Each scatter is at the genuine common E frame. ERASE checks +the exact original snapshot and restores the private cell to integer zero +before reuse. Forward and reversed lifecycles are both checked. The nine +tariffs are + + 6,6,6,6,5,6,6,5,6, with sum 52. + +The two tariff-five sources are helpers 475 and 478 at frames 514 and 517; +the other seven source frames are FULL. The private frame is 636, the actual +coordinate E2 frame. This is one sequentially reused zero field, not nine +free snapshots or nine simultaneously available private fields. + +This billing uses the predecessor's nested COPY/ERASE contract: the COPY has +the stated rank-difference tariff, and its matching ERASE closes the immutable +snapshot. The finite review checks that interface's premises and does not +independently admit an all-size COPY implementation. + +## Complete signed and binary operators + +The verifier uses dense signed rows, starting with all independent ordinary +input columns, and executes each literal emitted word. Every MOVE has the +declared current frame, strict nesting, and exact positive rank difference. +Every ADD uses distinct registers at the same actual frame. Every source and +ordinary helper output row is exactly its original integer unit row. Every +target retains exactly its own old-y coefficient and no other old-y input. +The private row, when present, is exactly zero. + +Modulo two, the full map in every case is + + (x,y,h) -> (x,y+x,h), + +with the private zero restored. The endpoint integer operator has form I+T, +where only target rows of T are nonzero and every target input column of T +is zero. Hence T^2=0 and its exact inverse is I-T. A separate literal reversed +replay, starting from arbitrary identity columns and a zero private cell, +matches every entry of I-T. This proves both inverse compositions over the +integers, rather than checking only parity or an inverse on clean helpers. + +Each R429 orientation compares 423,801 entries. Each R438 orientation compares +436,260 entries, including the private row. The forward maxima of the complete +prefix row L1 norm are 874, 8,770 and 31,416, respectively. The target matrices +have 6,497, 36,182 and 44,884 nonzero even helper coefficients, respectively. +These provide explicit evidence that the clean target map is only a binary +VALUE claim. Signed targets are preserved with their actual integer lift. + +## Complete local bill + +| Fixed word | H by query rank | Mass | ADDs | Ordinary helper residuals | Private peak | +|---|---|---:|---:|---|---:| +|Ten rank-one entrances|{1:1396,2:1342,3:79,4:44,5:93,6:11,7:9}|5087|12884|10 width7 +419 width8|0| +|R429 common E2|{1:1184,2:1254,3:108,4:89,5:7,6:9}|4461|34620|318 width6 +111 width8|0| +|R438 CLEAN common E2|{1:1170,2:1254,3:108,4:94,5:13,6:16}|4539|34643|327 width6 +111 width8|1| + +The histograms include every literal MOVE and every paid COPY. They are +independently regenerated, including ADD counts and prefixes. The ten-entrance +histogram equals the pinned R429 FULL histogram minus 10 H1. The complete +coverage checks are + + 5087 = 111*(7+8) + 419*8 + 10*7, + 4461 = 111*(7+8) + 111*8 + 318*6 = 5097-318*2, + 4539 = 111*7 + 28*7 + 83*8 + 111*8 + 327*6 + 52. + +Equivalently, the old CLEAN baseline mass is 5,121 with original COPY sum 63, +and 4539 = 5121 - 327*2 + 83 + (52-63). No old target cap or copied-total +tariff is retained for free after its frame changes. + +## Actual rational ADDRESS implementations + +For every used frame U, choose independent integer root rows B. The independent +projector is + + P_U = B^t (B B^t)^(-1) B. + +It is compared entrywise with the saved projector. Its span, dimension, +symmetry, idempotence, RREF basis and saved Gram determinant are independently +checked. The two words use the same 434 actual frames. Their MOVE/COPY pair +sets contain 1,589 and 1,599 pairs; the former is a subset of the latter, so +1,599 distinct pairs cover both complete words. There are 160 used frames +whose projectors have odd denominators. + +For each nested pair A subset U, P_U P_A=P_A=P_A P_U. Thus + + W=P_U-P_A, W^2=W, rank W=dim U-dim A. + +For the supplied invertible rational C, the verifier checks both inverse +products and + + C diag(I_rankW,0) C^-1 = W. + +Writing D_P=[[I-P,P],[P,I-P]], every one of the 16 ADDRESS columns is checked +in the identity + + diag(C,C) D_coord(rankW) diag(C^-1,C^-1) + = D_W = D_U D_A. + +This includes every copied-total source/private pair, whose nested difference +has the paid COPY rank. It is not a substitution of scalar rank for an +unverified ADDRESS operator. + +Both the independently selected integer-root Gram determinants and the saved +rational bases/projectors/GL inverses have exceptional prime factors only +2,3,5. Away from these characteristics, the root bases keep their rank, the +Gram inverses and GL charts are defined, and the exact matrix identities +specialize. The exclusions are a sufficient set for these explicit charts; +no minimal-exclusion theorem is claimed. + +These C matrices are rational GL adapters. Odd denominators really occur. +They therefore do not establish compatibility with an orthogonal/dyadic +recursive-query alphabet, an allowed all-size compiler, scalar scan costs or +a physical tape implementation. Those remain admission obligations even +though the complete finite matrix identities hold. + +## Paired physical helper contract + +For a helper supplied physically as u at entrance E, define its logical dirt +to be h=D_E^-1 u. This is a coordinate description of an arbitrary input, not +an executed entrance query. Since the literal non-target scalar row is h at +exit U, the actual physical output is + + D_U h = D_U D_E^-1 u. + +Over binary VALUE arrays the target coefficients of this arbitrary logical +dirt cancel. Consequently the paired contract is independent of an external +choice of dirt value. Integer target dirt need not cancel, as noted above. +An owner must route the physical pair (E,U); using only the exit width or +requiring the former ZERO-coordinate interpretation would be a different +contract. + +Here U=FULL. For each of the ten actual rank-one entrances, the checker +verifies all 16 ADDRESS columns of + + D_FULL D_E^-1 = D_(E-perp), rank(E-perp)=7. + +For common E2 the residual is the coordinate width-six interchange. The +literal coordinate permutation with row order (2,3,4,5,6,7,0,1) maps E-perp +to the first six axes; its conjugation is checked. The 111 pivot helpers +retain ZERO/FULL residual width eight. These paired residual identities do +not themselves supply chronological helper owners or a bank caller. + +## Defect controls and limits + +For each fixed word, removing its actual inverse basis causes an arbitrary +dirty-helper column to leak into another helper. Removing one matching setup +and inverse basis pair while retaining the new compensation exposes odd +target dirt. Restoring a selected helper's old ZERO entrance fails an actual +typed frame check. In the old word, deleting an actual ERASE fails the next +snapshot lifecycle check. A one-entry perturbation of a residual projector +fails an explicit ADDRESS column. Each control changes the candidate and is +checked against its intended failure predicate. + +This review does not search other common planes, other ranks or partitions. +The seven-coordinate hybrid census, bank lower bound and chronological owner +result are separate mathematical obligations. Nothing here admits a positive +full caller, rounded suffix-error bound, all-size source/tape realization, +unconditional multiplication theorem or new kappa value. + +The historical `GLOBAL-KERNEL-BOOST.md` section “Selective variants and source +snapshot control” is expressly outside this result. Its finite selective +screens, exposure-mask searches and proposed snapshot corridor are not +replayed or certified here. Their preservation as historical text supplies no +additional theorem to this three-word package. diff --git a/research/bit-paired-helper-boundaries/README.md b/research/bit-paired-helper-boundaries/README.md new file mode 100644 index 0000000000..ae4c7ab9e3 --- /dev/null +++ b/research/bit-paired-helper-boundaries/README.md @@ -0,0 +1,167 @@ +# Paired helper entrances for three fixed BIT words + +Changing the logical entrance of arbitrary dirty helpers removes local queries +in three literal R429/R438 words. The complete local words and paired physical +residuals are verified here, together with a dedicated helper-bank construction +and a conditional rejection of the uniform common-prefix caller. These local +savings do not establish a native supplier or a new κ. +Scientific pin: `20ecf2891d80b5acf18d980b2164fb44ea7faa90`. + +| Fixed word | Ordinary inputs | Helper residual widths | ADDs | Native rank mass | Private fields | +|---|---:|---|---:|---:|---:| +| R429 ten rank-one entrances | 651 | 10 of width7,419 of width8 | 12,884 | 5,087 | 0 | +| R429 common coordinate E2, FULL target | 651 | 318 of width6,111 of width8 | 34,620 | 4,461 | 0 | +| R438 common coordinate E2, hybrid target | 660 | 327 of width6,111 of width8 | 34,643 | 4,539 | 1 required zero | + +All ordinary sources, old targets and helpers are arbitrary. Public helper +cancellation and the target shear are over **F2 VALUE coefficients**. Source +and helper rows restore exactly over the integers, and the literal inverse +returns every ordinary input. Signed integer targets retain nonzero even +helper coefficients; no exact integer clean shear is claimed. ADDRESS maps +are exact rational operators, with the stated finite-field exclusions. + +The ten rank-one variant saves 10H1 relative to its FULL predecessor and +contains six basis ADDs. In each E2 variant the actual 111-by-R semantic dirty +matrix has rank111. Choosing111 pivot columns gives S=I+N, where destinations +are pivots and sources are dependent columns, so N²=0 over the integers. +Initial compensation uses D*S modulo2; the dependent columns vanish. Pivots +climb to the common entrance E before S, every later frame is joined with E, +and S^-1 runs at FULL. Every forced public climb is included in the word. + +The complete histograms are: + +- Ten entrances: H={1:1396,2:1342,3:79,4:44,5:93,6:11,7:9}. +- R429 E2: H={1:1184,2:1254,3:108,4:89,5:7,6:9}. +- R438 E2: H={1:1170,2:1254,3:108,4:94,5:13,6:16}. + +The R438 E2 word enlarges83 old target caps to FULL. Its nine copied totals +have ranks6,6,6,6,5,6,6,5,6, totaling52. A single required-zero private field +is reused with literal erasure. Those costs cannot be removed when comparing +its hybrid public interface with the earlier CLEAN word. + +## Physical boundary and native limitation + +For an arbitrary physical array u entering at E, define logical dirt +h=D_E^-1 u. This is a bijective interpretation, not an executed entrance +query. The exact helper row gives physical residual D_U D_E^-1. If E is +contained in U, that residual is D_(U intersect E-perp). Public independence +holds over F2 for all joint inputs, including correlated entering arrays. +Keeping the old ZERO logical-dirt identification is a different contract +and requires the corresponding entrance queries. + +The native certificates reconstruct each actual joined frame, projector and +MOVE/COPY residual. Explicit rational GL charts conjugate coordinate swaps +to those residuals. Their specialization excludes primes2,3,5; some projectors +have odd denominators. These exact ADDRESS identities do not admit the charts +into a narrower orthogonal/dyadic recursive-query alphabet. Adapter lowering, +source access, scan costs and the physical tape implementation remain open. + +[PROOF-NATIVE.md](PROOF-NATIVE.md) gives the complete fixed-word argument and +its independent exact checks. [PROOF-CALLER.md](PROOF-CALLER.md) separates the +arbitrary-cover proof, finite fixture and conditional all-bank cost screen. + +## Dedicated helper banks and the caller screen + +The dedicated cover assignment g=d Pi_j^-1 requires the entire finite cover +to act through diag(g,g), centralizing the full head/tail swap. Every required +adapter must belong to it; helper banks are separate from public/private +families, and m covers each complete local footprint, including spectators. +Same-call adapters are distinct, residual coordinate blocks are disjoint, +and complete local calls run serially. Pay +padding on every uncovered coordinate. Local spectator axes can overlap a +later role's residual block because each complete endpoint is identity there +and the next call accepts arbitrary dirt. This is a helper-only construction; +it supplies no recycled public-family pending windows. + +The m=36 cyclic fixture checks all432 coordinate columns and36 assignments. +For12 R429 E2 replicas, all5148 roles fit636 width-six banks and333 width-eight +banks. The latter pay333 rank-four pads: total helper mass34884=36*969. +Per replica, stock323/4 and mass2796+111=2907 agree. This does not supply a +public-bank dividend or solve the missing native admission. + +For one fixed nontrivial common involution N and N-independent scalar bank-GL +adapters, d=N+I has d²=0 over F2. Every hybrid query contributes a rank-one +coefficient to the linear d term. Requiring N on n independent banks therefore +needs k>=n queries. This written proof covers every bank count within that +alphabet, beyond the finite faithful seed check. + +A deficit conclusion additionally requires the explicit uniform common-prefix +coverage invoice: n public banks retain all111 independent ports and receive +at most111n common-coordinate units of credit. For each of seven +leading-coordinate prefixes the pair +(remaining cap ports,COPY rank sum) is +(56,56),(28,52),(12,44),(11,35),(3,27),(2,18),(1,9). +Charging each call's F FULL lifts and C copied-total rank gives +D<=111n-k(F+C)<=k(111-F-C)<=0. Completed helper banks earn no extra dividend. +The rank theorem alone is not an unconditional cost or owner obstruction. +Mixed E, port mixing, operator-valued free adapters, changed source cuts and +changed endpoint credits require another proof. + +## Reproduction and evidence + +From the repository root with Python3.12: + +```sh +python3.12 -B scripts/research_package.py --package research/bit-paired-helper-boundaries +``` + +Seven mathematical stages reconstruct five complete producer receipts, all +five complete emitted word/geometry bodies and two independent receipts. +The native reviewer imports no producer mathematics; the caller reviewer +uses raw integer geometry, faithful binary operators and explicit role +placement. The launcher authenticates every frozen input before and after +each stage and compares full receipts with JSON types preserved. Explicit +path/output adapters preserve the original arithmetic and loops. Integrity +controls run through this same launcher. + +Independent reviews cover actual omitted inverse bases, changed kernel +vectors, endpoint/owner defects, missing COPY/lift/padding tariffs and +corrupted certificate coverage. Finite exact computations, written all-bank +and arbitrary-cover proofs, and formal-kernel proofs are different evidence; +no formal-kernel or independent human certification is claimed. + +Original historical bytes and notes remain in `frozen/`. Their statements +are read with the current proofs' explicit F2 and alphabet premises. The +historical GLOBAL note also describes selective/mixed-entrance screens and +snapshot experiments: those are **not replayed or claimed by this package**. +The separate all273-partition B11 result is also outside this contribution. + +## Sources and credit + +Sagar Thakrar's R438 transport and the eumemic, DreamingOfClouds and Ali Romman +E8/BIT lineage provide the immutable geometry and predecessor words. The +R429 source-code ancestry appears in +[PR3645](https://github.com/CrocSwap/integer-mult-bounds/pull/3645), and its +FULL-compensation interface in +[PR4039](https://github.com/CrocSwap/integer-mult-bounds/pull/4039). +No new E8 geometry or predecessor interface is claimed. + +The dedicated whole-bank cover method is inherited from +[PR386](https://github.com/CrocSwap/integer-mult-bounds/pull/386), credited to +Zhihao Chen with Dylan Crow's PR370 local ancestry. Yiyang Lu's +[PR2857](https://github.com/CrocSwap/integer-mult-bounds/pull/2857) supplies the +compensation-kernel repacking lineage, including its credit to Philippe Van +Velzen's concurrent PR2853 and Jeremy Kothe's predecessor words. Jeremy +Diviney's [PR2908](https://github.com/CrocSwap/integer-mult-bounds/pull/2908) +supplies the paired input/output extraction lineage. Those earlier complex +constructions retain their premises and do not certify these changed BIT words. +Karl Appel's [PR369](https://github.com/CrocSwap/integer-mult-bounds/pull/369) +also studies two rank-two BIT kernel entries and compatible retimings on a +different PR364/366 predecessor, with its own charged entrance ranks and +banking. That prior kernel-entry work is related, not evidence for the +three changed words here. The exact origin map and hashes are in +`ORIGINS.json` and `FROZEN-SHA256.json`; all original notices are retained. + +Prepared by Ross Richardson with substantial OpenAI Codex assistance and +separate AI reviews. Apache-2.0. Live overlap searches are leads, not novelty +certificates. The selected repository frontier is unchanged. + +## Open next questions + +Can the actual rational GL routes be implemented in the intended native +alphabet with paid scalar scans, source access and private storage? Supply +that complete lowering before treating the rank profile as an admitted supplier. + +Can a changed public caller overcome the uniform-prefix deficit while meeting +all public-window, helper-owner and padding obligations? The helper fixture +and fixed scalar-GL screen do not establish or exclude such a changed caller. diff --git a/research/bit-paired-helper-boundaries/REVIEW-CALLER.md b/research/bit-paired-helper-boundaries/REVIEW-CALLER.md new file mode 100644 index 0000000000..7106bcc10f --- /dev/null +++ b/research/bit-paired-helper-boundaries/REVIEW-CALLER.md @@ -0,0 +1,106 @@ +# Independent B10 caller and dedicated-owner review + +**Pass within the explicit paired-boundary, dedicated-cover and uniform +common-prefix models.** This does not complete B10's separate native-word +review or admit a supplier. Only this owned directory was written; original +sources and other worktrees remain unchanged. + +## Verified results + +* The arbitrary-physical-dirt interpretation is a bijective input-coordinate + change: h=D_E^-1 u gives residual D_U D_E^-1 without executing a new + entrance query. It requires the actual complete helper row and public + coefficient theorem. Public independence is over F2 VALUE arrays; signed + integer target coefficients can be nonzero even numbers. Exact integer + source/helper restoration remains a separate premise. +* The dedicated assignment g=d Pi_j^-1 is a bijection for each role. Distinct + same-call Pi_j prohibit physical-family collisions. At each fixed owner, + disjoint residual swaps commute and, with paid padding, give full swap. + Doubled-chart centrality and serial complete calls are essential. Local + spectator overlap with another role's residual block is permitted only + under that arbitrary-input completed-endpoint contract. +* A separately implemented m=36 cyclic fixture matches all 36 assignments + and verifies all 432 independent ADDRESS columns across six owners. The + actual coordinate-E2 word first needs its fixed local permutation into the + fixture's canonical footprint; that permutation is not claimed to be in + the smaller cyclic cover itself. +* Explicit placement of all 5,148 roles from 12 replicas yields 636 width-six + banks and 333 width-eight banks. All bank slots and same-call adapter + exclusions check. The latter banks pay 333 rank-four pads. Total mass is + 34,884=36*969; per-replica helper stock is 323/4. This is helper-only stock, + not a full public caller ledger or a public-family window allocation. +* The raw geometric reconstruction checks all 111 target caps for each of + seven leading-coordinate prefixes and all 63 COPY tariffs. It reproduces + the seven (remaining caps,total COPY rank) pairs + (56,56),(28,52),(12,44),(11,35),(3,27),(2,18),(1,9). +* A faithful four-by-four binary representation verifies all coefficients of + both hybrid seeds and the squared FULL seed. The written square-zero + derivative argument proves k>=n for every bank count, allowing only fixed + common nontrivial N and N-independent scalar bank-GL adapters. +* With the explicitly stated uniform common-prefix coverage invoice, + D<=111n-k(F+C)<=k(111-F-C)<=0. The cost inequality needs its endpoint-credit + and complete FULL-lift/COPY assumptions in addition to the algebraic rank + theorem. It is not an unconditional owner or native supplier obstruction. + +## Defect sensitivity + +The independent checker mutates actual operations, assignments or tariffs: + +| Change | Observed defect | +| --- | --- | +| Omit the paired entrance action | 144 wrong owner coordinate columns | +| Omit one role per invocation | 72 wrong owner coordinate columns | +| Duplicate a same-call adapter | Physical-family collision rejected | +| Shift only one ADDRESS half | Full-swap centrality fails | +| Omit rank-four bank padding | 8 wrong coordinate columns on that bank | +| Omit the middle FULL seed call | Complete hybrid operator changes | +| Omit first d=1 COPY tariff | False deficit upper allowance +6 | +| Omit one d=1 FULL target lift | False deficit upper allowance +1 | + +These deliberately changed cases are controls, not candidate constructions. + +## Scope needed in the package + +The local E2 R429/R438 words and ten rank-one precursor still need their +construction review's literal all-input replays, exact source/helper integer +rows, F2 target map, native paired charts and cleanup. This review did not run +the global multi-megabyte receipts or import their producer code. + +Keep the proposed dedicated helper banks separate from pending-window public +owners. Free rational GL charts have not been admitted to a narrower native +alphabet. Charge adapters, source access, private work, scans and physical +controller costs before transferring to a supplier. Do not infer a complete +owner implementation, all-size dispatcher, rounded precision theorem or +tape theorem from the fixture. + +The rank screen excludes mixed-E families, nonuniform/port-mixing codes, +operator-valued free bank adapters, different source cuts and changed +endpoint-credit contracts. Its seven leading coordinate planes are not the +separate B11 all-273-partition computation. No positive exponent or kappa +claim follows. + +## Attribution and reproduction + +`PROOF-CALLER.md` explicitly credits PR386's retained dedicated-bank +construction (Zhihao Chen, with Dylan Crow's PR370 local ancestry), Yiyang +Lu's PR2857 compensation-kernel repacking and Jeremy Diviney's PR2908 paired +extraction lineage. Historical claims retain their original premises; +none certifies the changed BIT word by inheritance. + +Run from this directory: + +```sh +python3 independent_check.py --output INDEPENDENT-RESULT.json +python3 -O independent_check.py --output INDEPENDENT-RESULT-O.json +``` + +Both modes pass and produce byte-identical receipts. The checker uses exact +fraction-free integer rank, reverse cut discovery, faithful binary matrices, +direct column actions and explicit role placement. It does not import any +historical producer. `VALIDATION.json` records command outcomes and hashes; +`FINAL-CHECK.json` binds frozen review files and unchanged source bytes. + +The arbitrary-cover and all-bank statements are written proofs; the fixture +and seven-plane geometry checks are finite exact computations. Neither is a +formal-kernel proof or independent human review. Substantial OpenAI Codex +assistance; Apache-2.0. diff --git a/research/bit-paired-helper-boundaries/REVIEW-NATIVE.md b/research/bit-paired-helper-boundaries/REVIEW-NATIVE.md new file mode 100644 index 0000000000..7bdf09ea9a --- /dev/null +++ b/research/bit-paired-helper-boundaries/REVIEW-NATIVE.md @@ -0,0 +1,140 @@ +# B10 independent construction and native review + +Verdict: **PASS for the three fixed local words and their stated rational +paired native residuals.** The pass retains the binary VALUE target contract +and all compiler, owner, rounding and physical-tape admission boundaries. +No arithmetic defect was found. Substantial OpenAI Codex assistance; +Apache-2.0. + +The immutable scientific source pin is +`20ecf2891d80b5acf18d980b2164fb44ea7faa90`. Reviewed inputs were read from the +parent's frozen B10 staging set and were not modified. The independent checker +imports no producer mathematics. It uses dense signed input columns, a +low-pivot dense binary factorization, independent integer-root Gram inverses, +and direct ADDRESS-column calculations. The parent owns producer replay and +repository/publication gates. + +## Exact finite coverage + +| Word | Arbitrary inputs | Matrix entries per orientation | Complete mass | Basis ADDs | Prefix row L1 | +|---|---:|---:|---:|---:|---:| +|Ten rank-one entrances, R429|651|423801|5087|6|874| +|Global coordinate E2, R429|651|423801|4461|25512|8770| +|Old CLEAN coordinate E2, R438|660 plus one zero private|436260|4539|22778|31416| + +All rows are checked over the integers in both orientations. Source/helper +rows are identity, the old-y block is identity, and the private row is zero. +Every target column agrees with the intended clean shear modulo two. The +reverse word is replayed on arbitrary identity input columns, and its full +matrix is compared to I-T when the forward map is I+T. The checked support +of T makes T^2=0, so both inverse compositions follow exactly. This is stronger +than an inverse test only on one clean input. + +The historical inverse profiles begin from the forward endpoint matrix; this +checker's separately recorded inverse profiles begin from identity columns. +Their prefix quantities describe different initial symbolic states. The +forward profiles are compared exactly to the historical complete receipts. + +The independent uncompensated signed replay reconstructs every column of D, +and compares it to every literal initial compensation column. Both D matrices +have binary rank 111. This semantic check is separate from syntactic +compensation extraction; the global producer's `factor_dirty` itself reads +the literal compensation list. The new independent check supplies the direct +semantic bridge for that variant. + +For the global words, independently reconstructed pivots and unique dependent +column expansions match every emitted setup ADD. Disjoint pivot destinations +and dependent sources prove N^2=0 over Z. Every inverse basis gate and every +entry of the new compensation D S modulo two is checked. For the local word, +all ten actual kernel supports and first frames are checked, including the +three duplicate-column pairs and seven zero columns. + +The source-to-join check compares each inherited ADD's roles, sign, +chronology and actual joined frame; it also compares all COPY/ERASE source and +private joins and every final-frame join. The ten-local check matches its +unchanged scalar core and exact MOVE multiset after deleting ten H1 queries. +The old E2 word checks all 222 public paths, all 83 changed target caps, and +all nine paid COPY ranks (sum 52). The one private cell is freshly zero at +each COPY, its source remains immutable, and ERASE restores the exact snapshot. + +Baseline masses 5097 and 5121, the original COPY sum 63, and every claimed +mass difference are independently calculated. The residual inventories are +10 width7 +419 width8; 318 width6 +111 width8; and 327 width6 +111 width8. + +## Native matrix coverage + +The common E2 words use 434 distinct frames. All stored RREF bases, +projectors, Gram determinants and ranks match independent integer-root +calculations. Their 1589 and 1599 query-pair sets have union size 1599. The +checker verifies both GL inverse products, the exact residual projector and +all 16 ADDRESS columns of both its coordinate conjugation and its actual +nested-frame composition. COPY source/private pairs are included. + +The independent integer Gram certificates and rational adapters yield the +same sufficient excluded-prime set {2,3,5}. There are 160 used frames with odd +projector denominators. Consequently these are exact rational GL charts with +the stated finite-field specialization; they are not a proof of an +orthogonal/dyadic or all-size recursive compiler. The ten rank-one residuals +and the common-E2 coordinate-complement residual are checked separately on +all ADDRESS columns. The stored width-six coordinate permutation is checked +against the actual complement projector. + +## Required scope in publication prose + +The target's nonzero even helper coefficients number 6497, 36182 and 44884 +for the three variants. Their nonvanishing is retained in the receipt, so +“all public helper dependence cancels” must be qualified as a binary VALUE +claim. Integer source/helper restoration remains exact. The proof supplies +the correct paired interpretation h=D_E^-1 u for arbitrary physical dirt, +with residual D_FULL D_E^-1. It does not identify that residual with the +old ZERO/FULL contract or charge an entrance query merely to name h. + +Every basis ADD, public forced climb, target lift, copied-total tariff and +private lifetime is in the literal finite word. A smaller local helper width +does not imply a chronological owner allocation or a positive full caller. +Scalar scan costs for the rational GL adapters, source access, tape, rounding +and all-size native admission remain open in this construction review. + +The historical `GLOBAL-KERNEL-BOOST.md` section “Selective variants and source +snapshot control” is expressly excluded. None of its 162/120/153 selective +censuses, exposure-class search claims or snapshot-corridor proposal is part +of this review or certified by these three word replays. The seven-coordinate +hybrid census, bank lower bound and paired owner result are assigned to the +other reviewer. B11's mixed-plane/partition work is separate. + +## Defect-sensitive checks + +- Omitting inverse basis gates changes actual helper output columns in all + three variants: witnessed inputs are helpers 242,241,246, respectively. +- Removing one corresponding setup/inverse pair while retaining the new + compensation causes odd target dirt on those same inputs. The receipt + retains every affected target in each witness. +- Resetting the first selected helper to its former ZERO entrance fails the + intended frame predicate at a concrete record in every variant. +- Deleting the first ERASE in the old word fails the snapshot lifecycle at + the subsequent COPY, even though the private register remains allocated. +- Perturbing one residual-projector entry fails a specific ADDRESS column. + +Controls are accepted only when the intended predicate detects the actual +mutation. Independent dense endpoint comparison and exact N^2=0 establish +the signed basis behavior; commutation also permits equivalent reorderings +of setup gates. These are targeted controls, not a universal fault model. + +## Reproduction + +The checker uses Python's standard library and no assert-based acceptance. +Normal and optimized execution compare the whole independent receipt: + +```sh +python3 -B /Users/ross/git/math/.research-automation/runs/unpublished-contributions-20261019T0916Z/b10-native-review/independent_check.py +python3 -B -O /Users/ross/git/math/.research-automation/runs/unpublished-contributions-20261019T0916Z/b10-native-review/independent_check.py +``` + +`--write` freezes a new receipt; default execution never rewrites it. Input +paths deliberately point to the immutable external B10 staging tree. A +portable package may adapt paths and expected source pins while preserving +the mathematical checks. `RESULT.json` retains all input SHA256 values, every +semantic dirty row, every basis pair, full profiles, complete endpoint matrix +hashes, all 434 independent frame certificates, all 1599 query pairs and all +defect witnesses. `FREEZE.json` pins the final review files and validation. +No original sources, repository files or external services were modified. diff --git a/research/bit-paired-helper-boundaries/SOURCES.json b/research/bit-paired-helper-boundaries/SOURCES.json new file mode 100644 index 0000000000..166b141534 --- /dev/null +++ b/research/bit-paired-helper-boundaries/SOURCES.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "files": [ + { + "path": "certificates/selected-result.json", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "usage": "provenance" + }, + { + "path": "docs/research/agent-task-catalog.json", + "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5", + "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0", + "usage": "provenance" + }, + { + "path": "docs/research/research-family-status.md", + "git_blob": "9b7d65650d8fcd6247a758936b24426b40e40efa", + "sha256": "9b98ab42364e90588e90410fd2773f9bc4bf5050f514101bed0a0246881b5b7e", + "usage": "provenance" + }, + { + "path": "research/bit-r438-transport-rehost/words/r438-t154.json.gz", + "git_blob": "e12a566658a4b2c8b6ae0ecc34fd41290f68f5e8", + "sha256": "a353999bceac4ac957f540adfd3e5f8768297138b27132eeb83332e2ea4b1022", + "usage": "provenance" + }, + { + "path": "research/e8-bit-carrier-skeleton/data/bit/bitE8-r865.json.gz", + "git_blob": "8bec1751f7e33c3a1e4673ef5dbc34d6f205321e", + "sha256": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55", + "usage": "provenance" + }, + { + "path": "research/bit-r438-transport-rehost/README.md", + "git_blob": "f94092e67129f60b2ec39b9c78ef343a17961e6b", + "sha256": "ca62c113c07282e25230cd22fabdd0affc2bf35a792b3251444e3551dab75474", + "usage": "provenance" + }, + { + "path": "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt", + "git_blob": "31efe312680fdafba0ccfb630bb6b711acad5944", + "sha256": "c5f077b849e9add9957ab4ee36095dd47bc678dee7e09baa146dac4c0a0d66b2", + "usage": "provenance" + }, + { + "path": "research/shared-kernel-repacking/README.md", + "git_blob": "5397917b93f00712922f3ae045449ab786c5fc5d", + "sha256": "814b37dba638ba5550b955438e8acca84f004853ba3e24232bb253f4534cc01e", + "usage": "provenance" + }, + { + "path": "research/two-sided-helper-extraction/README.md", + "git_blob": "87f1421e9eaacc691ac5000cd953cdf3bf40e79b", + "sha256": "c8667c41bf605ba13f5527dcb3e6c9369eb4dd3d237112632b10c0961a97c24a", + "usage": "provenance" + } + ] +} diff --git a/research/bit-paired-helper-boundaries/TASK.json b/research/bit-paired-helper-boundaries/TASK.json new file mode 100644 index 0000000000..6864313bd8 --- /dev/null +++ b/research/bit-paired-helper-boundaries/TASK.json @@ -0,0 +1,67 @@ +{ + "schema_version": 1, + "task_id": "bit-helper-contract", + "original_card": { + "id": "bit-helper-contract", + "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/r439-bsection-stars-seed01/README.md", + "research/r439-copy-path-sharing-barrier/README.md" + ], + "methods": [ + "Derive a replacement interface lemma and price its implementation.", + "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement." + ], + "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/r439-bsection-stars-seed01/verify.py" + ], + "expected": "PASS_R439_BSECTION_STARS", + "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.", + "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.", + "allowed_variations": [ + "Choose one helper-star or quartet instance; narrow to one boundary implication." + ], + "scope_change_triggers": [ + "Changing only source count or scalar addition count without an interface argument." + ], + "overlap_terms": [ + "H2_D_frame0_targets_from_helpers", + "K_equals_D", + "helper-star" + ] + }, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "priority_revision": 6, + "author": "Ross Richardson", + "ai_assistance": "Substantial OpenAI Codex assistance and separate AI mathematical and integrity reviews; no independent human or formal-kernel certification.", + "scope_status": "changed", + "scope_change_reason": "User assigned completion and reviewed publication of preserved unpublished contributions. This package finishes one paired helper-boundary method on its three fixed source variants, with the complete local profiles and conditional caller/owner boundaries; no construction search or positive supplier.", + "actual_scope": "Ten rank-one R429 entrances and common-E2 R429/R438 compensation-kernel words; actual rational ADDRESS charts; dedicated-cover helper fixture and conditional uniform-prefix hybrid screen.", + "bottleneck_link": "Replace ZERO helper entrances by actual paired boundaries while pricing forced public climbs, copied totals, native adapter limitations and whole-bank padding.", + "budget_minutes": 240, + "outcome": "completed", + "evidence": "All-column signed/binary literal words and inverse checks, exact native charts, independent construction and caller/owner certificates, full typed receipts and complete word/geometry comparisons.", + "stop_rule": "Finish the fixed three-word boundary package; exclude selective/mixed-E and B11 all-partition searches.", + "open_questions": [ + { + "question": "Can the changed rational GL ADDRESS routes be lowered in the intended native alphabet?", + "why_it_matters": "Odd denominators and rational GL charts alone do not certify the inherited orthogonal/dyadic recursive compiler.", + "first_step": "Give literal admitted scalar routes and charge source access, scans, private buffers and physical tape costs.", + "blocked_by": "No such compiler and complete source/tape invoice is supplied." + }, + { + "question": "Can a different public caller overcome the fixed common-prefix deficit?", + "why_it_matters": "The all-bank rank bound plus explicit uniform exposure accounting gives nonpositive deficit.", + "first_step": "Specify a changed endpoint or scalar adapter model and complete all public/helper/private owner costs.", + "blocked_by": "No complete changed caller or public-window allocation is supplied." + } + ] +} diff --git a/research/bit-paired-helper-boundaries/VERIFY.json b/research/bit-paired-helper-boundaries/VERIFY.json new file mode 100644 index 0000000000..673631f15c --- /dev/null +++ b/research/bit-paired-helper-boundaries/VERIFY.json @@ -0,0 +1,110 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py", + "--stage", + "ten-entrances" + ], + "timeout_seconds": 90, + "checks": "All651 columns, ten actual rank-one entrances, six basis ADDs, exact integer helper/source rows and inverse, complete word/profile." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py", + "--stage", + "full-e2" + ], + "timeout_seconds": 300, + "checks": "R429 common-E2 literal word, all651 columns, semantic rank111 kernel, full word and rational geometry receipts and every ADDRESS chart." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py", + "--stage", + "clean-e2" + ], + "timeout_seconds": 300, + "checks": "R438 common-E2 word, all660 columns plus required-zero private field, all nine COPY/ERASE lifetimes,83 paid FULL lifts and complete charts." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py", + "--stage", + "hybrid" + ], + "timeout_seconds": 30, + "checks": "Seven leading-coordinate prefix/COPY tariff vectors and faithful fixed-port hybrid identities." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py", + "--stage", + "owners" + ], + "timeout_seconds": 30, + "checks": "Dedicated cyclic-cover fixture,432 ADDRESS columns,36 assignments, paired entrances and paid integral helper inventory." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py", + "--stage", + "independent-native" + ], + "timeout_seconds": 300, + "checks": "Separate dense integer/binary forward and inverse maps, semantic dirty extraction, source-to-join binding, actual native charts and destructive controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py", + "--stage", + "independent-caller" + ], + "timeout_seconds": 60, + "checks": "Separate raw geometry ranks, faithful seed coefficients, explicit5148-role inventory, all-bank written rank proof and conditional accounting controls." + }, + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/controls.py" + ], + "timeout_seconds": 30, + "checks": "Frozen source, typed complete receipts, complete word/geometry artifacts, actual nested poisoned-source-cache and coverage/corruption/path controls." + } + ] +} diff --git a/research/bit-paired-helper-boundaries/controls.py b/research/bit-paired-helper-boundaries/controls.py new file mode 100644 index 0000000000..a65fc89ab4 --- /dev/null +++ b/research/bit-paired-helper-boundaries/controls.py @@ -0,0 +1,126 @@ +#!/usr/bin/env python3 +"""Bounded source, complete ADDRESS-chart and whole-artifact controls.""" +import copy +import gzip +import importlib.machinery +import importlib.util +import json +import os +from pathlib import Path +import py_compile +import shutil +import tempfile + + +ROOT = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location('paired_verify', ROOT / 'verify.py') +verify = importlib.util.module_from_spec(spec) +exec(compile((ROOT / 'verify.py').read_bytes(), str(ROOT / 'verify.py'), + 'exec', dont_inherit=True, optimize=0), verify.__dict__) + + +def reject(action, marker): + try: + action() + except ValueError as error: + verify.need(marker in str(error), 'wrong rejection: ' + str(error)) + else: + raise ValueError('mutation accepted: ' + marker) + + +def main(): + with tempfile.TemporaryDirectory(prefix='paired controls ') as directory: + root = Path(directory) / 'relocated package' + shutil.copytree(ROOT, root, ignore=shutil.ignore_patterns('__pycache__')) + p = verify.Portable(root) + p.check_all() + folder = root / 'frozen/changed/bit-native-caller' + source = folder / 'cold_cosets.py' + saved = source.read_bytes() + source.write_bytes(saved + b'\n# changed source\n') + reject(p.check_all, 'frozen input changed') + source.write_bytes(saved) + receipt = folder / 'KERNEL-ENTRANCES.json' + raw = receipt.read_bytes() + receipt.write_bytes(raw + b' ') + reject(p.check_all, 'frozen input changed') + receipt.write_bytes(raw) + actual = json.loads(raw) + verify.need(p.equal(receipt, actual), 'positive receipt control') + changed = copy.deepcopy(actual) + changed['compensation_kernel_witnesses'].pop() + reject(lambda: p.equal(receipt, changed), 'receipt mismatch') + changed = copy.deepcopy(actual) + changed['no_new_kappa'] = 1 + reject(lambda: p.equal(receipt, changed), 'receipt mismatch') + changed = copy.deepcopy(actual) + old_key = next(iter(changed['sources'])) + mapped_key = p.normalize(old_key) + verify.need(old_key != mapped_key, 'path alias fixture') + original_hash = changed['sources'][old_key] + changed['sources'][old_key] = 'MUTATED_PROVENANCE_HASH' + changed['sources'][mapped_key] = original_hash + reject(lambda: p.equal(receipt, changed), 'normalized key collision') + + chart_path = folder / 'GLOBAL-KERNEL-E2.json' + charts = json.loads(p.authenticate(chart_path)) + verify.need(p.equal(chart_path, charts), 'positive complete chart receipt') + old_entry = charts['native_rational_ADDRESS_MOVE_charts'][0]['ADDRESS_C_inverse'][0][0] + charts['native_rational_ADDRESS_MOVE_charts'][0]['ADDRESS_C_inverse'][0][0] = 'CORRUPTED_RATIONAL' + reject(lambda: p.equal(chart_path, charts), 'receipt mismatch') + charts['native_rational_ADDRESS_MOVE_charts'][0]['ADDRESS_C_inverse'][0][0] = old_entry + charts['native_rational_ADDRESS_MOVE_charts'].pop() + reject(lambda: p.equal(chart_path, charts), 'receipt mismatch') + + names = ['KERNEL-ENTRANCES-WORD.json.gz', 'GLOBAL-KERNEL-E2-WORD.json.gz', + 'GLOBAL-KERNEL-E2-GEOMETRY.json.gz', 'OLD-KERNEL-E2-WORD.json.gz', + 'OLD-KERNEL-E2-GEOMETRY.json.gz'] + for name in names: + path = folder / name + body = gzip.decompress(p.authenticate(path)) + p.word_equal(path, body) + reject(lambda: p.word_equal(path, body[:-1]), 'complete word/geometry mismatch') + verify.need(p.words_compared == {str((folder / n).relative_to(root)) for n in names}, + 'all five complete artifact comparisons') + for name, field in [('GLOBAL-KERNEL-E2-WORD.json.gz', 'records'), + ('GLOBAL-KERNEL-E2-GEOMETRY.json.gz', 'frames')]: + path = folder / name + body = gzip.decompress(p.authenticate(path)) + # Regenerated compression choices do not enter the body comparison; + # the frozen container itself remains authenticated by its hash. + different_container = gzip.compress(body, compresslevel=1, mtime=123) + verify.need(different_container != path.read_bytes(), 'different gzip fixture') + p.word_equal(path, gzip.decompress(different_container)) + value = json.loads(body) + value[field].pop() + reject(lambda: p.word_equal(path, verify.canonical(value).encode()), + 'complete word/geometry mismatch') + + cache = Path(importlib.util.cache_from_source(str(source))) + cache.parent.mkdir(parents=True, exist_ok=True) + poison = Path(directory) / 'poison.py' + payload = b"raise RuntimeError('POISONED_PAIRED_CACHE')\n#" + verify.need(len(payload) < len(saved), 'cache fixture source size') + poison.write_bytes(payload + b' ' * (len(saved) - len(payload))) + info = source.stat() + os.utime(poison, ns=(info.st_atime_ns, info.st_mtime_ns)) + py_compile.compile(str(poison), cfile=str(cache), doraise=True, + invalidation_mode=py_compile.PycInvalidationMode.TIMESTAMP) + try: + exec(importlib.machinery.SourceFileLoader('cache_probe', str(source)).get_code('cache_probe'), {}) + except RuntimeError as error: + verify.need(str(error) == 'POISONED_PAIRED_CACHE', 'wrong cache fixture failure') + else: + raise ValueError('poisoned cache fixture was not admitted') + p.install() + module = p.load('frozen/changed/bit-native-caller/global_kernel_boost.py') + verify.need(list(module.bits(5)) == [0, 2], 'authenticated nested source execution') + verify.need('frozen/changed/bit-native-caller/cold_cosets.py' in p.executed, + 'nested source was not compiled') + p.check_all() + cache.unlink() + print('PASS_PAIRED_CONTROLS source receipt complete_charts scalar_types path_collisions five_whole_artifacts compression_equivalence poisoned_cache nested_imports') + + +if __name__ == '__main__': + main() diff --git a/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/GLOBAL-KERNEL-BOOST.md b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/GLOBAL-KERNEL-BOOST.md new file mode 100644 index 0000000000..4f17e23bfb --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/GLOBAL-KERNEL-BOOST.md @@ -0,0 +1,153 @@ +# Exact common-plane helper kernel construction + +The local construction is exact, but its old CLEAN variant cannot retain a +positive uncovered dividend in a uniform common-prefix bank caller. No new +kappa is asserted. + +Scientific pin: `20ecf2891d80b5acf18d980b2164fb44ea7faa90`. The two producers +read only pinned predecessor words. Every output is in this lane. + +## Literal helper transformation + +Let D be the actual111-by-R binary helper-to-target dirty matrix. It has +rank111 for both the R429 FULL box and old R438 CLEAN box. Choose111 original +pivot columns. Each remaining column j is the XOR of a specified set I_j of +pivot columns. Write + +`S=I+sum_(j dependent,i in I_j) E_(i,j)`. + +Since every destination i is a pivot and every source j is dependent, the +off-diagonal part has square zero over the integers. All setup ADDs commute, +and replacing their signs gives the literal integer inverse. D*S modulo2 has +unchanged pivot columns and zero dependent columns. + +Give each dependent helper entrance E, keep each pivot entrance ZERO, and +retain FULL exits. Execute initial compensation only from pivot columns at +ZERO. Lift pivots to E, execute S at common E, and replace every later old +frame f by its actual rational span(f,E). Execute S^-1 at FULL. Every forced +public climb is in the emitted word. The dependent helpers are never read at +ZERO. + +For an arbitrary physical helper u, its logical entrance variable is +`h=D_E^-1 u`. All public dependence on h cancels. Thus the physical helper +residual is `D_FULL D_E^-1`; interpreting arbitrary dirt this way does not +require an executed entrance query. A chronological owner implementation +must route that paired residual. Our coordinate E has a literal coordinate +permutation route for E-perp. Requiring the predecessor's ZERO logical-dirt +identification instead would add the removed entrance queries; that is an +additional restriction rather than an intrinsic price of this contract. + +## Exact finite results + +For E=span(e0,e1), `global_kernel_boost.py` emits the R429 FULL variant: + +- 318 width6 helpers and111 width8 helpers, zero private fields; +- H={1:1184,2:1254,3:108,4:89,5:7,6:9}, mass4461=5097-636; +- all651 binary VALUE columns, exact integer source/helper restoration and + literal inverse; +- unchanged source rank1 entrances/FULL exits and target ZERO/FULL cuts. + +`old_kernel_boost.py` emits the old R438 CLEAN variant: + +- 327 width6 helpers and111 width8 helpers; +- all nine copied totals paid, with tariffs6,6,6,6,5,6,6,5,6, sum52; +- one zero private field reused for the nine snapshots and literally erased; +- H={1:1170,2:1254,3:108,4:94,5:13,6:16}, mass4539; +- all660 binary VALUE columns, integer source/helper rows, literal inverse; +- 83 old target caps enlarged to FULL, with every changed public path saved. + +The two scripts reconstruct semantic dirty columns independently. In the old +word they also compare the semantic result to every literal original +compensation column. No syntactic dirty-support count substitutes for that +test. + +## Actual rational ADDRESS moves + +For every used joined frame U, the receipts include a rational basis, its +Gram determinant and the exact orthogonal projector P_U. Every MOVE checks +nesting, `P_U P_E=P_E=P_E P_U`, and the idempotence and exact rank of +`W=P_U-P_E`. A stored invertible rational matrix C obeys + +`C diag(I_rankW,0) C^-1=W`. + +Consequently the complete16-by-16 ADDRESS identity is + +`diag(C,C) D_coord(rankW) diag(C^-1,C^-1)=D_W=D_U D_E`. + +This is a symbolic exact matrix proof covering every ADDRESS column, rather +than a scalar-rank tariff substitution. Finite excluded primes are2,3,5. +Some joined projectors have odd denominators. These explicit GL adapters do +not silently import a narrower orthogonal/dyadic recursive-query compiler; +compatibility with the chosen conditional native alphabet, its scalar scans, +source access and tape invoice remains a separate admission obligation. + +## Why the old hybrid does not give a dividend + +Let epsilon_p=1 if E is not contained in target cap K_p. With +`N=D_Pp`, `N^2=I`, and fresh cap progress G, the normalized per-port map is + +`F_epsilon=[[I,0],[N^(1-epsilon),N^epsilon]]`. + +Each epsilon1 target FULL lift is already paid locally. The epsilon0 ports +are the only potential unpaid common-rank ports. For the seven leading +coordinate E choices of ranks1 through7, the exact pair +(remaining cap ports,total copied-total query rank) is + +`(56,56),(28,52),(12,44),(11,35),(3,27),(2,18),(1,9)`. + +Even granting one unpaid common output per remaining cap port per call, +rank1 gives zero available deficit and ranks2 through7 give negative +deficit. Equivalently, in a bank-GL caller put d=N+I, d^2=0. Every hybrid +query contributes one rank-one bank coefficient to the linear d term. +Obtaining N on n banks requires a sum of rank-one matrices equal to I_n, +so k>=n. No chronological helper-owner assumption is needed for this +necessary rejection. + +For clarity, the three-call F/B/F seed has maps + +`epsilon0: [[0,N],[N,0]]`, + +`epsilon1: [[I+N,N],[I,I+N]]`. + +The epsilon1 matrix squares to N I2, but using that extra word does not +remove the already paid FULL target exposure. This is not a positive caller. + +## Selective variants and source snapshot control + +`selective_boost_screen.py` computes a causal OR propagation model. An E +promotion propagates across a scalar gate below E and stops once the old +frame contains E. This allows changed later public source paths. It also +permits a nonzero compensation residual at common E on cold target ports, +provided those target promotions have no additional exposure. + +All162 leading-coordinate planes of ranks1-4, and all120 actual E8 root +lines plus153 actual rank2 frames, have zero kernel on their zero target/COPY +exposure helper set, even after the stated cold-target quotient. This is a +finite scoped screen, not an obstruction to retimed words or other planes. +The single exposure-mask cohorts in the native screen have best rank-mass +saving-7; unions of exposure classes were not enumerated. + +Isolating immutable A-phase source reads with snapshots gives additional +kernel nominations. The cheapest tested example is helper pair444,474 at +live root77 (frame79), whose remaining exposure is source57. Source57 never reaches that +root during its immutable A phase. At its relevant rank1 read, a snapshot +must climb to span(P57,P77) and return before erasure, costing two rank1 +queries. The helper saves only one entrance rank. That corridor increases +rank mass by1 and is not promoted to a supplier. + +Reproduce with `python3` and `python3 -O`, adding `--write` only to regenerate +this lane's saved receipts: + +```sh +python3 global_kernel_boost.py --rank 2 +python3 old_kernel_boost.py --rank 2 +python3 selective_boost_screen.py +python3 selective_boost_screen.py --native +``` + +No chronological owner, rounded suffix-error, full source/tape or all-size +outer theorem is supplied by this package. The underlying R438, E8 and R429 +word ancestry retains its original authorship. This lane supplies the +changed entrance basis, exact joined word, paired residuals, actual ADDRESS +charts and explicitly scoped negative caller screens. 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zc0_~vZ4&ZG4B=f6e!3nv-_HgGl~a77(W&TG{T|kN?Ny1%!$Y2@it?WcH=NwGF?Q2z%&^a|Ym;i%2LCP5N6RPL3$%^@z3qSe^Y8x4fBjGY z`M>_VfBzpollZ6p^q={2{ycyF{`t)4#}Gc}#m}qrbGrO&RG)L_=M!l^fA(iG)}Q$4 z?$0aaqxWaZKdbaJ_&+~oO@A!r&&xahd8-!vdGAa8^JCS2|9tHI^V#zJ&CiPMzkfd84xdN+d82$5_2*slF~iSW z==0(GIfH$+gR}m8K2|>Os?T=u*+o7tx6l4^&Y$!A`D{L)J?Z%w^`Fls_SB!xG4Qj) zJ)hA&e?D8{=k)kFRDRBypU>j&1) + a[p],a[j]=a[j],a[p] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + need([r&((1<>n for r in a] + +def rankmod(mask,roots,stop=8): + b={} + for p in bits(mask): + v=[x%PRIME for x in roots[p]] + for k,a in sorted(b.items()): + f=v[k] + if f:v=[(x-f*y)%PRIME for x,y in zip(v,a)] + k=next((i for i,x in enumerate(v)if x),None) + if k is not None: + f=pow(v[k],-1,PRIME);b[k]=[(x*f)%PRIME for x in v] + if len(b)>=stop:return len(b) + return len(b) + +def receipt(): + need(sha256(RAW.read_bytes()).hexdigest()=='a353999bceac4ac957f540adfd3e5f8768297138b27132eeb83332e2ea4b1022','raw pin') + w=json.loads(gzip.decompress(RAW.read_bytes())) + full=json.loads(gzip.decompress(FULL.read_bytes()))['lines'] + comp=json.loads(COMP.read_bytes());roots=w['lines'] + rows=[1<>j&1)<

>i&1)<>j&1 for j in range(9)),'all nine special readers have self-pairing1') + orth=[sum((not sum(a*b for a,b in zip(q,r)))<

=7,'a nonzero actual codeword fits two rank<=6 flats') + minimum=min(minimum,r);total+=1 + out[name]={'flats':len(flats),'live_support_sizes':dict(sorted(sizes.items())), + 'minimum_modular_rank_outside_flat':minimum, + 'canonical_flat_data_sha256':sha256(json.dumps(sorted((S,list(pair))for S,pair in flats.items()),separators=(',',':')).encode()).hexdigest()} + need(total==2503900,'all4900 flat/511 nonzero codeword tests') + # A wrong reader outside the code is actually admitted by the low-rank + # support condition, demonstrating that code membership is essential. + fake=(1<<0)|(1<<1) + need(fake not in lookup and rankmod(fake,roots)<=2,'two-source non-code control') + return {'status':'PASS_R429_LOW_RANK_FLAT_COSET_UNIQUENESS_AND_TEN_FACTOR_COLD_FLOOR55', + 'scientific_pin':'20ecf2891d80b5acf18d980b2164fb44ea7faa90','no_new_kappa':True, + 'sources':{str(p):sha256(p.read_bytes()).hexdigest()for p in(RAW,FULL,COMP)}, + 'R':R,'K':K,'live_roots':roots,'full_E8_root_lines':full, + 'minimum_D_word_weight':48,'self_pairing_inverse_form_rows':dual, + 'all_nine_special_self_pairings':1,'families':out, + 'rank_field':PRIME,'flat_codeword_tests':total, + 'coset_theorem':'Every coset z+D contains at most one nonzero scalar readout whose source-root support has rational span<=6. E6/D6 frames are covered by the exact4900-flat certificates. Every other rank<=6 root flat has at most21 lines, so two cover at most42<48 source coordinates.', + 'nine_term_floor':'Both sides lie in D; their only span7 directions are the same nine special reader lines. In dual bases a shared label must occupy the same factor because its self-pairing is1. Pairing rank total>=72−union_of_special_labels>=63.', + 'ten_term_floor':'By Sylvester, at least one side has rank9. If both do, every term pairs two spans>=7 and total>=60. Otherwise orient the full-rank side as10 independent source readers spanning D+1: all low<=6 readers lie in its sole nonzero quotient coset, so at most one; full source-span sum>=64. The target side lies in D; generic targets span8 and special targets span7 can each discount at most1. At most9 distinct special targets occur, so total pairing-rank>=55. A duplicate target merges to9 terms without raising projected source rank and instead gives floor63.', + 'cost_model':'Exact binary scalar factorization KR=sum b_i c_i^T; term cost is at least rational rank of pairing between the source-root span U_i and target-root span V_i. This necessary tariff is not a native COPY compiler or a complete supplier.', + 'scope':['No attaining55-cost factorization or word.','The proof uses standard E8 parabolic classification and orthogonal-complement types E6/A2 and D6/A1^2, not a formal-kernel proof.','No restriction on11-or-more terms, shared native queries, operator-valued readers, changed KR or changed caller.'], + 'negative_control':'A two-source non-code word has span<=2 and violates the required outside-span condition; code membership is essential.'} + +def main(): + ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--write',action='store_true');args=ap.parse_args() + out=json.loads(json.dumps(receipt()));path=HERE/'COLD-COSETS.json' + if args.write:path.write_text(json.dumps(out,sort_keys=True,indent=2)+'\n') + else:need(json.loads(path.read_bytes())==out,'stored cold-coset receipt differs') + print(out['status']);print('4900 E6/D6 flats;2503900 rank lower certificates; no two low-span readers in one coset; nine-term63 and ten-term55 necessary floors') +if __name__=='__main__':main() diff --git a/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/global_kernel_boost.py b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/global_kernel_boost.py new file mode 100644 index 0000000000..81a6dd7913 --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/global_kernel_boost.py @@ -0,0 +1,252 @@ +#!/usr/bin/env python3 +"""Literal global-E helper-kernel entrances with actual rational ADDRESS cuts. + +Arbitrary physical dirt is interpreted in each entrance frame. New MOVE charts are rational +GL charts; the retained orthogonal-query compiler is not silently assumed. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json +from cold_cosets import bits,need +from helper_tail_retime import WORD,RAW,replay,rankQ +from kernel_entrances import parity + +HERE=Path(__file__).resolve().parent + +def basis(rows): + out={} + for row in rows: + row=list(map(Q,row)) + for j,v in sorted(out.items()): + c=row[j] + if c:row=[x-c*y for x,y in zip(row,v)] + j=next((j for j,x in enumerate(row)if x),None) + if j is not None: + c=row[j];row=[x/c for x in row] + for k,v in list(out.items()): + c=v[j] + if c:out[k]=[x-c*y for x,y in zip(v,row)] + out[j]=row + return [out[k]for k in sorted(out)] + +def contains(B,v): + v=list(map(Q,v)) + for b in B: + j=next(j for j,x in enumerate(b)if x) + c=v[j] + if c:v=[x-c*y for x,y in zip(v,b)] + return not any(v) + +def inv(A): + n=len(A);Z=[list(map(Q,row))+[Q(i==j)for j in range(n)]for i,row in enumerate(A)] + for j in range(n): + k=next(i for i in range(j,n)if Z[i][j]);Z[j],Z[k]=Z[k],Z[j] + c=Z[j][j];Z[j]=[x/c for x in Z[j]] + for i in range(n): + if i!=j: + c=Z[i][j] + if c:Z[i]=[x-c*y for x,y in zip(Z[i],Z[j])] + return [r[n:]for r in Z] + +def mm(A,B):return [[sum(x*y for x,y in zip(r,c))for c in zip(*B)]for r in A] +def tr(A):return list(map(list,zip(*A))) +def matkey(A):return [[str(x)for x in r]for r in A] +def eye(n):return [[Q(i==j)for j in range(n)]for i in range(n)] + +def projector(B): + if not B:return [[Q(0)]*8 for _ in range(8)] + return mm(mm(tr(B),inv(mm(B,tr(B)))),B) + +def det(A): + A=[r[:]for r in A];v=Q(1) + for j in range(len(A)): + k=next(i for i in range(j,len(A))if A[i][j]) + if k!=j:A[j],A[k]=A[k],A[j];v=-v + c=A[j][j];v*=c + for i in range(j+1,len(A)): + a=A[i][j]/c + for k in range(j+1,len(A)):A[i][k]-=a*A[j][k] + return v + +def primefactors(v): + v=abs(v);out=[];p=2 + while p*p<=v: + if v%p==0: + out.append(p) + while v%p==0:v//=p + p+=1 if p==2 else 2 + if v>1:out.append(v) + return out + +def frames(raw,d): + roots=raw['lines'];old=raw['frames'];base=[basis(roots[j]for j in f)for f in old] + E=basis(roots[j]for j in range(d)) + need(E==[eye(8)[i]for i in range(d)],'selected common E is literal coordinate plane') + new=dict(raw);new['frames']=[f[:]for f in old] + table={tuple(tuple(r)for r in B):i for i,B in enumerate(base)} + def get(B): + k=tuple(tuple(r)for r in B) + if k not in table: + table[k]=len(base);base.append(B) + new['frames'].append([p for p,q in enumerate(roots)if contains(B,q)]) + return table[k] + ef=get(E);joins=[] + for f in range(len(old)):joins.append(get(basis(base[f]+E))) + return new,ef,joins,base + +def factor_dirty(records): + cols={h:0 for h in range(222,651)} + for op,t,h,c,f,ph in records: + if op==1 and ph==10: + need(c==1 and f==0 and 111<=t<222,'literal compensation atZERO') + cols[h]^=1<<(t-111) + B={};pivots=[];dependent=[];setup=[];witness=[] + for h,v in cols.items(): + z=v;c=0 + while z: + j=z.bit_length()-1 + if j not in B: + B[j]=(z,c^(1<0,'strict join climb') + records.append([0,r,old,f,delta,ph]);current[r]=f + # D*S overF2 has the original pivot columns and zero dependent columns. + records.extend(r[:]for r in base['records']if r[-1]==10 and r[2]not in dependent) + for r,f in enumerate(base['start']):move(r,joins[f],80) + need(all(current[h]==E for h in range(222,651)),'all helpers at the actual common E setup cut') + records.extend([1,k,h,1,E,81]for k,h in setup) + for op,r,s,c,f,ph in base['records']: + if ph==10:continue + if op==0:move(r,joins[c],ph) + else: + need(current[r]==current[s]==joins[f],'old ADD becomes a true joined common-frame ADD') + records.append([1,r,s,c,joins[f],ph]) + need(all(current[h]==1 for h in range(222,651)),'all helpersFULL before inverse setup') + records.extend([1,k,h,-1,1,82]for k,h in reversed(setup)) + new=dict(base);new.update(start=start,records=records,format='R429-global-coordinate-E-kernel-entrances-v1') + return new,geom,E,joins,B,pivots,sorted(dependent),setup,witness + +def native_charts(new,geom,B): + I=eye(8);used={f for r in new['records']for f in([r[2],r[3]]if r[0]==0 else[r[4]])} + Ps={f:projector(B[f])for f in used};frame_rows=[];bad={2};odd=[] + for f in sorted(used): + P=Ps[f];need(mm(P,P)==P and tr(P)==P,'actual rational orthogonal frame projector') + gram=mm(B[f],tr(B[f]));g=det(gram)if gram else Q(1) + need(g>0,'all used rational frames nondegenerate') + for v in [g]+[x for r in P for x in r]: + bad.update(primefactors(v.denominator)) + bad.update(primefactors(g.numerator)) + if any(x.denominator&(x.denominator-1)for r in P for x in r):odd.append(f) + frame_rows.append({'frame':f,'rank':len(B[f]),'root_basis_rref':matkey(B[f]),'projector':matkey(P),'gram_det':str(g)}) + pairs=sorted({(r[2],r[3])for r in new['records']if r[0]==0});charts=[] + for a,b in pairs: + P,Qp=Ps[a],Ps[b] + need(mm(P,Qp)==P==mm(Qp,P),'actual ADDRESS nested-projector compatibility') + W=[[Qp[i][j]-P[i][j]for j in range(8)]for i in range(8)] + need(mm(W,W)==W and tr(W)==W,'actual residual is an orthogonal projector') + rank=len(B[b])-len(B[a]);K=basis(W);Kperp=basis([[I[i][j]-W[i][j]for j in range(8)]for i in range(8)]) + need(len(K)==rank and len(K)+len(Kperp)==8,'actual native residual rank') + C=tr(K+Kperp);Ci=inv(C) + expected=[[C[i][j]if j0,'native MOVE exact frame/containment/rank') + frames[d]=new;H[f]+=1 + else: + need(op==1 and d!=s and frames[d]==frames[s]==f,'common-frame ADD') + rows[d]=plus(rows[d],rows[s],-c if back else c);adds+=1 + prefix=max(prefix,sum(abs(x)for x in rows[d].values())) + need(frames==(program['start']if back else program['final']),'all native endpoint frames') + return rows,{'H':dict(sorted(H.items())),'mass':sum(k*v for k,v in H.items()),'ADDs':adds,'prefix_row_L1':prefix} + +def build(base,raw): + records=[r[:]for r in base['records']];dims=[rankQ(raw['lines'][j]for j in f)for f in raw['frames']] + selected=[(i,r)for i,r in enumerate(records)if r[0]==1 and r[-1]==5] + moved=[] + for i,g in selected: + need(records[i]is g,'earlier leftward moves preserve unprocessed positions') + _,d,s,c,f,ph=g;fd=fs=f;best=None + for j in range(i-1,-1,-1): + r=records[j] + if fd==fs and dims[fd]<=7:best=(j+1,fd) + if r[0]==1: + _,a,b,_,_,_=r + if a==s or b==d:break + else: + need(r[0]==0,'no private opcode in input') + if r[1]==d:need(fd==r[3],'reverse destination frame');fd=r[2] + if r[1]==s:need(fs==r[3],'reverse source frame');fs=r[2] + if j==0 and fd==fs and dims[fd]<=7:best=(0,fd) + if best is not None: + k,nf=best + need(k>i&1 and b>>j&1:z^=1<<((i+j)%2) + return z + +def mm(A,B): + return [[mul(A[i][0],B[0][j])^mul(A[i][1],B[1][j])for j in range(2)]for i in range(2)] + +def receipt(): + raw=json.loads(gzip.decompress(RAW.read_bytes()));Bs=[basis(raw['lines'][p]for p in f)for f in raw['frames']] + current=raw['start'][:] + for f,h,ss in raw['A']: + for r in[h]+ss:current[r]=f + census=[] + for d in range(1,8): + E=basis(raw['lines'][:d]) + lifted=[p for p in range(111)if not all(contains(Bs[raw['final'][111+p]],q)for q in E)] + C=[len(basis(Bs[current[h]]+E))-d for h in raw['ret']] + cap=111-len(lifted);bill=sum(C) + need(cap<=bill,'coordinate-plane uniform caller has no positive uncovered dividend') + census.append({'E_axes':list(range(d)),'target_FULL_lifts':len(lifted),'remaining_cap_ports':cap, + 'nine_COPY_ranks':C,'private_query_rank':bill,'D_per_call_upper':cap-bill}) + need([(z['remaining_cap_ports'],z['private_query_rank'])for z in census]==[(56,56),(28,52),(12,44),(11,35),(3,27),(2,18),(1,9)],'frozen coordinate-plane price census') + F0=[[1,0],[2,1]];B0=[[1,2],[0,1]] + F1=[[1,0],[1,2]];B1=[[2,1],[0,1]] + T0=mm(mm(F0,B0),F0);T1=mm(mm(F1,B1),F1) + need(T0==[[0,2],[2,0]],'old cap FBF seed') + need(T1==[[3,2],[1,3]]and mm(T1,T1)==[[2,0],[0,2]],'FULL hybrid FBF and squared seed') + return {'status':'PASS_EXACT_HYBRID_SEEDS_AND_COORDINATE_PLANE_NECESSARY_BUDGET','no_new_kappa':True, + 'source':{str(RAW):sha256(RAW.read_bytes()).hexdigest()},'ring':'F2[N]/(N^2-I)', + 'coefficient_encoding':{'0':0,'1':'I','2':'N','3':'I+N'}, + 'cap_F':F0,'cap_B':B0,'FULL_F':F1,'FULL_B':B1,'cap_FBF':T0,'FULL_FBF':T1, + 'FULL_FBF_squared':mm(T1,T1),'coordinate_planes':census, + 'written_all_parameter_rank_argument':'In a fixed port put d=I+N, d^2=0. Each normalized hybrid local call equals an invertible constant bank matrix times I+d*R with rank(R)=1. Arbitrary constant bank-GL adapters preserve that rank. In a product, the coefficient of d is a sum of k conjugated rank-one matrices because all degree>=2 terms vanish. A final common N on n independent banks requires this sum to equal I_n after the constant endpoint is removed, hence n<=k by rank subadditivity. There are111 common-rank units per bank, while each call already pays one common unit on every FULL-lifted target port plus all nine private COPY query ranks. Therefore D<=111*n-k*(number_FULL_lifts+private_rank)<=k*(remaining_cap_ports-private_rank). All seven stored coordinate planes give D<=0.', + 'domain':'Uniform repeated hybrid local family and common-prefix scalar bank-GL callers, all111 ports retained, every target lift and copied-total tariff charged. No owner/stock premise is used for this necessary rejection.', + 'limits':['Port-mixing operator-valued bank adapters, nonuniform E families, changed public codes or source cuts are outside this rank argument.','No all-parameter native supplier or formal-kernel proof is claimed.']} + +def main(): + ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--write',action='store_true');a=ap.parse_args();out=receipt();p=HERE/'HYBRID-BUDGET.json' + if a.write:p.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + else:need(json.loads(p.read_bytes())==out,'saved hybrid budget differs') + print(out['status']);print('D_per_call_upper',[z['D_per_call_upper']for z in out['coordinate_planes']]) + +if __name__=='__main__':main() diff --git a/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/kernel_entrances.py b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/kernel_entrances.py new file mode 100644 index 0000000000..7eb1692681 --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/kernel_entrances.py @@ -0,0 +1,149 @@ +#!/usr/bin/env python3 +"""Ten literal rank1-entrance helper contracts from compensation kernels. + +The owner must implement each paired residual; arbitrary physical dirt can be interpreted in its declared entrance frame. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +""" +from collections import Counter,defaultdict +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json +from cold_cosets import bits,need,rank2 +from helper_tail_retime import WORD,RAW,replay,rankQ + +HERE=Path(__file__).resolve().parent + +def kernel(V): + B={};out=[] + for i,v in enumerate(V): + c=1<=222:first.setdefault(d,(i,r)) + groups=defaultdict(list) + for h,(i,r)in first.items(): + need(r[2]==0,'old helper first frameZERO') + need(not any(z[0]==1 and z[-1]!=10 and h in(z[1],z[2])for z in records[:i]), + 'no forward helper incidence before first MOVE') + groups[r[3]].append(h) + witnesses=[];selected={};active=set();setup=[];post=[] + for f,hs in sorted(groups.items()): + ker=kernel([cols[h]for h in hs]) + if not ker:continue + need(rankQ(raw['lines'][p]for p in raw['frames'][f])==1 and len(ker)==1, + 'this constructor uses actual one-dimensional first-frame kernels') + v=ker[0];support=[hs[j]for j in bits(v)];h=support[-1] + need(not selected.keys()&set(support),'disjoint exact entrance groups') + selected[h]=f;active.update(support) + others=[k for k in support if k!=h] + total=0 + for k in support:total^=cols[k] + need(total==0,'actual compensation-kernel column') + setup.extend([1,k,h,1,f,71]for k in others) + post.extend([1,k,h,-1,1,72]for k in reversed(others)) + witnesses.append({'frame':f,'selected_helper':h,'kernel_helpers':support, + 'forward_S_ADDs':[[k,h,1]for k in others], + 'inverse_S_ADDs':[[k,h,-1]for k in reversed(others)], + 'old_compensation_column_weights':[cols[k].bit_count()for k in support]}) + need(len(selected)==10,'ten exact first-frame kernel directions') + first_ids={id(first[h][1])for h in active} + lifted=[first[h][1][:]for h in sorted(active-selected.keys())] + for r in lifted:r[-1]=70 + start=base['start'][:] + for h,f in selected.items():start[h]=f + prefix=[r[:]for r in records if r[-1]==10 and r[2]not in selected] + tail=[r[:]for r in records if r[-1]!=10 and id(r)not in first_ids] + lastC=max(i for i,r in enumerate(tail)if r[-1]==5)+1 + tail[lastC:lastC]=post + new=dict(base);new['start']=start;new['records']=prefix+lifted+setup+tail + new['format']='R429-ten-paired-nonzero-helper-entrances-v1' + return new,witnesses,selected,setup,post + +def receipt(write=False): + need(sha256(WORD.read_bytes()).hexdigest()=='0f461dbc7e82a02faedb4a5129103963507c9f063a0a3679ba5d20ad94df160e','frozen full box') + need(sha256(RAW.read_bytes()).hexdigest()=='a353999bceac4ac957f540adfd3e5f8768297138b27132eeb83332e2ea4b1022','frozen geometry') + base=json.loads(gzip.decompress(WORD.read_bytes()));raw=json.loads(gzip.decompress(RAW.read_bytes())) + new,witnesses,selected,setup,post=build(base,raw) + rows,rec=replay(new,raw);oldrows,oldrec=replay(base,raw) + need(all(rows[h]=={h:1}for h in list(range(111))+list(range(222,651))), + 'all111 sources and429 arbitrary helpers restored exactly overZ') + expected=[1<=222 for j in rows[p]),'target oldy exact self row') + need(all(not v&1 for j,v in rows[p].items()if j>=222),'new target helper leakage is even') + closed,invrec=replay(new,raw,rows,True) + need(closed==[{j:1}for j in range(651)],'literal signed inverse every column') + H=Counter({int(k):v for k,v in rec['H'].items()});oldH=Counter({int(k):v for k,v in oldrec['H'].items()}) + need(H==oldH-Counter({1:10})and rec['mass']==5087,'exact ten H1 reduction') + wrapper=[] + from fractions import Fraction as Q + from native_seed_binding import eye,mm,rank + def D(P): + n=len(P);C=[[Q(i==j)-P[i][j]for j in range(n)]for i in range(n)] + return[C[i]+P[i]for i in range(n)]+[P[i]+C[i]for i in range(n)] + I=eye(8) + for h,f in sorted(selected.items()): + q=raw['lines'][raw['frames'][f][0]];P=[[Q(x*y,4)for y in q]for x in q] + K=[[I[i][j]-P[i][j]for j in range(8)]for i in range(8)] + need(rank(P)==1 and rank(K)==7 and mm(D(I),D(P))==D(K),'actual paired (E,FULL) native residual rank7') + wrapper.append({'helper':h,'entrance_frame':f,'entrance_root':q,'terminal_frame':1, + 'residual_rank':7,'native_residual':'D_FULL D_E^-1 =D_(E-perp)'}) + # An old ZERO entrance or compensation column is a typed error. + bad=dict(new);bad['start']=new['start'][:];bad['start'][next(iter(selected))]=0 + try:replay(bad,raw) + except ValueError:zero_control=True + else:raise ValueError('oldZERO entrance mutation escaped') + bad=dict(new);bad['records']=[r[:]for r in new['records']if r[-1]!=72] + br,_=replay(bad,raw) + need(any(br[h]!={h:1}for h in range(222,651)),'omitting inverse basis fails integer helper restoration') + # Delete one member of a nontrivial kernel from both S directions while + # retaining the zero compensation column; the target leaks dirty parity. + chosen=next(w for w in witnesses if len(w['kernel_helpers'])>1);d=chosen['kernel_helpers'][0];s=chosen['selected_helper'] + bad=dict(new);bad['records']=[r[:]for r in new['records']if not(r[-1]in(71,72)and r[1]==d and r[2]==s)] + br,_=replay(bad,raw) + need(parity(br)!=expected,'perturbed kernel basis leaks arbitrary helper dirt') + canonical=json.dumps(new,sort_keys=True,separators=(',',':')).encode() + out={'status':'PASS_R429_TEN_LITERAL_PAIRED_RANK1_ENTRANCE_FULL_EXIT_HELPERS', + 'scientific_pin':'20ecf2891d80b5acf18d980b2164fb44ea7faa90','no_new_kappa':True, + 'sources':{str(p):sha256(p.read_bytes()).hexdigest()for p in(WORD,RAW)}, + 'all651_signed_integer_columns':True,'literal_inverse':invrec,'profile':rec,'old_profile':oldrec, + 'ordinary_helpers':429,'private_fields':0,'helper_inventory_by_residual_width':{7:10,8:419}, + 'paired_native_wrappers':wrapper,'compensation_kernel_witnesses':witnesses, + 'new_basis_scalar_ADDs':len(setup)+len(post),'word_canonical_sha256':sha256(canonical).hexdigest(), + 'contract':'Ten explicitly listed arbitrary dirty helpers enter at their rank1 first frame E_h and exitFULL. The other419 helpers enterZERO and exitFULL. Each changed residual is D_FULL D_Eh^-1 of rank7; every scalar source/helper row is restored exactly overZ and target is the same clean shear overF2. Source and target physical native cuts are inherited unchanged.', + 'complete_local_price':'Delete10 first H1 queries. Other first MOVEs are merely advanced to the same frame before S; no new recursive query, COPY, private field or target lift. The helper basis S acts at a genuine common E; S^-1 acts atFULL. Initial compensation D*S mod2 has zero selected columns and therefore never reads a nonZERO entrance atZERO. New histogram is the frozen H minus10H1. Source/target coverage111*15 plus419*8+10*7 equals5087, so the old uncovered deficit is unchanged.', + 'entrance_gate':'The owner must implement the physical paired residual D_FULL D_Eh^-1 with public helper dependence cancelled. An arbitrary physical helper u can be interpreted as logical dirt h=D_Eh^-1u; this requires no executed entrance query merely to name h. If one instead insists on the old ZERO logical-dirt identification, ten explicit entrance queries restore the old5097 mass. Chronological paired owner routing remains open.', + 'controls':{'old_ZERO_entrance_rejected':zero_control,'omitted_inverse_basis_fails_Z_helpers':True,'perturbed_kernel_leaks_F2_dirt':True}, + 'limits':['No chronological owner/stock construction for the nonzero entrances.','No changed rounded suffix-error or physical source/tape invoice.','A local residual-width reduction is not an admitted supplier or new exponent.'], + 'attribution':'Underlying R429/E8/signed-word ancestry is pinned in the frozen full compensation source. The helper-boundaries skill compensation-kernel lesson guided the changed entrance. This lane constructs the literal staged S, modified compensation, exact inverse and paired native wrappers.'} + if write: + (HERE/'KERNEL-ENTRANCES-WORD.json.gz').write_bytes(gzip.compress(canonical,mtime=0)) + else:need(gzip.decompress((HERE/'KERNEL-ENTRANCES-WORD.json.gz').read_bytes())==canonical,'saved kernel-entrance word differs') + return json.loads(json.dumps(out)) + +def main(): + ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--write',action='store_true');args=ap.parse_args() + out=receipt(args.write);path=HERE/'KERNEL-ENTRANCES.json' + if args.write:path.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + else:need(json.loads(path.read_bytes())==out,'saved kernel-entrance receipt differs') + print(out['status']);print('10 rank7 residuals;419 rank8;0private; all651 signed/F2 columns; local mass5087; owner entrance gate open') + +if __name__=='__main__':main() diff --git a/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/native_seed_binding.py b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/native_seed_binding.py new file mode 100644 index 0000000000..fe1670c8f1 --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/native_seed_binding.py @@ -0,0 +1,258 @@ +#!/usr/bin/env python3 +"""Bind the seeded BIT star to actual E8 dyadic ADDRESS operators. + +All changed FULL-box scalar/native-frame records are replayed independently. +Old CLEAN boxes remain the explicitly named retained R438 interface premise. +No owners, rounded theorem, or physical all-size tape claim is supplied. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json + +HERE = Path(__file__).resolve().parent +BASE = Path('/Users/ross/git/math') +RAW = BASE / 'integer-mult-bounds/research/bit-r438-transport-rehost/words/r438-t154.json.gz' +OLDER = BASE / '.research-automation/runs/kappa-major-20261018T1330Z' +WORD = OLDER / 'bit-endpoint/BIT-FULL-COMPENSATION-WORD.json.gz' +OLD_STAR = OLDER / 'shared-helper-algebra/BIT-SEEDED-STAR.json' +PIN = '20ecf2891d80b5acf18d980b2164fb44ea7faa90' +NEW_H = Counter({1:1406,2:1342,3:79,4:44,5:93,6:11,7:9}) +OLD_H = Counter({1:1322,2:1342,3:79,4:44,5:102,6:11,7:18}) + +def need(x, message): + if not x: + raise ValueError(message) + +def eye(n): + return [[Q(i == j) for j in range(n)] for i in range(n)] + +def tr(a): + return list(map(list, zip(*a))) + +def mm(a, b): + return [[sum(x*y for x,y in zip(row,col)) for col in zip(*b)] for row in a] + +def rank(rows): + b = {} + for row in rows: + row = list(map(Q,row)) + for k,v in sorted(b.items()): + c = row[k] + row = [x-c*y for x,y in zip(row,v)] + k = next((i for i,x in enumerate(row) if x), None) + if k is not None: + b[k] = [x/row[k] for x in row] + return len(b) + +def add(a,b,c=1): + z = a.copy() + for k,v in b.items(): + z[k] = z.get(k,0)+c*v + if not z[k]: + del z[k] + return z + +def replay(w, program, backward=False, initial=None, omit_lift=False): + n = 651 + frames = (program['final'] if backward else program['start'])[:] + out = [{i:1} for i in range(n)] if initial is None else [r.copy() for r in initial] + dims = [rank(w['lines'][p] for p in f) for f in w['frames']] + masks = [sum(1 << p for p in f) for f in w['frames']] + H = Counter() + adds = moves = 0 + peak = 1 + for op,d,s,c,f,phase in reversed(program['records']) if backward else program['records']: + if omit_lift and op == 0 and d == 111 and phase == 42: + continue + if op == 0: + old,new = (c,s) if backward else (s,c) + lo,hi = (new,old) if backward else (old,new) + need(frames[d] == old, 'actual MOVE entry frame') + need(not masks[lo] & ~masks[hi] and dims[hi]-dims[lo] == f > 0, + 'actual MOVE containment/rank') + frames[d] = new + H[f] += 1 + moves += 1 + else: + need(op == 1 and d != s and frames[d] == frames[s] == f, + 'actual common-frame ADD') + out[d] = add(out[d],out[s],-c if backward else c) + adds += 1 + peak = max(peak,sum(abs(v) for v in out[d].values())) + need(frames == (program['start'] if backward else program['final']), 'actual final frames') + need(H == NEW_H and (adds,moves) == (12932,2984), 'complete changed local profile') + return out, {'ADD':adds,'MOVE':moves,'histogram':dict(sorted(H.items())), + 'mass':sum(r*n for r,n in H.items()),'signed_integer_prefix_L1':peak} + +def port_identities(w): + from physical_code import actual_routes + rhos,projectors,_=actual_routes(w) + I = eye(8) + hashes = [] + for rho,P in zip(rhos,projectors): + A = [row[8:] for row in rho[:8]] + need(all(x.denominator & (x.denominator-1) == 0 for row in rho for x in row), 'dyadic chart') + K = [[I[i][j]-P[i][j] for j in range(8)] for i in range(8)] + need(mm(P,P) == P and rank(P) == 1 and rank(K) == 7, 'actual P/K projectors') + need(mm(A,tr(A)) == K and mm(tr(A),A) == eye(7), 'actual cap isometry') + need(not any(x for row in mm(P,A) for x in row), 'P A=0') + # These checked block relations imply exactly, for this actual rho: + # rho diag(K,0) rho=diag(0,I7), + # rho diag(I8,0) rho=diag(P,I7). + # Consequently the source and old cap target progress are G=D_E7; + # the FULL target progress is G N, N=D_P. No scalar rank9 code is used. + body=json.dumps([[str(x) for x in row] for row in rho],separators=(',',':')).encode() + hashes.append(sha256(body).hexdigest()) + need(len(hashes) == 111, 'all111 actual ports') + return hashes + +def row_xor(a,b): + return [x ^ y for x,y in zip(a,b)] + +def left(row, generator_mask): + return [{x ^ generator_mask for x in coefficient} for coefficient in row] + +def native_star(L=9, omit_terminal=False, wrong_full_target=False): + need(L >= 3, 'three seed stages') + n = L-1 + rows = [[{0} if i == j else set() for j in range(n)] for i in range(n)] + levels = [-1]*n + events = [] + H_idle = Counter() + def idle(bank, last): + old = levels[bank] + if last == old: + return + need(last > old, 'native idle chronology') + mask = sum(1 << (s+1) for s in range(old+1,last+1)) + rows[bank] = left(rows[bank],mask) + d = 7*(last-old) + H_idle[d] += 111 + levels[bank] = last + events.append({'kind':'native_idle','bank':bank,'old':old,'new':last, + 'children':111,'rank_each':d,'actual_projector':'orthogonal sum of listed G_s supports'}) + def call(stage, kind, source, target): + idle(source,stage-1) + idle(target,stage-1) + g = 1 << (stage+1) + x,y = rows[source],rows[target] + if kind == 'OLD_F': + rows[source] = left(x,g) + rows[target] = row_xor(left(y,g),left(x,g|1)) + elif kind == 'OLD_B': + rows[source] = row_xor(left(x,g),left(y,g|1)) + rows[target] = left(y,g) + else: + need(kind == 'NEW_F','actual declared local alphabet') + rows[source] = left(x,g) + rows[target] = row_xor(left(x,g),left(y,g if wrong_full_target else g|1)) + levels[source] = levels[target] = stage + events.append({'kind':kind,'stage':stage,'source':source,'target':target, + 'source_progress_rank':7,'target_progress_rank':8 if kind == 'NEW_F' else 7, + 'cross':'G_s' if kind == 'NEW_F' else 'G_s N_p', + 'helpers':429 if kind == 'NEW_F' else 438, + 'literal_local_word':str(WORD) if kind == 'NEW_F' else str(RAW)}) + call(0,'OLD_F',0,1) + call(1,'OLD_B',0,1) + call(2,'OLD_F',0,1) + rows[0],rows[1] = rows[1],rows[0] + events.append({'kind':'whole_bank_SWAP','banks':[0,1],'field_SWAPS':111, + 'binary_VALUE_implementation_XOR_ADDs':333}) + for j in range(2,n): + call(j+1,'NEW_F',0,j) + for bank in range(n): + idle(bank,L-1) + for j in reversed(range(2,n)): + if omit_terminal and j == 2: + continue + rows[j] = row_xor(rows[j],rows[0]) + events.append({'kind':'terminal_common_front_CNOT','source':0,'target':j, + 'ADDs':111,'native_children':0}) + final_mask = (1 << (L+1))-1 + expected = [[{final_mask} if i == j else set() for j in range(n)] for i in range(n)] + return rows,expected,events,H_idle + +def receipt(): + need(sha256(RAW.read_bytes()).hexdigest() == 'a353999bceac4ac957f540adfd3e5f8768297138b27132eeb83332e2ea4b1022','R438 raw pin') + need(sha256(WORD.read_bytes()).hexdigest() == '0f461dbc7e82a02faedb4a5129103963507c9f063a0a3679ba5d20ad94df160e','changed word pin') + w = json.loads(gzip.decompress(RAW.read_bytes())) + program = json.loads(gzip.decompress(WORD.read_bytes())) + need(len(program['start']) == len(program['final']) == 651,'all ordinary roles') + need(all(f == 0 for f in program['start'][111:]), 'all target/helper entries atZERO') + a,forward = replay(w,program) + _,inverse = replay(w,program,True) + need(all(a[p] == {p:1} for p in list(range(111))+list(range(222,651))), + 'all source and429 arbitrary helper columns restored exactly overZ') + for p in range(111): + parity = {k for k,v in a[111+p].items() if v & 1} + need(parity == {p,111+p},'actual target y+x overF2') + back,_ = replay(w,program,True,a) + need(back == [{i:1} for i in range(651)],'literal full integer inverse all651 columns') + try: + replay(w,program,omit_lift=True) + except ValueError as error: + lift_control = str(error) + else: + raise ValueError('omitted actual target lift escaped') + port_hashes = port_identities(w) + rows,expected,events,H_idle = native_star() + need(rows == expected,'actual native ADDRESS exchange group algebra all eight raw banks') + bad,_,_,_ = native_star(omit_terminal=True) + need(bad != expected,'missing common-front CNOT rejected') + bad,_,_,_ = native_star(wrong_full_target=True) + need(bad != expected,'dropping physical target common N rejected') + for L in (3,5,7,11,13): + z,e,_,_ = native_star(L) + need(z == e,'native operator star all checked arities') + local = Counter({r:3*OLD_H[r]+6*NEW_H[r] for r in set(OLD_H)|set(NEW_H)}) + return {'status':'PASS_NATIVE_E8_SEEDED_STAR_OPERATOR_BINDING_WITH_IMPORTED_OLD_CLEAN_INTERFACE', + 'scientific_pin':PIN,'no_new_kappa':True, + 'sources':{str(p):sha256(p.read_bytes()).hexdigest() for p in (RAW,WORD,OLD_STAR,HERE/'physical_code.py')}, + 'changed_local_all651_Z_columns_replayed':True, + 'changed_local_forward':forward,'changed_local_literal_inverse':inverse, + 'changed_local_helpers_restored':429,'private_fields':0, + 'all111_actual_rho15_hashes':port_hashes, + 'actual_native_local_blocks':{ + 'old_F':'[[G_s,0],[G_s N_p,G_s]]', + 'old_B':'[[G_s,G_s N_p],[0,G_s]] over binary VALUE', + 'new_F':'[[G_s,0],[G_s,G_s N_p]]', + 'N_p':'actual D_(q_p q_p^T/4) on the common8-space', + 'G_0':'D_(I8-q_p q_p^T/4), rank7', + 'G_s_s_positive':'D_(fresh E_s), rank7 after the actual rho15 chart', + 'full_parent':'N_p G_0 ... G_(L-1) = D_I_m, m=1+7L, on each physical port'}, + 'word':events, + 'binary_VALUE_public_banks':8, + 'conditional_local_histogram_before_helpers_hosted':dict(sorted(local.items())), + 'public_idle_histogram_before_helpers_hosted':dict(sorted(H_idle.items())), + 'new_words_total_ADD':6*12932, + 'terminal_CNOT_ADD':6*111,'bank_SWAP_field_scans':111, + 'raw_deficit_if_all_owners_exact':2*111-3*63, + 'native_scope':'All111 actual E8 ports and exact dyadic rho block identities; literal changed651-role scalar/frame stream; native outer word in the group algebra of explicitly orthogonal ADDRESS exchanges, valid on all binary VALUE functions over every odd ADDRESS field. No scalar-rank9 replacement or dropped target lift is used.', + 'remaining_premises':[ + 'The old CLEAN R438 F/B contract and its signed/native compiler remain imported, not newly independently compiled here.', + 'No chronological whole-helper owner allocation, complete hosted histogram, fallback or stock certificate.', + 'No rounded child-error/suffix weights, source-access/tape realization or all-size supplier admission.', + 'The root independently rejects this seeded profile at primitive exponent .002; this reusable binding is not a positive exponent claim.'], + 'executed_controls':{'omitted_target_lift':lift_control, + 'omitted_terminal_CNOT':True,'wrong_full_target_G_instead_of_GN':True}} + +def main(): + ap=argparse.ArgumentParser(description=__doc__) + ap.add_argument('--write',action='store_true') + args=ap.parse_args() + out=json.loads(json.dumps(receipt())) + path=HERE/'NATIVE-SEED-BINDING.json' + if args.write: + path.write_text(json.dumps(out,sort_keys=True,indent=2)+'\n') + else: + need(json.loads(path.read_bytes()) == out,'stored native binding differs') + print(out['status']) + print('111 actual rho charts;651 integer columns;8 native raw-input banks; all lifts paid') + +if __name__=='__main__': + main() diff --git a/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/old_kernel_boost.py b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/old_kernel_boost.py new file mode 100644 index 0000000000..2b497fb9ba --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/old_kernel_boost.py @@ -0,0 +1,188 @@ +#!/usr/bin/env python3 +"""Global common-E compensation-kernel entrances for the old CLEAN R438 word. + +All nine nested copied totals and all changed target caps remain priced. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +import argparse +import gzip +import json +from global_kernel_boost import HERE,RAW,basis,contains,frames,native_charts,matkey,eye +from cold_cosets import bits,need +from helper_tail_retime import plus +from kernel_entrances import parity + +N=660 + +def old_word(raw): + B=[basis(raw['lines'][p]for p in f)for f in raw['frames']] + current=raw['start'][:];records=[] + def move(r,f): + old=current[r] + if old!=f: + need(all(contains(B[f],q)for q in B[old]),'old original climb nested') + records.append([0,r,old,f,len(B[f])-len(B[old]),0]);current[r]=f + def phase(name,ph,c=1): + for f,d,ss in raw[name]: + for r in[d]+ss:move(r,f) + for s in ss:records.append([1,d,s,c,f,ph]) + phase('D',10);phase('A',2) + for i,h in enumerate(raw['ret']): + f=current[h];records.append([2,h,N,f,0,3]) + for p,ss in enumerate(raw['scatter']): + if i in ss: + need(current[111+p]==0,'old totals scatter at actualZERO') + records.append([1,111+p,N,1,0,3]) + records.append([3,h,N,f,0,3]) + phase('B',4);phase('C',5,-1) + for r,f in enumerate(raw['final']):move(r,f) + return {'start':raw['start'][:],'final':raw['final'][:],'records':records} + +def replay(program,geom,initial=None,back=False): + B=[basis(geom['lines'][p]for p in f)for f in geom['frames']] + current=(program['final']if back else program['start'])[:]+[None] + rows=[{j:1}for j in range(N)]+[{}]if initial is None else[r.copy()for r in initial] + H=Counter();adds=copies=0;peak=1;opened=None;copyrows=[] + for op,d,s,c,f,ph in reversed(program['records'])if back else program['records']: + if op==0: + a,b=(c,s)if back else(s,c) + lo,hi=(b,a)if back else(a,b) + need(current[d]==a and len(B[hi])-len(B[lo])==f>0 and all(contains(B[hi],v)for v in B[lo]),'actual old/new MOVE') + current[d]=b;H[f]+=1 + elif op==1: + need(d!=s and current[d]==current[s]==f,'actual common-frame ADD including copied scatter') + need(opened is None or d!=opened,'copied total immutable untilERASE') + rows[d]=plus(rows[d],rows[s],-c if back else c);adds+=1 + peak=max(peak,sum(abs(x)for x in rows[d].values())) + elif op==(3 if back else 2): + need(opened is None and s==N and not rows[N] and current[N]is None and current[d]==c,'fresh zero private COPY actual source frame') + need(all(contains(B[c],v)for v in B[f]),'nested paid COPY target') + tariff=len(B[c])-len(B[f]);need(tariff>0,'positive COPY tariff') + rows[N]=rows[d].copy();current[N]=f;opened=d;H[tariff]+=1;copies+=1 + copyrows.append({'source_helper':d,'source_frame':c,'private_frame':f,'query_rank':tariff}) + else: + need(op==(2 if back else 3)and opened==d and s==N and rows[N]==rows[d]and current[d]==c and current[N]==f,'literal ERASE original unchanged snapshot') + rows[N]={};current[N]=None;opened=None + need(current[:-1]==(program['start']if back else program['final'])and current[N]is None and opened is None,'every old/new endpoint') + return rows,{'H':dict(sorted(H.items())),'mass':sum(k*v for k,v in H.items()),'ADDs':adds,'COPYs':copies,'private_fields':1,'COPY_records':copyrows,'prefix_row_L1':peak} + +def dirty_factor(base,geom): + noD=dict(base);noD['records']=[r for r in base['records']if r[-1]!=10] + rows,_=replay(noD,geom) + cols={h:sum((rows[111+p].get(h,0)&1)<

0,'strict old-clean climb') + records.append([0,r,old,f,tariff,ph]);current[r]=f + records.extend(r[:]for r in base['records']if r[-1]==10 and r[2]not in deps) + for r,f in enumerate(base['start']):move(r,joins[f],80) + need(all(current[h]==E for h in range(222,N)),'actual commonE helper setup') + records.extend([1,k,h,1,E,81]for k,h in setup) + for op,r,s,c,f,ph in base['records']: + if ph==10:continue + if op==0:move(r,joins[c],ph) + elif op==1: + nf=E if s==N else joins[f] + need(current[r]==nf and(s==N or current[s]==nf),'joined old-clean common scalar frame') + records.append([1,r,s,c,nf,ph]) + else: + need(op in(2,3)and current[r]==joins[c],'actual joined copied-total cut') + records.append([op,r,s,joins[c],E,ph]) + need(all(current[h]==1 for h in range(222,N)),'old helperFULL inverse setup') + records.extend([1,k,h,-1,1,82]for k,h in reversed(setup)) + final=[joins[f]for f in base['final']] + new={'start':start,'final':final,'records':records,'format':'R438-global-coordinate-E-kernel-entrances-hybrid-v1'} + return new,geom,E,joins,B,piv,dep,setup,witness + +def receipt(d,write=False): + need(sha256(RAW.read_bytes()).hexdigest()=='a353999bceac4ac957f540adfd3e5f8768297138b27132eeb83332e2ea4b1022','old R438 exact source') + raw=json.loads(gzip.decompress(RAW.read_bytes()));base=old_word(raw) + oldrows,oldrec=replay(base,raw) + need(oldrec['H']=={1:1322,2:1342,3:79,4:44,5:102,6:11,7:18}and oldrec['mass']==5121,'entire retained clean profile') + expected=[1<>q&1 for p,q in edges),'actual source-code commutant edges') + cr,cp=commutant_rank(rhos,edges) + need(cr==224,'mod101 rank224 gives rational commutant dimension1') + # The identity is in the rational commutant, so its dimension is exactly1, + # not merely at most1. A common native projector commuting these couplings + # is therefore scalar, and idempotence leaves onlyZERO/FULL. + identity_coeff=[int(i==j)for i in range(15)for j in range(15)] + need(sum(identity_coeff)==15,'nonzero exact identity commutant control') + Hhash=[];coverage=[] + for p,rho in enumerate(rhos): + rs,rt=embed(rho,0),embed(rho,1);H=mm(rt,rs) + # H maps every old fresh basis column into the new fresh subspace. + need(all(H[i][j]==int(i==j+7)for i in range(22)for j in range(8,15)), + 'actual H sends completed old fresh exactly to future fresh') + P0=[[projectors[p][i][j]if i<8 and j<8 else Q(0)for j in range(22)]for i in range(22)] + need(mm(H,P0)==mm(P0,H),'actual H commutes common N_p projector') + Hhash.append(sha256(json.dumps(serial(H),separators=(',',':')).encode()).hexdigest()) + for p,q in edges: + rs_p,rs_q=embed(rhos[p],0),embed(rhos[q],0) + rt_p,rt_q=embed(rhos[p],1),embed(rhos[q],1) + hp,hq=mm(rt_p,rs_p),mm(rt_q,rs_q) + need(mm(hp,mm(rs_p,rs_q))==mm(mm(rt_p,rt_q),hq), + 'actual all-input ADDRESS intertwiner coefficient identity') + M=mm(rhos[3],rhos[0]) + witness=next((i,j,M[i][j])for i in range(8,15)for j in range(8)if M[i][j]) + return {'status':'PASS_PHYSICAL_REPAIRED_A_INTERTWINER_AND_EXPLICIT_COVERAGE_DEBT', + 'scientific_pin':'20ecf2891d80b5acf18d980b2164fb44ea7faa90','no_new_kappa':True, + 'sources':{str(p):sha256(p.read_bytes()).hexdigest()for p in(RAW,FULL,GEOMETRY,COMP,CODE)}, + 'R':R,'K':K,'W':W,'A':A,'J_rank':108,'A_rank':111,'literal_source_code_ADDs':1499, + 'A_order':28,'power_diagnostics':powers, + 'native_factor':'Let F be actual local FULL, N=diag(D_Pp), G=F N, a=N A N. Since F commutes scalar A and N, repaired local Fphys=diag(G,G) F_N diag(a,I). It has source A G and cross G A N. This statement uses the same actual rho conjugacy on all factors at later stages.', + 'routed_source_code':'A_s[p,q]=A[p,q] times VALUE push(rho_s,p rho_s,q). These exact rho_s,p are reconstructed from upstream geometry.py Weyl BFS, not chosen fresh gauges.', + 'all111_actual_rho15':[[[str(x)for x in row]for row in rho]for rho in rhos], + 'intertwiner':'H_p=rho_t,p rho_s,p: H A_s H^-1=A_t, H commutes N_p, and H(E_s)=E_t. H is an orthogonal ADDRESS transform; all its access and head movement remain paid.', + 'all111_intertwiner_H_sha256':Hhash, + 'coverage_debt':'H^-1 D_Et H D_Es=I on arbitrary VALUE functions, while the desired D_(Es+Et) has native rank14. The naive alignment/query/unwind word cancels its two rank7 fresh advances. This prices that word only.', + 'uniform_source_frame_commutant':{'active_dimension':15,'matrix_unknowns':225, + 'field_for_rank_lower_certificate':101,'actual_A_edges':edges, + 'modular_constraint_rank':224,'rank_progress':cp,'rational_commutant_dimension':1, + 'consequence':'A common orthogonal projector Q commuting the actual source-code coupling maps is scalar, hence Q=0 orI15. The routed source code cannot be treated as a code preserving an unchanged intermediate common native frame.'}, + 'actual_future_fiber_witness':{'output_port':3,'input_port':0,'row':witness[0], + 'column':witness[1],'coefficient':str(witness[2])}, + 'AN_native_orbit_screen':orbit_screen(A,w,full), + 'exact_commutator_fact':'For a scalar port code T, [T,N]_(p,q)=T_pq(D_Pq-D_Pp). Distinct actual E8 lines give distinct native permutations. Every A^k,1<=k<28, has an offdiagonal entry, so none commutes N. Low rank(A^14-I)=2 does not make its routed native coefficient a rank2 query.', + 'open_next_question':'Construct a caller using genuinely changing/port-dependent native frames or shared operator-valued readers so H coverage loss is compensated inside the actual word. No such positive complete word is supplied here.', + 'limits':['No general obstruction for arbitrary operator-valued or nonlinear callers.', + 'No chronological helper owners, rounded errors, source/tape bill, full recurrence or new conditional exponent.', + 'The AN test is a finite exact counterexample to periods<=224, not a proof of infinite order or a universal word lower bound.']} + +def main(): + ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--write',action='store_true');args=ap.parse_args() + out=json.loads(json.dumps(receipt()));path=HERE/'PHYSICAL-CODE.json' + if args.write:path.write_text(json.dumps(out,sort_keys=True,indent=2)+'\n') + else:need(json.loads(path.read_bytes())==out,'stored physical code receipt differs') + print(out['status']);print('literal A order28; actual rho intertwiner; native coverage debt14; commutant dimension1; AN periods<=224 rejected') +if __name__=='__main__':main() diff --git a/research/bit-paired-helper-boundaries/frozen/changed/budgets/PAIRED-HELPER-OWNERS.json b/research/bit-paired-helper-boundaries/frozen/changed/budgets/PAIRED-HELPER-OWNERS.json new file mode 100644 index 0000000000..f327ff9f97 --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/changed/budgets/PAIRED-HELPER-OWNERS.json @@ -0,0 +1,641 @@ +{ + "E2_helper_inventory_only": { + "local_helper_rank_mass": 2796, + "padding_per_call": { + "4": "111/4" + }, + "padding_rank_mass_per_call": 111, + "replicas": 12, + "stock_per_call": "323/4", + "width6_banks": 636, + "width8_banks": 333 + }, + "all72_coordinate_columns_per_owner": true, + "controls": { + "ignored_entrance_fails": true, + "missing_role_fails": true, + "same_call_family_alias_rejected": true + }, + "cover": "six cyclic shifts by6 axes", + "events": [ + { + "entrance_axes": [ + 6, + 7 + ], + "invocation": 0, + "owner": 0, + "role": 0, + "slot_axes": [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + }, + { + "entrance_axes": [ + 12, + 13 + ], + "invocation": 0, + "owner": 5, + "role": 1, + "slot_axes": [ + 6, + 7, + 8, + 9, + 10, + 11 + ] + }, + { + "entrance_axes": [ + 18, + 19 + ], + "invocation": 0, + "owner": 4, + "role": 2, + "slot_axes": [ + 12, + 13, + 14, + 15, + 16, + 17 + ] + }, + { + "entrance_axes": [ + 24, + 25 + ], + "invocation": 0, + "owner": 3, + "role": 3, + "slot_axes": [ + 18, + 19, + 20, + 21, + 22, + 23 + ] + }, + { + "entrance_axes": [ + 30, + 31 + ], + "invocation": 0, + "owner": 2, + "role": 4, + "slot_axes": [ + 24, + 25, + 26, + 27, + 28, + 29 + ] + }, + { + "entrance_axes": [ + 0, + 1 + ], + "invocation": 0, + "owner": 1, + "role": 5, + "slot_axes": [ + 30, + 31, + 32, + 33, + 34, + 35 + ] + }, + { + "entrance_axes": [ + 6, + 7 + ], + "invocation": 1, + "owner": 1, + "role": 0, + "slot_axes": [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + }, + { + "entrance_axes": [ + 12, + 13 + ], + "invocation": 1, + "owner": 0, + "role": 1, + "slot_axes": [ + 6, + 7, + 8, + 9, + 10, + 11 + ] + }, + { + "entrance_axes": [ + 18, + 19 + ], + "invocation": 1, + "owner": 5, + "role": 2, + "slot_axes": [ + 12, + 13, + 14, + 15, + 16, + 17 + ] + }, + { + "entrance_axes": [ + 24, + 25 + ], + "invocation": 1, + "owner": 4, + "role": 3, + "slot_axes": [ + 18, + 19, + 20, + 21, + 22, + 23 + ] + }, + { + "entrance_axes": [ + 30, + 31 + ], + "invocation": 1, + "owner": 3, + "role": 4, + "slot_axes": [ + 24, + 25, + 26, + 27, + 28, + 29 + ] + }, + { + "entrance_axes": [ + 0, + 1 + ], + "invocation": 1, + "owner": 2, + "role": 5, + "slot_axes": [ + 30, + 31, + 32, + 33, + 34, + 35 + ] + }, + { + "entrance_axes": [ + 6, + 7 + ], + "invocation": 2, + "owner": 2, + "role": 0, + "slot_axes": [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + }, + { + "entrance_axes": [ + 12, + 13 + ], + "invocation": 2, + "owner": 1, + "role": 1, + "slot_axes": [ + 6, + 7, + 8, + 9, + 10, + 11 + ] + }, + { + "entrance_axes": [ + 18, + 19 + ], + "invocation": 2, + "owner": 0, + "role": 2, + "slot_axes": [ + 12, + 13, + 14, + 15, + 16, + 17 + ] + }, + { + "entrance_axes": [ + 24, + 25 + ], + "invocation": 2, + "owner": 5, + "role": 3, + "slot_axes": [ + 18, + 19, + 20, + 21, + 22, + 23 + ] + }, + { + "entrance_axes": [ + 30, + 31 + ], + "invocation": 2, + "owner": 4, + "role": 4, + "slot_axes": [ + 24, + 25, + 26, + 27, + 28, + 29 + ] + }, + { + "entrance_axes": [ + 0, + 1 + ], + "invocation": 2, + "owner": 3, + "role": 5, + "slot_axes": [ + 30, + 31, + 32, + 33, + 34, + 35 + ] + }, + { + "entrance_axes": [ + 6, + 7 + ], + "invocation": 3, + "owner": 3, + "role": 0, + "slot_axes": [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + }, + { + "entrance_axes": [ + 12, + 13 + ], + "invocation": 3, + "owner": 2, + "role": 1, + "slot_axes": [ + 6, + 7, + 8, + 9, + 10, + 11 + ] + }, + { + "entrance_axes": [ + 18, + 19 + ], + "invocation": 3, + "owner": 1, + "role": 2, + "slot_axes": [ + 12, + 13, + 14, + 15, + 16, + 17 + ] + }, + { + "entrance_axes": [ + 24, + 25 + ], + "invocation": 3, + "owner": 0, + "role": 3, + "slot_axes": [ + 18, + 19, + 20, + 21, + 22, + 23 + ] + }, + { + "entrance_axes": [ + 30, + 31 + ], + "invocation": 3, + "owner": 5, + "role": 4, + "slot_axes": [ + 24, + 25, + 26, + 27, + 28, + 29 + ] + }, + { + "entrance_axes": [ + 0, + 1 + ], + "invocation": 3, + "owner": 4, + "role": 5, + "slot_axes": [ + 30, + 31, + 32, + 33, + 34, + 35 + ] + }, + { + "entrance_axes": [ + 6, + 7 + ], + "invocation": 4, + "owner": 4, + "role": 0, + "slot_axes": [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + }, + { + "entrance_axes": [ + 12, + 13 + ], + "invocation": 4, + "owner": 3, + "role": 1, + "slot_axes": [ + 6, + 7, + 8, + 9, + 10, + 11 + ] + }, + { + "entrance_axes": [ + 18, + 19 + ], + "invocation": 4, + "owner": 2, + "role": 2, + "slot_axes": [ + 12, + 13, + 14, + 15, + 16, + 17 + ] + }, + { + "entrance_axes": [ + 24, + 25 + ], + "invocation": 4, + "owner": 1, + "role": 3, + "slot_axes": [ + 18, + 19, + 20, + 21, + 22, + 23 + ] + }, + { + "entrance_axes": [ + 30, + 31 + ], + "invocation": 4, + "owner": 0, + "role": 4, + "slot_axes": [ + 24, + 25, + 26, + 27, + 28, + 29 + ] + }, + { + "entrance_axes": [ + 0, + 1 + ], + "invocation": 4, + "owner": 5, + "role": 5, + "slot_axes": [ + 30, + 31, + 32, + 33, + 34, + 35 + ] + }, + { + "entrance_axes": [ + 6, + 7 + ], + "invocation": 5, + "owner": 5, + "role": 0, + "slot_axes": [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + }, + { + "entrance_axes": [ + 12, + 13 + ], + "invocation": 5, + "owner": 4, + "role": 1, + "slot_axes": [ + 6, + 7, + 8, + 9, + 10, + 11 + ] + }, + { + "entrance_axes": [ + 18, + 19 + ], + "invocation": 5, + "owner": 3, + "role": 2, + "slot_axes": [ + 12, + 13, + 14, + 15, + 16, + 17 + ] + }, + { + "entrance_axes": [ + 24, + 25 + ], + "invocation": 5, + "owner": 2, + "role": 3, + "slot_axes": [ + 18, + 19, + 20, + 21, + 22, + 23 + ] + }, + { + "entrance_axes": [ + 30, + 31 + ], + "invocation": 5, + "owner": 1, + "role": 4, + "slot_axes": [ + 24, + 25, + 26, + 27, + 28, + 29 + ] + }, + { + "entrance_axes": [ + 0, + 1 + ], + "invocation": 5, + "owner": 0, + "role": 5, + "slot_axes": [ + 30, + 31, + 32, + 33, + 34, + 35 + ] + } + ], + "invocations": 6, + "m": 36, + "no_new_kappa": true, + "physical_owners": 6, + "roles_per_invocation": 6, + "scope": "Finite exact arbitrary-coordinate fixture for the dedicated bank theorem. It does not replay a local supplier or authorize recycling a public family. The actual local dirty cancellation, native wrappers, source/target stock and paid machine costs remain required.", + "status": "PASS_PAIRED_HELPER_DEDICATED_COVER_OWNER_FIXTURE" +} diff --git a/research/bit-paired-helper-boundaries/frozen/changed/budgets/PAIRED-HELPER-OWNERS.md b/research/bit-paired-helper-boundaries/frozen/changed/budgets/PAIRED-HELPER-OWNERS.md new file mode 100644 index 0000000000..042c156a12 --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/changed/budgets/PAIRED-HELPER-OWNERS.md @@ -0,0 +1,107 @@ +# Arbitrary dirt at a paired entrance and dedicated whole-bank owners + +Scientific pin `20ecf2891d80b5acf18d980b2164fb44ea7faa90`. +This is a conditional algebraic hosting lemma, not a new supplier or kappa. +It uses the dedicated cover-bank model of the retained PR386 BIT geometry. +It does not apply automatically to a public-family pending-window allocation. + +## The entrance is a coordinate interpretation + +Suppose a literal BIT word is checked for every independent logical source, +target and helper input, with helper h entering at E and leaving at U. +Suppose its complete logical helper row is h and its public output has zero +coefficient on h over F2. Write D_E,D_U for the actual ADDRESS operators. +Given an arbitrary physical helper array u, set h=D_E^-1 u in the proof. +There is no instruction to execute D_E on u. The word then has physical map + + u -> D_U D_E^-1 u, + +and its public output is independent of u. This also holds for correlated +entering arrays, since the independent-column identity holds pointwise for +every joint input. For the nested BIT pair E subset U, the residual is exactly +D_(U intersect E-perp), of rank dim(U)-dim(E). + +If instead one insists that the old ZERO-frame logical h must be the same +physical array u, implementing a new E interpretation by an explicit D_E +does cost a query. That is an extra identification, not a universal requirement +of a paired arbitrary-dirt contract. A useful caller must still host the actual +residual and pay all ADDRESS adapters, accesses and private work. + +## A dedicated cover-bank construction + +Let m be at least the complete local footprint, including spectator axes. +All source/target families are separate from these ordinary helper banks. +Let the finite cover group G contain each required ADDRESS adapter and act +on doubled BIT addresses by diag(g,g), so it centralizes D_I_m. For the +coordinate residuals below, the original orthogonal cover already contains +the required coordinate permutations. A physical family is a pair (bank,g), +with g in G; distinct cover classes mean distinct stored physical families. + +For each role j in one bank, choose disjoint coordinate blocks I_j. The +role's exact residual must be conjugated to D_Ij by an explicit adapter Pi_j. +At local cover invocation d, assign the role to physical family + + (bank, g=d Pi_j^-1). + +This gives a bijection between the d invocations and g owners for each role. +Require Pi_j != Pi_k for distinct roles in the same invocation and bank. +Then g differs as well, so two such helpers do not alias a physical family. +Different banks, and all public families, are disjoint by construction. + +At any fixed physical owner g, the assigned endpoint actions are the +conjugates by g of the disjoint block interchanges D_Ij. Their product is the +interchange on their union, independently of their chronological order. +Each invocation accepts the actual arbitrary array produced by all preceding +ones. Add and charge a native padding query on the uncovered coordinates. +The final action is D_I_m, which commutes with every common ADDRESS chart. +Run each entire local call before beginning the next; no intermediate helper +state is exposed to another invocation. The source-call order is preserved. + +The unused spectator coordinates in a role's *local* footprint need not form +a globally reserved untouched block of the owner. They can lie in another +role's residual block. The exact endpoint acts as identity on those spectator +coordinates, and the next invocation accepts arbitrary correlated input. +No simultaneous reuse of one physical family is permitted by this argument. + +For a concrete coordinate example, let m=36 and residual width6 with a +two-axis entrance E, giving local footprint8. Split the owner into six +successive width6 blocks. Pi_j is a cyclic shift by6j, mapping the residual +axes to block j and the two entrance axes to the first two axes of block j+1 +(indices cyclic). These six permutations are distinct. All six residuals +are disjoint and fill36; no spectator padding query is needed. The local +two spectator axes are nevertheless present in every invocation. This is a +cover-bank construction, not a claim that six roles fit an unrelated +public-source window or that a helper may be used twice simultaneously. + +For the checked coordinate-E2 word, there are318 width6 and111 width8 roles +per call. At m36, using12 replicas makes all dedicated groups integral: +636 width6 banks with six roles each;333 width8 banks with four roles each. +The latter each pay a rank4 padding query. Thus per call/replica the ordinary +stock is318/6+111/4=323/4 and padding histogram is(111/4) H4. +The local helper rank mass is318*6+111*8=2796; adding padding111 gives +2907=36*(323/4). This checks only the helper-bank part of an invoice. + +## Scope and missing integration + +The local dirty-column identity and native residual must be established +before this lemma applies; a nullspace dimension or narrower span is not +enough. Every Pi must preserve the actual allowed cover and have a paid +implementation. The local footprint, simultaneous-family exclusion and +separate public/private stock are hypotheses. Public source windows, +pending prefixes and recycled data owners require their own literal +allocation. The lemma does not admit rational GL internal queries into a +narrower recursive alphabet, establish precision/tape bounds, or repair the +global E2 hybrid's failed public-coverage budget. + +The stabilizer worker independently reviewed the coordinate interpretation, +cover assignment, spectator overlap and integer bank counts. Its centrality +hypothesis clarification is incorporated above. The finite cyclic-cover +fixture `paired_owner_fixture.py` checks all72 coordinate columns for each +of six owners, all36 assignments and three actual defect controls; it is +separate from the written arbitrary-cover argument. + +Credit the retained PR386 dedicated whole-block cover-bank construction and +the paired-entrance/terminal lineage in PR2857 and PR2908. The present +derivation applies arbitrary-input coordinate interpretation to the new +literal BIT kernel words and makes the spectator-overlap condition explicit. +Substantial OpenAI Codex assistance; Apache-2.0. All work remains local. diff --git a/research/bit-paired-helper-boundaries/frozen/changed/budgets/paired_owner_fixture.py b/research/bit-paired-helper-boundaries/frozen/changed/budgets/paired_owner_fixture.py new file mode 100644 index 0000000000..a3e29b8041 --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/changed/budgets/paired_owner_fixture.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python3 +"""Exact cover-owner fixture for paired helpers with overlapping spectators. + +Checks the complete declared finite cyclic-cover domain. The general cover +argument and missing supplier premises are in PAIRED-HELPER-OWNERS.md. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from fractions import Fraction as Q +from pathlib import Path +import argparse +import json + +HERE=Path(__file__).resolve().parent +M=36 + +def need(v,msg): + if not v: + raise ValueError(msg) + +def swap_axes(xs): + p=list(range(2*M)) + for j in xs: + p[j],p[M+j]=p[M+j],p[j] + return p + +def compose(a,b): + return [a[j] for j in b] + +def local_residual(slot,omit_entry=False): + block={(6*slot+j)%M for j in range(6)} + entrance={(6*slot+j)%M for j in (6,7)} + need(block.isdisjoint(entrance),'local footprint is eight distinct axes') + physical=swap_axes(block|entrance) + if not omit_entry: + physical=compose(physical,swap_axes(entrance)) + need(omit_entry or physical==swap_axes(block),'actual D_U D_E inverse is width6') + return physical,block,entrance + +def run(omit_entry=False,omit_role=False,duplicate_adapter=False): + owners=[list(range(2*M)) for _ in range(6)] + events=[] + for d in range(6): + assigned=set() + for role in range(5 if omit_role else 6): + slot=0 if duplicate_adapter and role==1 else role + g=(d-slot)%6 + need(g not in assigned,'one physical family per role at one invocation') + assigned.add(g) + op,block,entrance=local_residual(slot,omit_entry) + # Conjugate by the owner chart g: simultaneous cyclic shift of + # both address halves. The direction is fixed and checked here. + chart=[(j+6*g)%M for j in range(M)] + chart+= [M+(j+6*g)%M for j in range(M)] + inverse=[0]*(2*M) + for i,j in enumerate(chart): + inverse[j]=i + routed=compose(chart,compose(op,inverse)) + owners[g]=compose(routed,owners[g]) + events.append({'invocation':d,'role':role,'owner':g, + 'slot_axes':sorted(block),'entrance_axes':sorted(entrance)}) + return owners,events + +def main(): + ap=argparse.ArgumentParser(description=__doc__) + ap.add_argument('--write',action='store_true') + args=ap.parse_args() + owners,events=run() + full=swap_axes(range(M)) + need(all(p==full for p in owners),'every independent coordinate at every owner has full swap') + need(any(set(a['entrance_axes']) & set(b['slot_axes']) + for a in events[:6] for b in events[:6] if a['role']!=b['role']), + 'fixture actually overlaps spectator and another residual block') + need(any(p!=full for p in run(omit_entry=True)[0]),'ignoring paired entrance changes owner output') + need(any(p!=full for p in run(omit_role=True)[0]),'missing role leaves unpaid owner residual') + try: + run(duplicate_adapter=True) + except ValueError: + alias_control=True + else: + raise ValueError('duplicated adapter must alias the same physical family') + stock=Q(318,6)+Q(111,4) + helper_mass=318*6+111*8 + need(helper_mass+111==36*stock,'coordinate E2 dedicated helper mass with complete padding') + out={'status':'PASS_PAIRED_HELPER_DEDICATED_COVER_OWNER_FIXTURE', + 'no_new_kappa':True,'m':M,'cover':'six cyclic shifts by6 axes', + 'physical_owners':6,'roles_per_invocation':6,'invocations':6, + 'all72_coordinate_columns_per_owner':True,'events':events, + 'controls':{'ignored_entrance_fails':True,'missing_role_fails':True, + 'same_call_family_alias_rejected':alias_control}, + 'E2_helper_inventory_only':{'replicas':12,'width6_banks':636,'width8_banks':333, + 'stock_per_call':str(stock),'padding_per_call':{'4':str(Q(111,4))}, + 'local_helper_rank_mass':helper_mass,'padding_rank_mass_per_call':111}, + 'scope':'Finite exact arbitrary-coordinate fixture for the dedicated bank theorem. It does not replay a local supplier or authorize recycling a public family. The actual local dirty cancellation, native wrappers, source/target stock and paid machine costs remain required.'} + out=json.loads(json.dumps(out)) + dest=HERE/'PAIRED-HELPER-OWNERS.json' + if args.write: + dest.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + else: + need(json.loads(dest.read_text())==out,'saved owner fixture differs') + print(out['status']) + print('6 owners,36 roles,72 coordinate columns,3 defects; E2 helper-only stock',stock) + +if __name__=='__main__': + main() diff --git a/research/bit-paired-helper-boundaries/frozen/major/bit-endpoint/BIT-FULL-COMPENSATION-WORD.json.gz b/research/bit-paired-helper-boundaries/frozen/major/bit-endpoint/BIT-FULL-COMPENSATION-WORD.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..763c88cbdc09a2ba3f86ffa89887e0f72abe07b3 GIT binary patch literal 57926 zcmZ6y2|Sct_&07hW0}U5ZOBCS7`vfm%*YlRvbESLTiKORmKig$GgF8dOCh^dcqo!( zk}a|&daPNClqI}J&-;5nzyF{4%-r|6&$;e%pL3n-T-W#d-pAr042OSA2g^+p13vXP 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Actual native MOVE frames and containment are replayed on651 ordinaryroles. AllSIZE rounded/tape implementation remains a separate obligation.", + "endpoint": "Source x and429helpers unchanged exactly overZ. Target y unchanged exactly; target updatex modulo2; helper targetleakageeven. Both data banks atFULL. Exact literal integer inverse returns all inputs.", + "exact_ADDRESS_identity_columns": 3552, + "executed_controls": { + "missing_one_actual_scatter_changes_F2_endpoint": true, + "omitted_target_lift_rejected": "native common-frame ADD / immutable snapshot", + "wrong_unprepare_changes_Z_source_but_not_F2": true + }, + "forward": { + "copies": 0, + "prefix_row_l1": 874, + "profile": { + "1": 1406, + "2": 1342, + "3": 79, + "4": 44, + "5": 93, + "6": 11, + "7": 9 + }, + "rank_mass": 5097, + "records": { + "0": 2984, + "1": 12932 + } + }, + "global_accounting": "Direct n=L diagonal-call topology hasD0, not LN. The111 rank1 target lifts percall are counted here and cannot be omitted from an old common-axis invoice.", + "helpers_restored_over_Z": 429, + "literal_inverse": { + "copies": 0, + "prefix_row_l1": 874, + "profile": { + "1": 1406, + "2": 1342, + "3": 79, + "4": 44, + "5": 93, + "6": 11, + "7": 9 + }, + "rank_mass": 5097, + "records": { + "0": 2984, + "1": 12932 + } + }, + "native_progress": 5097, + "new_target_lift_ADDRESS_columns": 1776, + "new_target_lift_ADDRESS_sha256": [ + "d2c32afd4093f34ec86716dee5d659b01a512ad841f240b474b0fa2ea54ae54d", + "7b4fd24f48cdb1e61fccb02b30d0786b1407654074aeb0a7f994248a67eef537", + "7a0091f10e8d96cb299c51c0859346214486ddf454f73d9f5818cd26c5b068c4", + "2347c035967c527ab3beea7001e3b3eec3e94548395281921af8564928c11148", + "02d4462b7a05aedc9dc23ad5e13e7291a78dea07786daf450961571d5496ab23", + "2d1723ba6269642ebc257cbffada8df399465f71b2beea76e43f6e2439d7f235", + "784b4bdf3f514a0fe74b3f77365dca2efb8edcc3dec75163d04f8744bb087864", + 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Every KR row includes its own source and at least one other source, and its actual E8 source-line span has rank8. For this physical-output gather alphabet, no row can be prepared at target cap K_p, which omits own P_p. A FULL pure-query pivot needs one rank1 immutable COPY to a cap target, or a source descent+return costs2. Those bills do not beat the one target lift. A changed multi-output factor/native source-consumption word is not excluded by this census.", + "physical_block": "For arbitrary physical inputs, raw F=[[S,0],[S,T]], S=F8 D_P native7,T=F8 native8. 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"target_FULL_lifts": 109 + }, + { + "D_per_call_upper": -8, + "E_axes": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6 + ], + "nine_COPY_ranks": [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + "private_query_rank": 9, + "remaining_cap_ports": 1, + "target_FULL_lifts": 110 + } + ], + "omission_controls": { + "omit_first_COPY_D_per_call": 6, + "omit_one_FULL_lift_D_per_call": 1 + }, + "retained_total_cut_frames": { + "471": 510, + "472": 511, + "473": 512, + "474": 513, + "475": 514, + "476": 515, + "477": 516, + "478": 517, + "479": 518 + } + }, + "hybrid": { + "decoded_seed_matrices": { + "FULL_B": [ + [ + 2, + 1 + ], + [ + 0, + 1 + ] + ], + "FULL_F": [ + [ + 1, + 0 + ], + [ + 1, + 2 + ] + ], + "FULL_FBF": [ + [ + 3, + 2 + ], + [ + 1, + 3 + ] + ], + "FULL_FBF_squared": [ + [ + 2, + 0 + ], + [ + 0, + 2 + ] + ], + "cap_B": [ + [ + 1, + 2 + ], + [ + 0, + 1 + ] + ], + "cap_F": [ + [ + 1, + 0 + ], + [ + 2, + 1 + ] + ], + "cap_FBF": [ + [ + 0, + 2 + ], + [ + 2, + 0 + ] + ] + }, + "faithful_binary_N": [ + [ + 0, + 1 + ], + [ + 1, + 0 + ] + ], + "faithful_binary_d": [ + [ + 1, + 1 + ], + [ + 1, + 1 + ] + ], + "normalized_rank_one_derivatives": { + "FULL_B": [ + [ + 1, + 0 + ], + [ + 0, + 0 + ] + ], + "FULL_F": [ + [ + 0, + 0 + ], + [ + 0, + 1 + ] + ], + "cap_B": [ + [ + 0, + 1 + ], + [ + 0, + 0 + ] + ], + "cap_F": [ + [ + 0, + 0 + ], + [ + 1, + 0 + ] + ] + }, + "omitted_middle_B_changes_seed": true + }, + "limits": "No native supplier replay, mixed-E/port-mixing theorem, public-window owner fill, free rational-GL compiler, tape theorem or new kappa.", + "no_new_kappa": true, + "sources": { + "/Users/ross/git/math/.research-automation/runs/kappa-changed-endpoints-20261019T0153Z/bit-native-caller/HYBRID-BUDGET.json": "b1e743fcc6e7b5482dafeb131270715d70621103f42b46972b13800082d4da84", + "/Users/ross/git/math/.research-automation/runs/kappa-changed-endpoints-20261019T0153Z/budgets/PAIRED-HELPER-OWNERS.json": "1d729716c459ae62a89d114a4ab58c03e2326d1770093f58b2db0b6379601cb9", + "/Users/ross/git/math/integer-mult-bounds/research/bit-r438-transport-rehost/words/r438-t154.json.gz": "a353999bceac4ac957f540adfd3e5f8768297138b27132eeb83332e2ea4b1022" + }, + "status": "PASS_INDEPENDENT_B10_CALLER_OWNER", + "written_proofs": "PROOF-CALLER.md: arbitrary-dirt interpretation, arbitrary finite cover assignment, all-bank rank bound, conditional uniform-prefix deficit." +} diff --git a/research/bit-paired-helper-boundaries/frozen/reviews/caller/independent_check.py b/research/bit-paired-helper-boundaries/frozen/reviews/caller/independent_check.py new file mode 100644 index 0000000000..acd9e2091f --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/reviews/caller/independent_check.py @@ -0,0 +1,281 @@ +#!/usr/bin/env python3 +"""Independent exact B10 caller/owner certificates; no producer imports. + +Apache-2.0. Substantial OpenAI Codex assistance. The arbitrary-cover and +all-bank proofs, and their cost/interface hypotheses, are in PROOF-CALLER.md. +""" +from collections import Counter, defaultdict +from fractions import Fraction +from hashlib import sha256 +from math import gcd +from pathlib import Path +import argparse +import gzip +import json + +BASE = Path('/Users/ross/git/math') +LANE = BASE / '.research-automation/runs/kappa-changed-endpoints-20261019T0153Z' +RAW = BASE / 'integer-mult-bounds/research/bit-r438-transport-rehost/words/r438-t154.json.gz' +HYBRID = LANE / 'bit-native-caller/HYBRID-BUDGET.json' +OWNERS = LANE / 'budgets/PAIRED-HELPER-OWNERS.json' +PINS = { + RAW: 'a353999bceac4ac957f540adfd3e5f8768297138b27132eeb83332e2ea4b1022', + HYBRID: 'b1e743fcc6e7b5482dafeb131270715d70621103f42b46972b13800082d4da84', + OWNERS: '1d729716c459ae62a89d114a4ab58c03e2326d1770093f58b2db0b6379601cb9', +} + + +def require(value, message): + if not value: + raise ValueError(message) + + +def rank_integer(rows): + """Exact rational rank by fraction-free row reduction and gcd content.""" + a = [list(row) for row in rows if any(row)] + if not a: + return 0 + rank = 0 + for col in range(len(a[0])): + pivot = next((i for i in range(rank, len(a)) if a[i][col]), None) + if pivot is None: + continue + a[rank], a[pivot] = a[pivot], a[rank] + for i in range(rank + 1, len(a)): + if a[i][col]: + x, y = a[rank][col], a[i][col] + a[i] = [x * u - y * v for u, v in zip(a[i], a[rank])] + content = 0 + for entry in a[i]: + content = gcd(content, entry) + if content: + a[i] = [entry // content for entry in a[i]] + rank += 1 + if rank == len(a): + break + return rank + + +def geometry(raw, saved): + lines = raw['lines'] + require(lines[:8] == [[2 * (i == j) for j in range(8)] for i in range(8)], 'literal coordinate prefix') + frames = [[lines[i] for i in frame] for frame in raw['frames']] + # Reverse chronology finds each retained total's actual last A-phase cut. + cuts = {} + for frame, destination, sources in reversed(raw['A']): + for helper in raw['ret']: + if helper not in cuts and helper in [destination, *sources]: + cuts[helper] = frame + for helper in raw['ret']: + cuts.setdefault(helper, raw['start'][helper]) + census = [] + for dim in range(1, 8): + remaining = [] + for port in range(111): + frame = frames[raw['final'][111 + port]] + # Quotient by E: dim(K+E) = dim(E)+rank(project_(E-perp) K). + if dim + rank_integer([row[dim:] for row in frame]) == rank_integer(frame): + remaining.append(port) + copy = [rank_integer([row[dim:] for row in frames[cuts[h]]]) for h in raw['ret']] + census.append({'E_axes': list(range(dim)), 'target_FULL_lifts': 111 - len(remaining), + 'remaining_cap_ports': len(remaining), 'nine_COPY_ranks': copy, + 'private_query_rank': sum(copy), 'D_per_call_upper': len(remaining) - sum(copy)}) + require(census == saved['coordinate_planes'], 'every leading-coordinate cap and COPY tariff') + require(all(row['D_per_call_upper'] <= 0 for row in census), 'fixed uniform common-prefix necessary budget') + # Remove an actual COPY or FULL lift from the rank-one prefix invoice. + first = census[0] + omit_copy = first['remaining_cap_ports'] - sum(first['nine_COPY_ranks'][1:]) + omit_lift = 111 - (first['target_FULL_lifts'] - 1) - first['private_query_rank'] + require(omit_copy == 6 and omit_lift == 1, 'actual tariff omissions detected') + return {'retained_total_cut_frames': {str(h): cuts[h] for h in raw['ret']}, + 'coordinate_planes': census, 'omission_controls': {'omit_first_COPY_D_per_call': omit_copy, + 'omit_one_FULL_lift_D_per_call': omit_lift}} + + +def add(a, b): + return [[x ^ y for x, y in zip(row, other)] for row, other in zip(a, b)] + + +def multiply(a, b): + return [[sum(x * y for x, y in zip(row, col)) % 2 for col in zip(*b)] for row in a] + + +def block(a, b, c, d): + return [a[i] + b[i] for i in range(2)] + [c[i] + d[i] for i in range(2)] + + +def binary_rank(rows): + packed = [sum(v << j for j, v in enumerate(row)) for row in rows] + pivots = {} + for value in packed: + while value: + p = value.bit_length() - 1 + if p in pivots: + value ^= pivots[p] + else: + pivots[p] = value + break + return len(pivots) + + +def seeds(saved): + I, Z, N = [[1, 0], [0, 1]], [[0, 0], [0, 0]], [[0, 1], [1, 0]] + d = add(I, N) + images = [Z, I, N, d] + require(len({tuple(map(tuple, a)) for a in images}) == 4, 'faithful representation of all four ring elements') + require(multiply(N, N) == I and multiply(d, d) == Z and d != Z, 'nontrivial square-zero d') + operations = {'cap_F': block(I, Z, N, I), 'cap_B': block(I, N, Z, I), + 'FULL_F': block(I, Z, I, N), 'FULL_B': block(N, I, Z, I)} + operations['cap_FBF'] = multiply(multiply(operations['cap_F'], operations['cap_B']), operations['cap_F']) + operations['FULL_FBF'] = multiply(multiply(operations['FULL_F'], operations['FULL_B']), operations['FULL_F']) + operations['FULL_FBF_squared'] = multiply(operations['FULL_FBF'], operations['FULL_FBF']) + def decode(matrix): + return [[images.index([row[2*j:2*j+2] for row in matrix[2*i:2*i+2]]) for j in range(2)] for i in range(2)] + decoded = {name: decode(matrix) for name, matrix in operations.items()} + require(all(saved[name] == value for name, value in decoded.items()), 'complete faithful binary seed identities') + normalized = {} + # A is the N=I constant matrix; C is the coefficient of d=N+I. + constants = {'cap_F': [[1, 0], [1, 1]], 'FULL_F': [[1, 0], [1, 1]], + 'cap_B': [[1, 1], [0, 1]], 'FULL_B': [[1, 1], [0, 1]]} + derivatives = {'cap_F': [[0, 0], [1, 0]], 'FULL_F': [[0, 0], [0, 1]], + 'cap_B': [[0, 1], [0, 0]], 'FULL_B': [[1, 0], [0, 0]]} + for name in constants: + A, C = constants[name], derivatives[name] + R = multiply(A, C) # These four constant matrices are involutions. + require(multiply(A, A) == I and binary_rank(R) == 1, 'normalized derivative rank one') + rebuilt = block(*[add(I if A[i][j] else Z, d if C[i][j] else Z) + for i, j in ((0, 0), (0, 1), (1, 0), (1, 1))]) + require(rebuilt == operations[name], 'all actual derivative coefficients') + normalized[name] = R + wrong_seed = multiply(operations['FULL_F'], operations['FULL_F']) + require(wrong_seed != operations['FULL_FBF'], 'omitted middle hybrid call detected') + return {'faithful_binary_N': N, 'faithful_binary_d': d, 'decoded_seed_matrices': decoded, + 'normalized_rank_one_derivatives': normalized, 'omitted_middle_B_changes_seed': True} + + +M = 36 +FULL_MASK = (1 << M) - 1 + + +def swap_mask(vector, mask): + change = (vector ^ (vector >> M)) & mask + return vector ^ change ^ (change << M) + + +def mask_axes(axes): + return sum(1 << a for a in axes) + + +def fixture(ignore_entry=False, omit_last=False, alias=False): + owners = [[1 << i for i in range(2 * M)] for _ in range(6)] + events = [] + for invocation in range(6): + used = set() + for role in range(5 if omit_last else 6): + slot = 0 if alias and role == 1 else role + owner = (invocation - slot) % 6 + require(owner not in used, 'same-call physical family collision') + used.add(owner) + residual = {(6 * slot + j) % M for j in range(6)} + entrance = {(6 * slot + j) % M for j in (6, 7)} + require(not residual & entrance, 'eight distinct local footprint axes') + actual_E = mask_axes({(a + 6 * owner) % M for a in entrance}) + actual_U = mask_axes({(a + 6 * owner) % M for a in residual | entrance}) + # Execute each paired endpoint directly on every binary ADDRESS + # coordinate column, without composing permutation tables. + for col, value in enumerate(owners[owner]): + if not ignore_entry: + value = swap_mask(value, actual_E) + owners[owner][col] = swap_mask(value, actual_U) + events.append({'invocation': invocation, 'role': role, 'owner': owner, + 'slot_axes': sorted(residual), 'entrance_axes': sorted(entrance)}) + return owners, events + + +def owner_certificate(saved): + actual, events = fixture() + expected = [swap_mask(1 << i, FULL_MASK) for i in range(72)] + require(actual == [expected] * 6, '432 independent ADDRESS columns reach full swap') + require(events == saved['events'], 'all 36 exact owner assignments') + for j in range(6): + require(set(events[j]['entrance_axes']) <= set(events[(j + 1) % 6]['slot_axes']), 'every local spectator is in next residual block') + bad_entry = sum(a != b for owner in fixture(ignore_entry=True)[0] for a, b in zip(owner, expected)) + bad_role = sum(a != b for owner in fixture(omit_last=True)[0] for a, b in zip(owner, expected)) + require(bad_entry > 0 and bad_role > 0, 'omitted paired entrance and role change actual endpoint') + try: + fixture(alias=True) + except ValueError: + alias_rejected = True + else: + alias_rejected = False + require(alias_rejected, 'actual duplicated adapter rejected') + # Actual E2={0,1}, U={0,...,7} is first canonically permuted so that + # its residual is {0,...,5} and its two spectators are {6,7}. + initial_chart = [6, 7, 0, 1, 2, 3, 4, 5] + list(range(8, 36)) + require(set(initial_chart) == set(range(36)), 'canonical E2 embedding permutation') + require({initial_chart[i] for i in range(2, 8)} == set(range(6)), 'actual E2 residual chart') + # Check centrality for all six diagonal charts on all 72 columns. + def chart(index, shift, one_half=False): + half, axis = divmod(index, M) + return half * M + ((axis + shift) % M if not one_half or half == 0 else axis) + for g in range(6): + for col in range(72): + require(chart((col + M) % 72, 6 * g) == (chart(col, 6 * g) + M) % 72, 'diagonal chart centralizes full swap') + require(any(chart((col + M) % 72, 6, True) != (chart(col, 6, True) + M) % 72 for col in range(72)), 'non-diagonal chart centrality defect') + inventory = {} + for width, per_replica, slots in ((6, 318, 6), (8, 111, 4)): + banks = defaultdict(list) + same_call = defaultdict(set) + for replica in range(12): + for helper in range(per_replica): + bank, slot = divmod(replica * per_replica + helper, slots) + require(slot not in same_call[(replica, bank)], 'same-call adapter distinctness in 12-replica fill') + same_call[(replica, bank)].add(slot) + banks[bank].append((replica, helper, slot)) + require(all(sorted(x[2] for x in roles) == list(range(slots)) for roles in banks.values()), 'every whole bank receives every role exactly once') + inventory[str(width)] = {'roles': 12 * per_replica, 'banks': len(banks), 'slots': slots} + require(inventory['6']['banks'] == 636 and inventory['8']['banks'] == 333, 'integral bank counts') + stock = Fraction(318, 6) + Fraction(111, 4) + mass, pad = 318 * 6 + 111 * 8, 111 + require(stock == Fraction(323, 4) and mass + pad == 36 * stock, 'helper-only exact complete mass') + require(12 * mass + 333 * 4 == 36 * (636 + 333), 'all replicated bank padding paid') + expected_inventory = {'replicas': 12, 'width6_banks': 636, 'width8_banks': 333, + 'stock_per_call': str(stock), 'padding_per_call': {'4': str(Fraction(111, 4))}, + 'local_helper_rank_mass': mass, 'padding_rank_mass_per_call': pad} + require(saved['E2_helper_inventory_only'] == expected_inventory, 'complete retained helper invoice') + omitted_padding = sum(swap_mask(1 << col, (1 << 32) - 1) != expected[col] for col in range(72)) + require(omitted_padding == 8, 'actual unpaid width-eight-bank padding leaves wrong endpoint') + return {'m': M, 'cover_invocations': 6, 'physical_owners': 6, 'checked_columns': 432, + 'events': events, 'canonical_E2_chart': initial_chart, + 'twelve_replica_inventory': inventory, 'stock_per_replica': str(stock), + 'local_helper_mass': mass, 'padding_mass_per_replica': pad, + 'padding_query_rank': 4, 'padding_query_count_twelve_replicas': 333, + 'controls': {'ignored_entrance_wrong_columns': bad_entry, 'omitted_role_wrong_columns': bad_role, + 'same_call_alias_rejected': alias_rejected, 'non_diagonal_chart_fails_centrality': True, + 'omitted_rank4_padding_wrong_columns': omitted_padding}} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--output', type=Path) + args = parser.parse_args() + for path, digest in PINS.items(): + require(sha256(path.read_bytes()).hexdigest() == digest, str(path)) + raw = json.loads(gzip.decompress(RAW.read_bytes())) + hybrid = json.loads(HYBRID.read_bytes()) + owner = json.loads(OWNERS.read_bytes()) + result = {'status': 'PASS_INDEPENDENT_B10_CALLER_OWNER', 'no_new_kappa': True, + 'sources': {str(p): h for p, h in PINS.items()}, + 'geometry': geometry(raw, hybrid), 'hybrid': seeds(hybrid), + 'dedicated_owners': owner_certificate(owner), + 'written_proofs': 'PROOF-CALLER.md: arbitrary-dirt interpretation, arbitrary finite cover assignment, all-bank rank bound, conditional uniform-prefix deficit.', + 'limits': 'No native supplier replay, mixed-E/port-mixing theorem, public-window owner fill, free rational-GL compiler, tape theorem or new kappa.'} + content = json.dumps(result, indent=2, sort_keys=True) + '\n' + if args.output: + args.output.write_text(content) + else: + print(content, end='') + + +if __name__ == '__main__': + main() diff --git a/research/bit-paired-helper-boundaries/frozen/reviews/native/RESULT.json b/research/bit-paired-helper-boundaries/frozen/reviews/native/RESULT.json new file mode 100644 index 0000000000..c8755de9f5 --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/reviews/native/RESULT.json @@ -0,0 +1,113164 @@ +{ + "baseline_costs": { + "R429_FULL": { + "ADDs": 12932, + "H": { + "1": 1406, + "2": 1342, + "3": 79, + "4": 44, + "5": 93, + "6": 11, + "7": 9 + }, + "mass": 5097 + }, + "R438_CLEAN": { + "ADDs": 24248, + "COPY_records": [ + { + "private_frame": 0, + "query_rank": 7, + "source_frame": 510, + "source_helper": 471 + }, + { + "private_frame": 0, + "query_rank": 7, + "source_frame": 511, + "source_helper": 472 + }, + { + "private_frame": 0, + "query_rank": 7, + "source_frame": 512, + "source_helper": 473 + }, + { + "private_frame": 0, + "query_rank": 7, + "source_frame": 513, + "source_helper": 474 + }, + { + "private_frame": 0, + "query_rank": 7, + "source_frame": 514, + "source_helper": 475 + }, + { + "private_frame": 0, + "query_rank": 7, + "source_frame": 515, + "source_helper": 476 + }, + { + "private_frame": 0, + "query_rank": 7, + "source_frame": 516, + "source_helper": 477 + }, + { + "private_frame": 0, + "query_rank": 7, + "source_frame": 517, + "source_helper": 478 + }, + { + "private_frame": 0, + "query_rank": 7, + "source_frame": 518, + "source_helper": 479 + } + ], + "COPYs": 9, + "H": { + "1": 1322, + "2": 1342, + "3": 79, + "4": 44, + "5": 102, + "6": 11, + "7": 18 + }, + "mass": 5121, + "private_fields": 1 + } + }, + "limits": [ + "Integer source/helper restoration; target clean shear only overF2.", + "Physical helper residual keyed by both entrance and exit.", + "No chronological owner, full caller, all-size compiler, rounded or tape admission.", + "Hybrid coordinate census and bank lower bound reviewed separately." + ], + "native": { + "coordinate_complement_route": [ + [ + 0, + 0, + 1, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 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+"""Independent exact audit of three fixed changed-helper-boundary words. + +Dense signed rows; semantic binary dirt; integer Gram projectors; direct +ADDRESS-column tests. No producer mathematics imported. Standard library only. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse, gzip, json + +HERE=Path(__file__).resolve().parent +FROZEN=HERE.parent/'b10-staging/frozen' +LANE='changed/bit-native-caller/' +RAW='upstream/research/bit-r438-transport-rehost/words/r438-t154.json.gz' +BASE='major/bit-endpoint/BIT-FULL-COMPENSATION-WORD.json.gz' +# The exact input hash map is appended below before main() is called. + +class Rejection(ValueError): + def __init__(self,kind,detail):self.kind=kind;super().__init__(kind+': '+detail) +def need(ok,message): + if not ok:raise ValueError(message) +def typed(ok,kind,detail): + if not ok:raise Rejection(kind,detail) +def canonical(x):return json.dumps(x,sort_keys=True,separators=(',',':')).encode() +def ident(n):return [[int(i==j) for j in range(n)] for i in range(n)] +def mm(a,b):return [[sum(x*y for x,y in zip(r,c)) for c in zip(*b)] for r in a] +def tr(a):return list(map(list,zip(*a))) +def sub(a,b):return [[x-y for x,y in zip(r,s)] for r,s in zip(a,b)] +def parse(a):return [list(map(Q,r)) for r in a] +def ser(a):return [[str(x) for x in r] for r in a] +def matvec(a,v):return [sum(x*y for x,y in zip(r,v)) for r in a] +def bits(x):return [j for j in range(x.bit_length()) if x>>j&1] +def rank2(rows): + rows=[r[:] for r in rows];k=0 + if not rows:return 0 + for j in range(len(rows[0])): + p=next((p for p in range(k,len(rows)) if rows[p][j]&1),None) + if p is None:continue + rows[k],rows[p]=rows[p],rows[k] + for p in range(k+1,len(rows)): + if rows[p][j]&1:rows[p]=[x^y for x,y in zip(rows[p],rows[k])] + k+=1 + if k==len(rows):break + return k +def rref(a): + a=[list(map(Q,r)) for r in a];k=0 + if not a:return [] + for j in range(len(a[0])): + p=next((p for p in range(k,len(a)) if a[p][j]),None) + if p is None:continue + a[k],a[p]=a[p],a[k];v=a[k][j];a[k]=[x/v for x in a[k]] + for p in range(len(a)): + if p!=k: + v=a[p][j] + if v:a[p]=[x-v*y for x,y in zip(a[p],a[k])] + k+=1 + if k==len(a[0]):break + return a[:k] +def inverse_det(a): + n=len(a);z=[list(map(Q,r))+s for r,s in zip(a,ident(n))];det=Q(1) + for j in range(n): + p=next(p for p in range(j,n) if z[p][j]) + if p!=j:z[p],z[j]=z[j],z[p];det=-det + v=z[j][j];det*=v;z[j]=[x/v for x in z[j]] + for p in range(n): + if p!=j: + v=z[p][j] + if v:z[p]=[x-v*y for x,y in zip(z[p],z[j])] + return [r[n:] for r in z],det +def primes(n): + n=abs(n);out=set();p=2 + while p*p<=n: + if n%p==0: + out.add(p) + while n%p==0:n//=p + p+=1 + if n>1:out.add(n) + return out +def dense_hash(rows): + h=sha256() + for r in rows:h.update((','.join(map(str,r))+'\n').encode()) + return h.hexdigest() +def load(name): + data=(FROZEN/name).read_bytes() + return json.loads(gzip.decompress(data) if name.endswith('.gz') else data) + +class Geometry: + def __init__(self,raw): + self.raw=raw;self.bases=[];self.originals=[];self.frame_basis_ports=[];self.projections={};self.nested_cache={} + for frame in raw['frames']: + echelon={};original=[];labels=[] + for p in frame: + v=list(map(Q,raw['lines'][p])) + for j,row in sorted(echelon.items()): + c=v[j] + if c:v=[x-c*y for x,y in zip(v,row)] + j=next((j for j,x in enumerate(v) if x),None) + if j is not None: + c=v[j];echelon[j]=[x/c for x in v];original.append(raw['lines'][p]);labels.append(p) + self.bases.append(rref(original));self.originals.append(original);self.frame_basis_ports.append(labels) + self.dims=list(map(len,self.bases)) + def nested(self,a,b): + key=(a,b) + if key not in self.nested_cache: + self.nested_cache[key]=len(rref(self.bases[a]+self.bases[b]))==self.dims[b] + return self.nested_cache[key] + def projector(self,f): + if f not in self.projections: + B=self.originals[f] + if B: + inv,det=inverse_det(mm(B,tr(B)));P=mm(mm(tr(B),inv),B) + else:det=Q(1);P=[[Q(0)]*8 for _ in range(8)] + need(P==tr(P) and mm(P,P)==P,'independent rational orthogonal projector') + need(det.denominator==1 and det>0,'integer-basis Gram determinant') + self.projections[f]=(P,det) + return self.projections[f][0] + +def replay(program,geom,back=False,initial=None,omit_comp=False,track_peak=True): + n=len(program['start']);has_private=any(r[0] in (2,3) for r in program['records']) + width=n if initial is None else len(initial[0]) + state=ident(n)+([[0]*n] if has_private else []) if initial is None else [r[:] for r in initial] + frames=(program['final'] if back else program['start'])[:]+([None] if has_private else []) + hist=Counter();adds=0;copies=[];opened=None;peak=max(sum(map(abs,r)) for r in state) + records=list(enumerate(program['records'])) + if back:records.reverse() + for at,(op,d,s,c,f,phase) in records: + detail=f'record {at}' + typed(0<=d0,'frame',detail) + frames[d]=b;hist[f]+=1 + elif op==1: + typed(d!=opened,'snapshot',detail) + typed(0<=sgeom.dims[f],'frame',detail) + cost=geom.dims[c]-geom.dims[f];hist[cost]+=1 + copies.append({'source_helper':d,'source_frame':c,'private_frame':f,'query_rank':cost}) + state[n]=state[d][:];frames[n]=f;opened=d + else: + typed(op==(2 if back else 3) and opened==d and s==n and state[n]==state[d],'snapshot',detail) + typed(frames[d]==c and frames[n]==f,'frame',detail) + state[n]=[0]*width;frames[n]=None;opened=None + typed(frames==(program['start'] if back else program['final'])+([None] if has_private else []),'frame','endpoint') + typed(opened is None and (not has_private or not any(state[n])),'snapshot','endpoint') + rec={'H':dict(sorted(hist.items())),'mass':sum(k*v for k,v in hist.items()),'ADDs':adds,'prefix_row_L1':peak} + if has_private:rec.update(COPYs=len(copies),private_fields=1,COPY_records=copies) + return state,rec + +def original_clean(raw,geom): + frames=raw['start'][:];records=[] + def move(d,f): + if frames[d]!=f: + records.append([0,d,frames[d],f,geom.dims[f]-geom.dims[frames[d]],0]);frames[d]=f + for name,phase,sign in [('D',10,1),('A',2,1),('B',4,1),('C',5,-1)]: + if name=='B': + for j,h in enumerate(raw['ret']): + records.append([2,h,660,frames[h],0,3]) + records += [[1,111+p,660,1,0,3] for p,ss in enumerate(raw['scatter']) if j in ss] + records.append([3,h,660,frames[h],0,3]) + for f,d,ss in raw[name]: + for r in [d]+ss:move(r,f) + records += [[1,d,s,sign,f,phase] for s in ss] + for d,f in enumerate(raw['final']):move(d,f) + return {'start':raw['start'],'final':raw['final'],'records':records} + +def semantic_dirty(base,geom): + n=len(base['start']);h=n-222;has_private=n==660 + initial=[[int(222+j==i) for j in range(h)] for i in range(n)]+([[0]*h] if has_private else []) + rows,cost= replay(base,geom,initial=initial,omit_comp=True,track_peak=False) + need(rows[:111]==[[0]*h for _ in range(111)] and rows[222:n]==ident(h),'semantic dirt replay restores every source/helper integer row') + D=[[v%2 for v in row] for row in rows[111:222]] + literal=[[0]*h for _ in range(111)] + for op,d,s,c,f,phase in base['records']: + if op==1 and phase==10: + need(111<=d<222 and 222<=s0,'actual native residual projector and rank') + C,Ci=parse(c['ADDRESS_C']),parse(c['ADDRESS_C_inverse']) + need(mm(C,Ci)==mm(Ci,C)==I and c['query_rank']==r and parse(c['residual_projector'])==W,'stored GL inverse and full residual') + coordinate=[[int(i==j and iFBTBi$e^UDBOHQecEq(lL63BVYXf z-u>}>p3gb=xu5&G&Ru7FMi&Km^zZZJ9?_wgz}yy#;hCzt-P=8>-9~GFQuJ;r)uHdz zD;bfvp%0o<+ySW>%pb8|hRZy@k-k3(xPb@UAq_WGL7Nj@Rrgob(x*o@_f->J3%LQ4 zcOFdvP1`H$>8TSnA8&f4v$+Pf!R&)OZ^yg~{#cf5A} zPp}m>cDzo;FKuI63${1KSE|J`Vsr3+qW$|OozHxOdoD9$tqM+kL)AP(3ifu;1VOpx zVtcVUy!?OTe8e6^dHL-PR;|RmJNw%`Lzo_xMCklalBoVc_tGSag;iR~Lx@Jw(B!lp zS7GE~z}`P)H(c0T*rWxmW3Mptzmd&v;tx6`AJ*>fpov5re4W2jKdjMj?nx7*Tw**sB3gGU?5rW$N%8=$W|N14n5c`cO3tZ5F)M(Z>N9o0ykmRu_*=HN;QSZv41wp ztzWzShfe$X#p*wF7$ZGWG-ENeE$TYYFBbmM3rq>}6Ju1ENcHR-tp5+-!$=Ud%EO3} zm}um~7Cq?4QgD-dK-%N%DD?m8Vh{hPu9csf`=6+eNHNpz9rXQho&5v!e;<|3&NnW3;Ev{`rIG)wCz?nDw{1ji(Q+ 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+import importlib.util +import json +from pathlib import Path +import sys + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(',', ':'), ensure_ascii=False) + + +class Portable: + def __init__(self, root): + self.root = Path(root).resolve() + self.hashes = json.loads((self.root / 'FROZEN-SHA256.json').read_text()) + self.patches = json.loads((self.root / 'ADAPTATIONS.json').read_text()) + self.executed = set() + self.compared = set() + self.words_compared = set() + old = '/Users/ross/git/math/' + self.prefixes = { + old + 'integer-mult-bounds/': self.root / 'frozen/upstream', + old + '.research-automation/runs/kappa-changed-endpoints-20261019T0153Z/': self.root / 'frozen/changed', + old + '.research-automation/runs/kappa-major-20261018T1330Z/': self.root / 'frozen/major', + old + '.research-automation/runs/kappa-3605-successor-20261018T0940Z/major-frontier/': self.root / 'frozen/old', + } + + def authenticate(self, path): + path = Path(path).resolve() + name = path.relative_to(self.root).as_posix() + need(name in self.hashes, 'unregistered frozen input: ' + name) + raw = path.read_bytes() + need(hashlib.sha256(raw).hexdigest() == self.hashes[name], 'frozen input changed: ' + name) + return raw + + def adapted(self, path): + name = Path(path).resolve().relative_to(self.root).as_posix() + source = self.authenticate(path).decode() + for edit in self.patches.get(name, []): + need(source.count(edit['old']) == 1, 'adaptation no longer unique: ' + name) + source = source.replace(edit['old'], edit['new']) + return source + + def check_all(self): + need(set(self.patches) <= set(self.hashes), 'unbound adaptation') + for name in self.hashes: + self.authenticate(self.root / name) + for name in self.patches: + self.adapted(self.root / name) + + def code(self, path): + path = Path(path).resolve() + source = self.adapted(path) + self.executed.add(path.relative_to(self.root).as_posix()) + return compile(source, str(path), 'exec', dont_inherit=True, optimize=0) + + def normalize(self, value): + if isinstance(value, str): + for prefix, target in self.prefixes.items(): + if value.startswith(prefix): + return str(target / value[len(prefix):]) + return value + if isinstance(value, dict): + result = {} + for key, item in value.items(): + normalized_key = self.normalize(key) + need(normalized_key not in result, 'normalized key collision') + result[normalized_key] = self.normalize(item) + return result + if isinstance(value, list): + return [self.normalize(v) for v in value] + return value + + def word_equal(self, path, body): + path = Path(path).resolve() + need(gzip.decompress(self.authenticate(path)) == body, 'complete word/geometry mismatch') + self.words_compared.add(path.relative_to(self.root).as_posix()) + return True + + def equal(self, path, value): + path = Path(path).resolve() + expected = json.loads(self.authenticate(path)) + actual = json.loads(json.dumps(value)) + # Compare every field, preserving JSON scalar types. Only original + # absolute provenance paths are mapped into this relocated package. + need(canonical(self.normalize(actual)) == canonical(self.normalize(expected)), + 'receipt mismatch: ' + path.name) + self.compared.add(path.relative_to(self.root).as_posix()) + return True + + def install(self): + portable = self + original_code = importlib.machinery.SourceFileLoader.get_code + original_exec = importlib.machinery.SourceFileLoader.exec_module + + def frozen(loader): + return Path(loader.path).resolve().is_relative_to(portable.root / 'frozen') + + def get_code(loader, fullname): + if frozen(loader): + return portable.code(loader.path) + return original_code(loader, fullname) + + def exec_module(loader, module): + if frozen(loader): + module.PORTABLE = portable + return original_exec(loader, module) + + importlib.machinery.SourceFileLoader.get_code = get_code + importlib.machinery.SourceFileLoader.exec_module = exec_module + sys.path.insert(0, str(self.root / 'frozen/changed/bit-native-caller')) + + def load(self, path): + spec = importlib.util.spec_from_file_location('portable_stage', self.root / path) + module = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = module + spec.loader.exec_module(module) + return module + + +PRE = 'frozen/changed/bit-native-caller/' +STAGES = { + 'ten-entrances': (PRE+'kernel_entrances.py',[PRE+'KERNEL-ENTRANCES.json'],[PRE+'KERNEL-ENTRANCES-WORD.json.gz']), + 'full-e2': (PRE+'global_kernel_boost.py',[PRE+'GLOBAL-KERNEL-E2.json'],[PRE+'GLOBAL-KERNEL-E2-WORD.json.gz',PRE+'GLOBAL-KERNEL-E2-GEOMETRY.json.gz']), + 'clean-e2': (PRE+'old_kernel_boost.py',[PRE+'OLD-KERNEL-E2.json'],[PRE+'OLD-KERNEL-E2-WORD.json.gz',PRE+'OLD-KERNEL-E2-GEOMETRY.json.gz']), + 'hybrid': (PRE+'hybrid_budget.py',[PRE+'HYBRID-BUDGET.json'],[]), + 'owners': ('frozen/changed/budgets/paired_owner_fixture.py',['frozen/changed/budgets/PAIRED-HELPER-OWNERS.json'],[]), + 'independent-native': ('frozen/reviews/native/independent_check.py',['frozen/reviews/native/RESULT.json'],[]), + 'independent-caller': ('frozen/reviews/caller/independent_check.py',['frozen/reviews/caller/INDEPENDENT-RESULT.json'],[]), +} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--stage', choices=STAGES, required=True) + args = parser.parse_args() + portable = Portable(Path(__file__).resolve().parent) + portable.check_all() + portable.install() + source, receipts, words = STAGES[args.stage] + sys.argv = [str(portable.root / source)] + module = portable.load(source) + module.main() + need(portable.compared == set(receipts), 'incomplete receipt coverage') + need(portable.words_compared == set(words), 'incomplete word/geometry coverage') + portable.check_all() + print(canonical({'status': 'PASS_PAIRED_HELPER_BOUNDARIES', 'stage': args.stage, + 'receipts': sorted(portable.compared), 'sources': sorted(portable.executed), + 'no_new_kappa': True})) + + +if __name__ == '__main__': + main() From a5ec08800cc9816feb2f43c3880cc90024ee6155 Mon Sep 17 00:00:00 2001 From: ross Date: Mon, 19 Oct 2026 23:06:03 +1100 Subject: [PATCH 2/2] Record independent review and completed replay evidence --- .../.gitattributes | 4 ++ .../REVIEW-PORTABILITY.md | 27 ++++++++++++ .../VALIDATION.md | 44 +++++++++++++++++++ 3 files changed, 75 insertions(+) create mode 100644 research/bit-paired-helper-boundaries/.gitattributes create mode 100644 research/bit-paired-helper-boundaries/REVIEW-PORTABILITY.md create mode 100644 research/bit-paired-helper-boundaries/VALIDATION.md diff --git a/research/bit-paired-helper-boundaries/.gitattributes b/research/bit-paired-helper-boundaries/.gitattributes new file mode 100644 index 0000000000..bbacdaf318 --- /dev/null +++ b/research/bit-paired-helper-boundaries/.gitattributes @@ -0,0 +1,4 @@ +# Complete mechanically generated native certificates remain required replay inputs. +frozen/changed/bit-native-caller/GLOBAL-KERNEL-E2.json linguist-generated=true +frozen/changed/bit-native-caller/OLD-KERNEL-E2.json linguist-generated=true +frozen/reviews/native/RESULT.json linguist-generated=true diff --git a/research/bit-paired-helper-boundaries/REVIEW-PORTABILITY.md b/research/bit-paired-helper-boundaries/REVIEW-PORTABILITY.md new file mode 100644 index 0000000000..46bb4e8864 --- /dev/null +++ b/research/bit-paired-helper-boundaries/REVIEW-PORTABILITY.md @@ -0,0 +1,27 @@ +PASS: no source-integrity defect remains in the final B10 package. This is an independent portability and source-to-replay audit, not a replacement for the native and caller mathematical reviews. + +All 30 retained files match their original bytes, recorded byte lengths, ORIGINS hashes and frozen manifest hashes. The 45 files in staging and `research/bit-paired-helper-boundaries` match byte-for-byte at final review. `FINAL-INTEGRITY.json` records every file digest and all original paths. The scientific replay is bound to commit `1b2638a3b34ffb7cf6cb5b90e8fd14ca7f216127`; later documentation/display metadata does not change its inputs. + +The 29 unique source adaptations comprise 19 path redirects, seven complete receipt comparisons and three complete word/geometry comparison sites. The last three sites cover five required emitted artifacts. Inspection found no changed arithmetic, scientific constants, loop bounds, rank assertions, COPY/ERASE checks or test domains. The two new independent scripts use standard-library arithmetic and import no producer mathematics. Their full receipts are mandatory outputs in separate stages. The caller's former JSON print is redirected to full typed equality; the native checker's former equality is replaced by the same stronger comparison. Neither result can be silently omitted because each stage checks its exact comparison set. + +The loader authenticates source bytes immediately before compilation, uses `dont_inherit=True, optimize=0`, and intercepts the frozen SourceFileLoader path for nested imports. Thus the historical assertions remain active when the registered launcher itself uses `-O`. Direct controls bootstrap the verifier from its source bytes. All declared source inputs are inside the retained closure. Producer imports reach cold_cosets, helper_tail_retime, kernel_entrances, global_kernel_boost and native_seed_binding as appropriate. The latter's unused port_identities entry point references physical_code; physical_code is retained provenance but is not executed by these seven stages. Preserved historical selective/mixed/snapshot entry points are not standalone supported replay commands. The observed registered source sets agree with this static closure. + +The verifier resets argv before main, so historical --write/--output branches are unreachable through its seven declared commands. It compares all five producer receipts and both independent receipts, without field filtering. Only recorded absolute provenance path prefixes are normalized, with normalized-key collisions rejected. Canonical JSON comparison retains scalar type distinctions. I independently checked positive full comparison and missing-field rejection for all seven receipts. Every emitted word/geometry comparison uses the entire uncompressed byte body, while authenticating the exact frozen gzip container first. Equivalent regenerated compression choices do not relax frozen input hashes. + +The final actual repository launcher controls passed on Python 3.12.14 in normal and optimized modes (1.010s and 0.999s). These exercise changed source/receipt bytes, omitted witnesses, scalar types, normalized-path collisions, a corrupted inverse-chart entry, omitted complete charts, all five truncated artifacts, omitted records/frames, gzip-body equivalence, and a timestamp/size-valid poisoned cold_cosets cache demonstrably accepted by the ordinary loader but bypassed by the authenticated nested loader. Cache construction works under the repository launcher's private pycache prefix. See FINAL-LAUNCHER-CONTROLS.log. I read the root's complete B10-FINAL-REPLAY.log: all seven scientific stages and controls passed. I also read its successful committed-export controls log. No heavy scientific stage was repeated in this review. Declared timeout sum remains 1140 seconds. + +README and proofs preserve the material contracts: 651 arbitrary inputs for the R429 words; 660 arbitrary inputs plus one required-zero private field for R438; exact integer source/helper restoration, binary clean target shear, and nonzero even integer target dirt; paired physical residual D_U D_E^-1; rational GL identities away from the stated exceptional primes without orthogonal/dyadic compiler admission; helper-only cover hosting and paid padding; fixed common involution/scalar-bank alphabet and explicit uniform-prefix invoice for the deficit bound. The independent finite computations do not certify public-window ownership, mixed-E/port mixing, rounded or tape realization, all-size transfer, or a new kappa. The written cover/rank arguments remain explicitly separate from finite replay and formal-kernel proof. B11 partitions and historical exploratory notes are excluded. + +The added .gitattributes is suitably narrow: exactly GLOBAL-KERNEL-E2.json (470462 lines), OLD-KERNEL-E2.json (475090 lines) and independent native RESULT.json (113164 lines) are marked linguist-generated=true. Those 1058716 generated lines remain tracked, hash-authenticated and fully compared. No binary/-diff rule or broad JSON glob hides scripts, proofs, manifests or small receipts. This improves review presentation without weakening reproducibility. + +Key final SHA256 bindings: + +- verify.py: `8e60891020fbb259d0fcd569f1c569aff9b2e0c7b3ef38de664deef6d5a8b5f3` +- controls.py: `d3c283ac57cbf1b9db41960bb93f8b4a28e9855146dcca1d58efcd34234f7f11` +- ADAPTATIONS.json: `5a302856732d3e245cad13949431be2a4fd22bef05954d5110c4775d89855b53` +- FROZEN-SHA256.json: `ef87cbb90c3b6a1b3e3e040880ec6d417be940b7e7f05c1042aa75112e891a31` +- ORIGINS.json: `26f26f0a17e6723d44f2580f75b6b6edac0437f0f55104c04646c9e33a7f0abe` +- VERIFY.json: `a9205e65302603ea5a7021c6a9513f81f1864a7d74c7022c5c9b041000003b21` +- .gitattributes: `9567c726af016562aa790e61c20bad852bd13a4086d26e363997f1a2c1b68426` + +Publication, hosted CI and merge state remain parent-owned; this review makes no claim about those later gates. diff --git a/research/bit-paired-helper-boundaries/VALIDATION.md b/research/bit-paired-helper-boundaries/VALIDATION.md new file mode 100644 index 0000000000..b6b0f47af5 --- /dev/null +++ b/research/bit-paired-helper-boundaries/VALIDATION.md @@ -0,0 +1,44 @@ +# Validation and evidence limits + +Scientific commit `1b2638a3b34ffb7cf6cb5b90e8fd14ca7f216127` passed the complete +registered replay on Python3.12.14: + +```sh +python3 -B scripts/research_package.py --package research/bit-paired-helper-boundaries +``` + +All five producer stages, the independent native and caller checkers, and +actual-launcher integrity controls passed. The tracked package stayed clean. +This reconstructs all three literal words, five whole word/geometry bodies, +five producer receipts and both complete independent receipts. It is not a +full recursive supplier, outer-release or fixed-tape replay. + +The native independent checker also passed normal and optimized Python3.14.6 +execution on the original source set; its final normal run took18.94seconds. +The caller checker passed normal and optimized execution with identical +receipts. Both final proofs separate finite exact computations from written +all-bank/arbitrary-cover statements and their explicit hypotheses. No +independent human or formal-kernel proof is claimed. + +All30 original inputs are retained byte-for-byte with SHA256 bindings and +absolute origins. The29 adapters change19 path sites, seven complete typed +receipt comparisons and three complete word/geometry comparison sites; +the latter cover five required emitted artifacts. Arithmetic, scientific +constants and loops are unchanged. The registered loader compiles authenticated +source bytes, including nested imports, independently of timestamp bytecode. + +Integrity controls reject changed source bytes, altered scalar JSON types, +omitted kernel witnesses, corrupted or missing ADDRESS charts, changed or +truncated word/geometry bodies, colliding normalized provenance paths and an +actually admitted poisoned nested bytecode cache. Equivalent gzip compression +of identical artifact bodies remains valid. Final metadata/source-history +preflight is recorded externally. Optimized controls also passed from a +fresh committed export in a path containing spaces; this was a controls-only +relocation check, not a second full replay. The three large generated native +receipts are marked for GitHub diff display only; every byte remains a required +authenticated input and every generated field is compared. Automatic hosted CI is reported in the PR +only after its exact head finishes. + +All native adapter, caller/public-window, rounded and tape obligations in the +README remain open. Historical selective/mixed-entrance notes are retained +provenance and are not covered by this replay.

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Public native coverage remains111*(7+8); helper coverage111*8+318*(8-d) equals the entire query mass. No private COPY or additional recursive adapter query is omitted. ADDRESS charts are rational GL maps with explicit finite prime exclusions; their scalar lowering/source/tape invoice and the retained self-recursive admission premise require review.", + "construction": "Choose111 original independent dirty columns; for each of318 dependent columns j, write it as XOR of pivots I_j. At a common actual E perform helper_i += helper_j for i in I_j. These integer shears commute because their destinations are pivots and sources are dependent, hence S=I+N with N^2=0 overZ. D*S mod2 has unchanged pivot columns and zero dependent columns, so initialZERO compensation never reads the318 nonzero-entrance helpers. Replace each subsequent native frame f by span(f,E), execute the old scalar word, then apply S^-1 atFULL.", + "contract": "318 explicitly selected arbitrary dirty helpers enter at coordinate E and leaveFULL;111 pivot helpers enterZERO and leaveFULL. All429 are restored exactly overZ. Source entrancesPp and all source/targetFULL exits are unchanged from the FULL box; target entrances remainZERO. Physical helper residual D_FULL D_E^-1 is coordinate-width8-d.", + "controls": { + "omitted_inverse_basis_fails_Z_helpers": true, + "perturbed_kernel_leaks_F2_dirt": true + }, + "dirty_compensation_rank": 111, + "finite_bad_prime_factors": [ + 2, + 3, + 5 + ], + "geometry_canonical_sha256": "efa667bb0cbc0dc6fc6eda320842c4bba3403081d3213cce7c6cc5b2c71256ac", + "helper_inventory_by_residual_width": { + "6": 318, + "8": 111 + }, + "joined_frames_with_odd_projector_denominators": [ + 643, + 644, + 645, + 646, + 647, + 648, + 649, + 650, + 655, + 656, + 657, + 658, + 659, + 660, + 661, + 662, + 672, + 673, + 674, + 675, + 676, + 677, + 678, + 679, + 695, + 696, + 697, + 698, + 699, + 700, + 701, + 702, + 704, + 705, + 706, + 707, + 710, + 711, + 712, + 713, + 715, + 716, + 717, + 720, + 721, + 722, + 723, + 725, + 726, + 727, + 728, + 730, + 731, + 732, + 733, + 734, + 735, + 737, + 738, + 739, + 740, + 741, + 743, + 744, + 745, + 746, + 747, + 749, + 750, + 751, + 752, + 753, + 755, + 756, 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No owner/stock premise is used for this necessary rejection.", + "limits": [ + "Port-mixing operator-valued bank adapters, nonuniform E families, changed public codes or source cuts are outside this rank argument.", + "No all-parameter native supplier or formal-kernel proof is claimed." + ], + "no_new_kappa": true, + "ring": "F2[N]/(N^2-I)", + "source": { + "/Users/ross/git/math/integer-mult-bounds/research/bit-r438-transport-rehost/words/r438-t154.json.gz": "a353999bceac4ac957f540adfd3e5f8768297138b27132eeb83332e2ea4b1022" + }, + "status": "PASS_EXACT_HYBRID_SEEDS_AND_COORDINATE_PLANE_NECESSARY_BUDGET", + "written_all_parameter_rank_argument": "In a fixed port put d=I+N, d^2=0. Each normalized hybrid local call equals an invertible constant bank matrix times I+d*R with rank(R)=1. Arbitrary constant bank-GL adapters preserve that rank. In a product, the coefficient of d is a sum of k conjugated rank-one matrices because all degree>=2 terms vanish. A final common N on n independent banks requires this sum to equal I_n after the constant endpoint is removed, hence n<=k by rank subadditivity. There are111 common-rank units per bank, while each call already pays one common unit on every FULL-lifted target port plus all nine private COPY query ranks. Therefore D<=111*n-k*(number_FULL_lifts+private_rank)<=k*(remaining_cap_ports-private_rank). 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The helper-boundaries skill compensation-kernel lesson guided the changed entrance. This lane constructs the literal staged S, modified compensation, exact inverse and paired native wrappers.", + "compensation_kernel_witnesses": [ + { + "forward_S_ADDs": [ + [ + 233, + 242, + 1 + ] + ], + "frame": 7, + "inverse_S_ADDs": [ + [ + 233, + 242, + -1 + ] + ], + "kernel_helpers": [ + 233, + 242 + ], + "old_compensation_column_weights": [ + 19, + 19 + ], + "selected_helper": 242 + }, + { + "forward_S_ADDs": [], + "frame": 29, + "inverse_S_ADDs": [], + "kernel_helpers": [ + 467 + ], + "old_compensation_column_weights": [ + 0 + ], + "selected_helper": 467 + }, + { + "forward_S_ADDs": [], + "frame": 49, + "inverse_S_ADDs": [], + "kernel_helpers": [ + 462 + ], + "old_compensation_column_weights": [ + 0 + ], + "selected_helper": 462 + }, + { + "forward_S_ADDs": [], + "frame": 52, + "inverse_S_ADDs": [], + "kernel_helpers": [ + 469 + ], + "old_compensation_column_weights": [ + 0 + ], + "selected_helper": 469 + }, + { + "forward_S_ADDs": [], + "frame": 54, + "inverse_S_ADDs": [], + "kernel_helpers": [ + 463 + ], + "old_compensation_column_weights": [ + 0 + ], + "selected_helper": 463 + }, + { + "forward_S_ADDs": [], + "frame": 56, + "inverse_S_ADDs": [], + "kernel_helpers": [ + 464 + ], + "old_compensation_column_weights": [ + 0 + ], + "selected_helper": 464 + }, + { + "forward_S_ADDs": [ + [ + 360, + 367, + 1 + ] + ], + "frame": 65, + "inverse_S_ADDs": [ + [ + 360, + 367, + -1 + ] + ], + "kernel_helpers": [ + 360, + 367 + ], + "old_compensation_column_weights": [ + 17, + 17 + ], + "selected_helper": 367 + }, + { + "forward_S_ADDs": [ + [ + 385, + 401, + 1 + ] + ], + "frame": 76, + "inverse_S_ADDs": [ + [ + 385, + 401, + -1 + ] + ], + "kernel_helpers": [ + 385, + 401 + ], + "old_compensation_column_weights": [ + 18, + 18 + ], + "selected_helper": 401 + }, + { + "forward_S_ADDs": [], + "frame": 79, + "inverse_S_ADDs": [], + "kernel_helpers": [ + 444 + ], + "old_compensation_column_weights": [ + 0 + ], + "selected_helper": 444 + }, + { + "forward_S_ADDs": [], + "frame": 94, + "inverse_S_ADDs": [], + "kernel_helpers": [ + 470 + ], + "old_compensation_column_weights": [ + 0 + ], + "selected_helper": 470 + } + ], + "complete_local_price": "Delete10 first H1 queries. Other first MOVEs are merely advanced to the same frame before S; no new recursive query, COPY, private field or target lift. The helper basis S acts at a genuine common E; S^-1 acts atFULL. Initial compensation D*S mod2 has zero selected columns and therefore never reads a nonZERO entrance atZERO. New histogram is the frozen H minus10H1. Source/target coverage111*15 plus419*8+10*7 equals5087, so the old uncovered deficit is unchanged.", + "contract": "Ten explicitly listed arbitrary dirty helpers enter at their rank1 first frame E_h and exitFULL. The other419 helpers enterZERO and exitFULL. Each changed residual is D_FULL D_Eh^-1 of rank7; every scalar source/helper row is restored exactly overZ and target is the same clean shear overF2. Source and target physical native cuts are inherited unchanged.", + "controls": { + "old_ZERO_entrance_rejected": true, + "omitted_inverse_basis_fails_Z_helpers": true, + "perturbed_kernel_leaks_F2_dirt": true + }, + "entrance_gate": "The owner must implement the physical paired residual D_FULL D_Eh^-1 with public helper dependence cancelled. An arbitrary physical helper u can be interpreted as logical dirt h=D_Eh^-1u; this requires no executed entrance query merely to name h. If one instead insists on the old ZERO logical-dirt identification, ten explicit entrance queries restore the old5097 mass. Chronological paired owner routing remains open.", + "helper_inventory_by_residual_width": { + "7": 10, + "8": 419 + }, + "limits": [ + "No chronological owner/stock construction for the nonzero entrances.", + "No changed rounded suffix-error or physical source/tape invoice.", + "A local residual-width reduction is not an admitted supplier or new exponent." + ], + "literal_inverse": { + "ADDs": 12884, + "H": { + "1": 1396, + "2": 1342, + "3": 79, + "4": 44, + "5": 93, + "6": 11, + "7": 9 + }, + "mass": 5087, + "prefix_row_L1": 815 + }, + "new_basis_scalar_ADDs": 6, + "no_new_kappa": true, + "old_profile": { + "ADDs": 12932, + "H": { + "1": 1406, + "2": 1342, + "3": 79, + "4": 44, + "5": 93, + "6": 11, + "7": 9 + }, + "mass": 5097, + "prefix_row_L1": 874 + }, + "ordinary_helpers": 429, + "paired_native_wrappers": [ + { + "entrance_frame": 7, + "entrance_root": [ + 0, + 0, + 0, + 0, + 0, + 2, + 0, + 0 + ], + "helper": 242, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + }, + { + "entrance_frame": 65, + "entrance_root": [ + 1, + -1, + 1, + -1, + 0, + 0, + 0, + 0 + ], + "helper": 367, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + }, + { + "entrance_frame": 76, + "entrance_root": [ + 0, + 1, + 0, + 1, + 1, + 0, + -1, + 0 + ], + "helper": 401, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + }, + { + "entrance_frame": 79, + "entrance_root": [ + 0, + 1, + 0, + -1, + 1, + 0, + 1, + 0 + ], + "helper": 444, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + }, + { + "entrance_frame": 49, + "entrance_root": [ + 0, + 1, + 1, + 0, + 0, + 1, + -1, + 0 + ], + "helper": 462, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + }, + { + "entrance_frame": 54, + "entrance_root": [ + 0, + 0, + 0, + 0, + 1, + 1, + 1, + -1 + ], + "helper": 463, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + }, + { + "entrance_frame": 56, + "entrance_root": [ + 0, + 0, + 0, + 0, + 1, + 1, + -1, + -1 + ], + "helper": 464, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + }, + { + "entrance_frame": 29, + "entrance_root": [ + 1, + -1, + 0, + 0, + 0, + 0, + 1, + -1 + ], + "helper": 467, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + }, + { + "entrance_frame": 52, + "entrance_root": [ + 0, + 1, + -1, + 0, + 0, + -1, + 1, + 0 + ], + "helper": 469, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + }, + { + "entrance_frame": 94, + "entrance_root": [ + 0, + 0, + 1, + -1, + 1, + 1, + 0, + 0 + ], + "helper": 470, + "native_residual": "D_FULL D_E^-1 =D_(E-perp)", + "residual_rank": 7, + "terminal_frame": 1 + } + ], + "private_fields": 0, + "profile": { + "ADDs": 12884, + "H": { + "1": 1396, + "2": 1342, + "3": 79, + "4": 44, + "5": 93, + "6": 11, + "7": 9 + }, + "mass": 5087, + "prefix_row_L1": 874 + }, + "scientific_pin": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "sources": { + "/Users/ross/git/math/.research-automation/runs/kappa-major-20261018T1330Z/bit-endpoint/BIT-FULL-COMPENSATION-WORD.json.gz": "0f461dbc7e82a02faedb4a5129103963507c9f063a0a3679ba5d20ad94df160e", + "/Users/ross/git/math/integer-mult-bounds/research/bit-r438-transport-rehost/words/r438-t154.json.gz": "a353999bceac4ac957f540adfd3e5f8768297138b27132eeb83332e2ea4b1022" + }, + "status": "PASS_R429_TEN_LITERAL_PAIRED_RANK1_ENTRANCE_FULL_EXIT_HELPERS", + "word_canonical_sha256": "31862390eb135eaac9088ccad8d8e2181ac440bcc930d8ca7663ec84912d83d1" +} diff --git a/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/KERNEL-ENTRANCES.md b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/KERNEL-ENTRANCES.md new file mode 100644 index 0000000000..389bfc004a --- /dev/null +++ b/research/bit-paired-helper-boundaries/frozen/changed/bit-native-caller/KERNEL-ENTRANCES.md @@ -0,0 +1,48 @@ +# Ten literal changed helper entrances + +`kernel_entrances.py` constructs a local R429 FULL-box word with ten ordinary +helpers entering at their actual first rank-one frame E instead of ZERO. +The helpers remain arbitrary dirty streams. All429 helpers and111 sources +are restored exactly over the integers; every one of651 binary input columns +has the original clean target shear. Source and target native cuts are unchanged. + +The selected helper IDs are242,467,462,469,463,464,367,401,444,470. Seven have +zero actual compensation columns. The other three share compensation columns +with233,360,385 respectively. These are columns of the actual semantic dirty +map, reconstructed from the literal initial compensation, rather than a +syntactic helper count. + +For a duplicate pair(h,k), the two helpers reach a genuine common E before +the forward word. Apply k+=h there and k-=h at FULL after cleanup. The new +initial compensation is D*S modulo2, whose h column is zero. Consequently no +ZERO-frame operation reads the helper already supplied at E. No added +recursive query or private buffer is required. The literal saved word includes +all six basis ADDs and all advanced companion entrances. + +The local histogram is exactly the frozen R429 FULL histogram minus10H1: +`{1:1396,2:1342,3:79,4:44,5:93,6:11,7:9}`, with mass5087. The helper residual +inventory is10 of width7 and419 of width8. For each actual root line E, the +receipt checks the complete16-by-16 rational ADDRESS identity +`D_FULL D_E^-1 = D_(E-perp)`. The paired owner wrapper must therefore be +keyed by(E,FULL). + +This is a changed local boundary, not a completed supplier. An arbitrary +physical helper u may be interpreted as logical dirt h=D_E^-1u: no entrance +query is inherently required for this interpretation, because all public +helper dependence cancels. The owner must route the paired physical residual +D_FULL D_E^-1. Ten extra entrance queries are needed only when retaining the +old ZERO logical-dirt identification, which restores the old5097 mass. No +chronological owner allocation, complete outer moment, rounding theorem or +improved kappa is asserted. + +Reproduce from this directory: + +```sh +python3 kernel_entrances.py +python3 -O kernel_entrances.py +``` + +Both modes compare the generated word and receipt against saved artifacts. +Controls reject an old ZERO entrance, omitted inverse basis and a perturbed +kernel vector. 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