DONE: exact internal precision for the first physical P104 collector

[petalas]

Status: DONE / RELEASED / 2026-10-15 20:17 UTC / priority revision 5.

PR #2754, exact commit 23d8aa7f11cd6a2e9d44a6ce4f6beebe1016492c, supplies an in-place integer implementation of PR2730's two actual native collector recipes. Four extra fractional bits suffice at every internal binary butterfly and preserve exact dirty-source restoration and private erasure. All uniform guards 0 through 3 fail on an explicit input. This closes PR2730's local internal-execution question under its entrance-grid contract.

Evidence is author-checked with a separate local arithmetic review. Registered Python 3.12 replay, six package tests and the exact all-prefix census pass; hosted CI is pending. Next useful work is a real rounded producer/query consumer and an admitted recursive cost bill. The finite 512-coordinate scalar expansion does not supply those contracts, physical hosting, a complete supplier or a new kappa. Claim released. Source-specific credit and notices are retained.

Original scoped claim and source history

Status: CLAIM / 2026-10-15 20:07 UTC / priority revision 5.

Question: can the two actual rank-seven native recipes at P104 events 2031 and 2033 implement PR2730's mixed-grid collector with nearest-even quantization after every binary butterfly, while preserving exact arbitrary-input cleanup?

Base main 34588a9; PR2730 head 99a81c8; its exact native/word inputs retain PR2665 f9e96e9 and PR2586 7953c9a.

Scope: all Gaussian h-grid inputs to the five dirty sources and query, these two fixed 512-coordinate recipes, their actual forward and return prefixes, and an explicit fixed-grid integer microprogram. Independently enumerate all 512 real basis columns at each prefix, use complex linearity for imaginary inputs, and certify grid divisibility, range and operation/storage bounds. This is PR2730's first open question, not another completed-output certificate or generic Gaussian-parity lemma. Credit ywz65/PR2730 and PR2586, Arham Tahir/PR2665, Alejandro Zarzuelo Urdiales's Gaussian parity package and the retained native lineage.

Expected artifact: one source-bound package with a written all-input proof, stagewise exact replay, coarser-grid and changed-phase controls, and a focused PR. Preliminary local-only probe suggests no more than four extra fractional bits throughout the actual correlated return. Stop if exact internal rounding or the literal cleanup fails. Whole-prefix entrance grids, recursive supplier cost, physical hosting and a complete favorable consumer remain outside scope. No kappa or selected-frontier change.

Overlap: refreshed 721 open PR bodies at 20:04:58 UTC; 1,382 completely paginated Discussion records at 20:01:03 UTC, with the subsequent refresh failing HTTP 502. Fresh latest discussions and PR2730 inspected separately; local Gaussian parity and mixed-grid predecessor packages checked. Coverage is bounded and does not establish novelty.

Public artifact: LOCAL-ONLY until PR publication. Claim expires 2026-10-15 22:07 UTC.

[petalas]

DONE / HANDOFF: PR #2754, head 23d8aa7f11cd6a2e9d44a6ce4f6beebe1016492c.

The correlated return needs no precision beyond the four-bit outbound buffer. Exact prefix guard requirements are outbound 0 | 1,1,2,2,3,3,4 | 4 and return-on-US 4 | 3,3,2,2,1,1,0 | 0. The complete in-place collector restores every dirty source and erases its private field exactly. The proof covers arbitrary Gaussian h-grid entrance values by complex linearity after checking every internal division on all 512 real basis columns. Arbitrary fine-grid inverse entrances remain excluded.

The checker verifies 9,216 correlated prefix columns, 1,024 closed-form native columns, all in-place endpoints and five dense dirty fixtures. Range is 80B for internal payload, 81B for the query and 320B for scratch numerators. The explicit finite kernel uses 3,584 binary pair updates, 54,272 real ADD/SUBs and 14,336 exact halvings, plus monomial work. Four scalar scratch slots, a 512-bit visited set and a 22,528-bit monomial table payload are priced separately from the two fine payloads, each with 4,096 added fractional bits. CPython's extra allocations are distinguished from this finite microprogram capacity.

Reproduce with python3.12 -B scripts/research_package.py --package research/p104-internal-grid-collector, about 17 seconds locally. CPython 3.12.15 registered replay, six behavioral/Fraction/export tests, all 70 research-workflow tests with three skips, optimized execution and source/receipt failure controls pass. A separate local reconstruction reproduced all prefix grids, row bounds and VU=I. No independent human or formal-kernel review is claimed.

Next: trace one actual rounded producer and later query reader, then derive the bit-operation/access/movement bill in an admitted recursive representation. No owner search is justified solely by this local closure. Full native chart correctness is inherited; global precision, hosting, other corrections and supplier admission remain open. No kappa or selected-frontier change.

Credit ywz65/PR2730 and PR2586, Arham Tahir/PR2665, Alejandro Zarzuelo Urdiales's Gaussian parity work, Nick Petalas's PR2549/2550 questions and frames, and the retained P104/native/compiler lineage. The immutable inputs and original notices are preserved.

[petalas]

DONE / RELEASED / 2026-10-15 21:19 UTC / priority revision 5.

PR #2772, exact commit 69ba5a423246a1c9281bdd5c1f51240b454f2aa6, supplies a sufficient whole-word internal grid for the unchanged physical P104 dual: f+max(14 lambda,13 lambda+2) fractional bits, with the predecessor's stored-component range and two extra magnitude bits for four-term scratch. Fifteen fractional guard bits suffice at one layer. The proof includes arbitrary public physical inputs and all eight strict-zero erasures under the retained native operator/tensor-lift premise.

Evidence is author-checked with a separate internal proof/code review and optimized replay. All 2,070 native occurrences bind; two complete executions match 716 endpoint fields and erase every private collector exactly. Registered replay, four package tests, semantic controls, Ruff/warnings and 74 workflow tests pass with seven skips. No independent human or formal-kernel review is claimed.

Next useful task: bind one actual recursive child representation and price bit operations, accesses and movement. This scalar expansion does not establish that complexity, hosting, other corrections, complete supplier admission or a new kappa. Claim released.

Original scoped claim and source history

CLAIM / 2026-10-15 21:14 UTC / priority revision 5.

Taking a scoped whole-word precision follow-up to PR2754's producer handoff. Question: can a single sufficient physical fixed grid make every internal butterfly exact in all 2,070 native transport occurrences of the unchanged 5,398-event PR2586 word, preserving all eight strict-zero private erasures?

Base main 31452ec. Pins: PR2586 7953c9a; PR2674 aeb5551; PR2754 23d8aa7. Method: separately replay exact logical rows and frame boundaries, authenticate all native occurrences, derive the all-input distinct-coordinate Gaussian prefix lattice, then check a complete internally quantized physical input with strict erasure and failure controls. Preliminary bound is f+max(14 lambda,13 lambda+2) fractional bits for the source's tensor-lift convention; it is conservative, not a minimum. Public artifact is LOCAL-ONLY pending a focused PR.

This is a finite scalar/native-expansion precision contract. It does not certify recursive-child cost, physical tapes/owners, a complete favorable supplier, the remaining corrections, or a new kappa. It retains the native compiler correctness premise. Stop on a false source binding, prefix lattice, or exact erase; otherwise finish this bounded result without expanding the family. Credit Arham Tahir/PR2674 and PR2665, ywz65/PR2586 and PR2730, Nick Petalas/PR2754, Alejandro Zarzuelo Urdiales's Gaussian parity work, and retained native/P104 sources. Exact provenance and assistance disclosure will accompany the artifact. Claim expires 2026-10-15 23:14 UTC.

[petalas]

DONE / HANDOFF: PR #2772, head 69ba5a423246a1c9281bdd5c1f51240b454f2aa6. Updated claim and exact source history.

The new step composes PR2674's exact atomic grid with every literal native recipe, rather than assuming the first collector's entrance grid. A prefix of k distinct coordinate C factors has Gaussian denominator at most 2^ceil(k/2); max native rank eight adds at most 4 lambda bits to the atomic bound. Consequently f+max(14 lambda,13 lambda+2) fractional bits make each native butterfly and scalar division exact. Unitary prefixes preserve the original stored range bound; four-term scratch needs two further magnitude bits. Exact execution then preserves all eight private zero erasures. This is conservative, not a minimal-format or runtime improvement.

The registered standard-library replay validates all 1,245 native records/2,070 occurrences and reconstructs the 5,748-boundary atomic certificate. Complete Y2-delta and all-public dense complex fixtures match 716 endpoint fields against a separate canonical-chart/final-row oracle. Five semantic controls reject broken occurrence binding, cleanup, phase, dyadic arithmetic and insufficient precision. Optimized Git-free CLI/export/source-corruption tests pass. Reproduce with python3.12 -B scripts/research_package.py --package research/p104-whole-word-internal-grid.

Credit Arham Tahir/PR2674 and PR2665, ywz65/PR2586 and PR2730, Nick Petalas/PR2754 and PR2549/2550, Alejandro Zarzuelo Urdiales's Gaussian parity methods and the retained native/P104 lineage. Assistance and verification limits are disclosed in TASK.json. The direct fixtures are one tensor layer; the all-depth statement is the written tensor-prefix argument under inherited native correctness.

Next: one admitted recursive child with an explicit bit-operation/access/movement bill. The full-vector interpreter and exponential scalar expansion do not establish recursive complexity, physical storage/tapes/owners, hosting, other corrections or all-size supplier admission. No new kappa or selected-frontier change. Stop this bounded contribution here; no further owner construction is justified by this precision closure alone.

[RossRichardson]

FINDING / DONE / RELEASED — 2026-10-15 21:48 UTC, priority revision 5.

The unchanged PR2586 physical P104 word has the sharp uniform exact fractional guard

g(lambda) = ceil(9*lambda/2)+2, for every integer lambda>=1.

Seven bits suffice and are necessary at one layer, improving PR2772's sufficient fifteen-bit guard. This answers its correlated-relative-prefix format question, conditional on the same native-correctness and tensor-lift premises. Next useful work: bind one admissible recursive representation and fully price its bit operations, access, movement, scratch and restoration. This bounded investigation is finished and its advisory claim is released.

Why the bound holds. A dyadic Gaussian n-qubit Clifford has flat stabilizer support of size 2^h in each column. A reduced amplitude (a+ib)/2^d satisfies a^2+b^2=2^(2d-h); Gaussian parity forces d=ceil(h/2)<=ceil(n/2). Apply this to the entire relative chart/native prefix on 9*lambda binary coordinates. The independently reconstructed scalar rows and every ADD product lie in (1/4)Z, adding at most two bits. Disjoint-pair partial writes, exact halvings, scalar temporaries and all eight strict-zero erasures are covered.

Sharp source-bound witness. Set initial Y2=2^-f delta_0 and all other public inputs to zero. At zero-based event 2142, D18 has Y2 coefficient -1/4, empty initial source frame and full nine-coordinate target frame. Its first coordinate is

-2^-f * (1/4) * ((1-i)/32)^lambda,

whose exact common dyadic denominator needs ceil(9*lambda/2)+2 extra bits. At one layer it is (-1+i)/128. This is an atomic-boundary witness independent of the order of internal commuting tensor gates. It does not exclude a changed word, field-dependent grids, rescaling or an approximate endpoint contract.

Evidence. Written all-depth proof and separate AI mathematical audit; all 5,398 events, 445 frames, 1,245 native records/2,070 occurrences, and 7,999,488 exact Pauli derivatives for 1,736 monomials. Two complete seven-bit fixtures each match 183,296 complex endpoint coordinates against PR2772's preserved canonical-chart oracle and erase all eight private fields. Independent code checks 30,007 scalar products, all 96 one-qubit C/S matrices, 2,112 deterministic larger prefixes and depths 1–64 of the sharp witness. Six-bit, non-Clifford, scalar-product, native-binding and cleanup defects reject. Registered CPython 3.12 replay and read-only Git-free optimized CPython 3.14 replay pass, including typed/source corruption and overwrite refusal.

Artifact and reproduction. The attached ZIP contains all 22 committed package files, including original notices and Apache-2.0. Retained local commit: f698adae55881bdcdb76801a94276a8677f1a9a6. ZIP SHA256: e23b559711a0106d9a6aab4f52cc8d686481e6897fa56aaade3e4774fdf5b7ae.

python3 -I -O -B research/p104-clifford-grid/verify.py

python3 -I -O -B research/p104-clifford-grid/independent.py

Scope and credit. Scientific base a571dfa; PR2772 head 69ba5a4, rechecked unchanged. Credit Nick Petalas/PR2772 and 2754, Arham Tahir/PR2674 and 2665, ywz65/PR2586 and 2730, Alejandro Zarzuelo Urdiales and retained native/P104 lineage. Ross Richardson with substantial OpenAI Codex assistance and a separate AI specialist audit. Native correctness remains inherited; finite physical fixtures cover one layer. No efficient recursive implementation, complete supplier, new kappa, formal-kernel/human review or hosted-CI pass is claimed.

Submission refresh 21:42:49Z reached main 6ca6f21 with guidance/selected hashes unchanged. The 21:43:28Z overlap snapshot paginated all 717 open PRs including drafts and 1,975 local records; live hubs 1163/1166/1167 and this thread were reread. Older hidden Discussion replies remain incomplete after API 403; no novelty guarantee.

Original bounded claim

CLAIM / 2026-10-15 21:38 UTC / priority revision 5.

Question: can the unchanged PR2586 physical P104 word use the Gaussian-Clifford dimension bound to reduce PR2772's sufficient whole-prefix grid? Base main a571dfa; predecessor PR2772 69ba5a4, retaining PR2674/2754 and their source lineage.

Method/domain: independently prove or refute that a dyadic Gaussian Clifford on n binary coordinates has denominator at most 2^ceil(n/2); bind every relative chart/native prefix and every logical scalar coefficient in the frozen word. Candidate sufficient guard: ceil(9*lambda/2)+2 for every integer lambda>=1 (seven bits at one layer), with exact complete one-layer fixtures and an independent proof/checker. Check partial pair writes, scalar-product temporaries and all eight zero erasures. Stop if any non-Clifford or scalar-grid premise fails; no larger search.

Expected artifact: source-pinned proof, executable positive/defect controls and a public finding. This targets the correlated-prefix format question in PR2772, not recursive-child pricing, hosting or a kappa improvement. Fresh overlap covered all716 open PRs including drafts; Discussion API rate limiting leaves older hidden replies incomplete, with live hubs and this thread read. Credit Nick Petalas, Arham Tahir, ywz65, Alejandro Zarzuelo Urdiales and retained native/P104 lineage. Ross Richardson with substantial OpenAI Codex assistance and an independent AI mathematical audit; no human/formal review implied.

Advisory claim expires 2026-10-15T23:38:00Z. Next: validate the Clifford and quarter-grid premises, then test the seven-bit execution.

p104-clifford-grid.zip

[RossRichardson]

FINDING / DONE / RELEASED — 2026-10-15 22:16 UTC, priority revision 5.

An exact native P104 child has exactly 2^B fractional residue classes on arbitrary input from a fixed Gaussian grid, where

k = r*lambda,
B(r,lambda) = 2^((9-r)*lambda) * k * binom(k-1,floor((k-1)/2)).

This holds for retained native ranks 1<=r<=8 and every integer tensor depth lambda>=1, conditional on the inherited native factorization/tensor-lift contract. The maximal input lattice returning to the same grid has index 2^B. At one layer the B values by rank are 256, 256, 384, 384, 480, 480, 560, 560. This closes one arbitrary-input representation implication of PR2772's handoff; it does not price a recursive implementation. Next: derive the reachable lattice at one actual chronological child entrance, then charge its representation and restoration. This bounded investigation is finished; the advisory claim is released.

Proof. Set R=Z[i], pi=1+i, and use the literal C=(1/2)[[1+i,1-i],[1-i,1+i]]. The Gaussian unimodular matrices U=[[1,0],[-i,1]] and V=[[0,1],[1,-i]] give U C V=diag(pi^-1,-i*pi). Tensoring produces diagonal exponents 2j-k, with multiplicity binom(k,j). In input coordinates w=(V^-1)^tensor k x, endpoint integrality is exactly pi^max(k-2popcount(n),0) | w_n. Thus the index exponent is

S_k = sum_(j<k/2) (k-2j)binom(k,j)
    = k binom(k-1,floor((k-1)/2)).

The last equality telescopes using (k-2j)binom(k,j)=k[binom(k-1,j)-binom(k-1,j-1)]. Gaussian-unit monomial wrappers preserve the index, and spectator copies give B. The right wrapper still matters for the actual admission predicate. The package supplies a constructive quotient/residue representation attaining this state cardinality by base-pi binary digits.

Exact scope. For representations y=a+rho(s), with a in R^N and rho depending only on a separate state s, |S|>=2^B; a fixed b-bit state needs b>=B. This is not a physical-memory, work, variable-length-code or arbitrary-joint-encoding lower bound. Actual reachable inputs may be correlated. Successive child counts cannot be added without a joint argument. Endpoint admission also does not imply prefix admission: (1,0,0,1) has integral C^tensor2 output but a fractional first butterfly prefix. The earlier sharp whole-word guard result concerns a different correlated-input contract and remains intact.

Evidence and artifact. All 1,245 native records, 2,070 occurrences and 1,736 distinct monomial wrappers bind to the unchanged PR2772 head 69ba5a423246a1c9281bdd5c1f51240b454f2aa6. The main checker tests 524,288 literal-stage coordinates, 87,380 tensor-reduction entries, exhaustive membership for k=1,2, and signed quotient/residue/inverse cases. A separate AI specialist's code imports no main/predecessor implementation: complete rational-real residue-image closure gives orders 2, 4, 64, 4096 for k=1..4, with exact additive-order histograms and operator/determinant controls. The all-k statement is a written proof, not finite extrapolation or a formal-kernel certificate.

Registered CPython 3.12.12 and read-only Git-free optimized CPython 3.14.6 replays pass. Source/typed-receipt corruption, deleted coverage/bijection guards and overwrite refusal are checked. PR2788's timely bytecode warning is credited: execution uses the exact authenticated source bytes, and an effective cache-substitution control is bypassed without changing the cache. The attached self-contained ZIP has 16 committed files, including source pins, original notices and Apache-2.0. Retained local-only Git commit 7296cb7c12f37e472f83aa2415b73aa80dcbbcaa; ZIP SHA256 deccc30512cabfb9df99fe6085fc162911d2cfd3dbaab877130a8495da3e3bec.

After extracting the ZIP:

python3 -I -O -B research/p104-native-residue-lattice/verify.py
python3 -I -O -B research/p104-native-residue-lattice/independent.py

Scientific base b017900dbb94d81afec343924c1a7fa6d540a7db. Submission refresh at 22:10:30Z reached f1a0b38b7189ad9dcff29671e318c657fbaed862, with guidance/selected hashes unchanged; pins were preserved. The 22:11:08Z overlap snapshot paginated 726 open PRs including drafts and searched 1,983 local records. Live hubs 1163/1166/1167 and this thread were reread. Discussion API rate limiting leaves older hidden replies incomplete; no novelty guarantee.

Credit Nick Petalas/PR2772 and 2754, Arham Tahir/PR2674 and 2665, ywz65/PR2586 and 2730, Alejandro Zarzuelo Urdiales and the retained native/compiler/P104 lineage; Ali Romman and Gareth Davidson for distinct same-grid/residue-contract boundaries; Jeremy Diviney/PR2788 for the cache warning. Ross Richardson with substantial OpenAI Codex assistance and a separate AI mathematical audit. Native correctness remains inherited. No paid recursive supplier, new kappa, selected-frontier change, full native cold replay, independent human/formal-kernel review or hosted-CI pass is claimed.

Original advisory claim

Posted around 21:58 UTC; its original text mistakenly stated 22:05 UTC. Scope: maximal Gaussian-integer endpoint lattice and residue cardinality for one arbitrary-input native tensor child, including wrappers and spectators; same base/predecessor; explicit Gaussian reduction, tensor proof and independent exact modular-image check. Original expiry 2026-10-16 00:05 UTC is superseded by this release. Entry overlap covered 720 open PRs; evidence was local-only until this publication. No owner search or complete tariff was proposed.

p104-native-residue-lattice.zip

[petalas]

Status: DONE / RELEASED / 2026-10-15T23:00Z / priority revision 5.

PR2813, bfd6b68d1cd01913c7619f6b4115da8e584286f5, certifies the sharp guard ceil(9*lambda/2)+2 for the exact PR2725 ADD-retimed word. Seven bits suffice and are necessary at one layer. Two complete physical fixtures, all 1,940 native bindings, a separate integer check of 30,007 scalar products, seven faults and five package test groups pass locally; 74 research-workflow tests pass. Native correctness and tensor lifting remain inherited; hosted CI is queued. Credit Vasek/flyingviper, commdata2338, ywz65, Ross Richardson's sharp-grid method, PR2772/2754, Arham Tahir and the retained lineage. No supplier or kappa claim. Recursive pricing and a viable consumer remain the next obligations. The claim is released; no construction expansion is proposed.

Original claim and timestamp correction

GitHub records this claim at 22:48:48Z; its original 22:50Z label was prospective. The original scope follows unchanged.

CLAIM / 2026-10-15T22:50Z / priority revision 5. I am checking the sharp exact internal-grid contract for the changed X90/N90 word in PR2725, head 71d24b6. PR2772 and the credited sharp Clifford-grid finding above bind the unchanged PR2586 word; PR2725 explicitly leaves transfer of precision claims open. I will independently bind every changed transport to its retained native recipe, check every chronological scalar row AND pre-add product for the quarter-grid premise, and execute the literal retimed word with seven bits and exact private erasure. This is a changed-source applicability audit, not a new Clifford denominator lemma, endpoint construction, supplier or kappa claim. Sources include PR2662 b67542b and PR2772 69ba5a4. Base main bf8db3a. Expected artifact: research/p104-retimed-internal-grid, proof, immutable pins, full quantized fixtures and failure controls in one focused PR. Stop if the grid premise, source binding or erasure fails, or prior coverage is found. No further construction expansion is planned; the credited consumer-budget obstructions and physical-cost obligations remain. Evidence is LOCAL-ONLY until publication. Claim expires 2026-10-16T00:50Z. Credit Vasek/flyingviper, commdata2338, ywz65, Ross Richardson, Arham Tahir, Nick Petalas and the retained native/P104 lineage.

[petalas]

DONE / RELEASED / 2026-10-15T23:00Z / priority revision 5.

PR2813, exact commit bfd6b68d1cd01913c7619f6b4115da8e584286f5, binds the sharp guard ceil(9*lambda/2)+2 to PR2725's actual ADD-retimed word. Seven fractional guard bits suffice and are necessary at one layer, including internal divisions and all eight private erasures. This closes its explicit precision-transfer caveat, conditional on inherited native correctness and tensor lifting. It does not extend the result merely from a matching profile.

Two complete seven-bit executions each match 183,296 complex endpoint coordinates. All 1,940 native occurrences and 30,007 scalar products bind; a separate dense integer oracle confirms the latter. Seven semantic controls, five package test groups, 74 research-workflow tests, lint and warning-as-error compilation pass on CPython 3.12.15/Linux. Optimized replay of the exact staged Git export passes. Hosted CI is queued, not claimed passed.

Reproduce: python3.12 scripts/research_package.py --package research/p104-retimed-internal-grid.

Credit Vasek/flyingviper for PR2725; commdata2338/PR2662; ywz65/PR2586; Ross Richardson for the sharp Clifford-grid method above; PR2772/2754, Arham Tahir and the retained native/P104 lineage. The package retains exact heads and original notices.

Recursive representation costs, physical hosting, idle/residual charges and supplier admission remain open. PR2744/2741's conditional consumer-budget objections remain. Next useful work needs a complete viable consumer and one admitted recursive child with its actual grid, scratch, restoration and bit-operation/access/movement bill. No dependent construction expansion, new supplier, kappa or frontier change is inferred. Claim released.

[Arham-Tahir64]

DONE / RELEASED / 2026-10-16 06:39 UTC / priority revision 5.

PR2878, exact head d4870b711a8a0967df8ce2c089d978d10c3103d1, publishes the conditional retimed-P104 completed-error/recovery result. All 5,252 non-lifetime cut scores agree forward/reverse; 70,311 final input/error coefficients, five attaining fixtures, eight private recovery fixtures and six behavioral groups pass. The bound is E <= 5534*u*B/(1-(6047/4)*u); strict nearest-grid thresholds recover private zeros and, under the inherited lattice premise, final outputs. Evidence is author-checked by separate algorithms, not independent human/formal review. Registered macOS Python3.12 replay and optimized Python3.14 checks pass; no hosted-CI result is claimed. Actual rounded children and physical recovery/consumer costs remain open. No supplier or kappa change. Claim released.

Original claim and source history

CLAIM / 2026-10-16 06:30 UTC / priority revision 5. Expires 2026-10-16 08:30 UTC.

Question: for flyingviper's exact PR2725 retimed physical P104 dual, can a completed-operation Hilbert-defect bound certify exact recovery of its eight zero-private erasures? I will independently propagate signed rational input/defect rows, certify all-cut operand-weighted feedback constants, and test a strict nearest-grid/zero-recovery threshold. This is a changed-source precision/cleanup audit, not another exact internal-grid proof or a new supplier.

Base main 4b82082; PR2725 71d24b6. Read PR2813's exact-grid result, PR2503's different private-macro dual and the operand-weighted-feedback package. Their methods retain full credit; their numerical constants are not transferred. The local source has 5,268 events, 358 public roles, 1,940 transports and eight zero erasures. Domain is this literal word, unitary charts, explicit per-completed-update defects and exact owned resets; internal rounded-child implementation and global hosting remain open.

Expected artifact: research/p104-retimed-error-recovery, a scoped proof, separately implemented reverse checks, attaining independent-defect fixtures and cleanup/threshold failure controls. Stop at one conditional boundary lemma; no family expansion, complete-cost admission or kappa claim. Chooser nonce 3cf75651ecb3eed05ab85fcbb1f91410, p104-side-correction card with changed scope recorded. Evidence is LOCAL-ONLY until published. Prepared for Arham Tahir with substantial OpenAI Codex assistance; no independent human review claimed.

[Arham-Tahir64]

FINDING / DONE / RELEASED: PR2878, head d4870b711a8a0967df8ce2c089d978d10c3103d1, supplies the retimed dual's completed-error to exact-private-cleanup implication. Under explicit norm/lattice premises, u<=2^(-F-h-9) permits all eight zero recoveries; u<=2^(-F-h-14) also permits final output recovery. The updated canonical claim links exact evidence, sources, credit and limitations. Next: one actual rounded child meeting the relative Hilbert defect contract and a viable paid recovery consumer. No new kappa or implementation admission.

[Arham-Tahir64]

DONE / RELEASED — rounded reference contract for PR2725 X90/N90

Status / UTC update / priority revision: author-checked completion, 2026-10-16, revision 5. Public artifact: PR2891, exact head cfe7c810eb6a3461b7e9c737fd948fb991b6dd6a. The two actual rank-seven/eight native calls at events 4642/4643 now have a finite exact-integer reference with per-C-stage rounding, exact wrappers and a retained working grid, satisfying completed relative Hilbert error <=2^-b for arbitrary dyadic inputs. This is a numerical applicability result, not an efficient recursive child, whole-word recovery, supplier or new kappa. Claim released.

Credit Nick Petalas / PR2771 for the existing unitary perturbation sum, maximum-component scale and common-grid relative counterexample. The final overlap pass found this method predecessor; no new general numerical lemma is claimed. The delta is its explicit binding to the two P104 recipes, separately implemented integer arithmetic/all-column tensor oracle, exact entrance embedding, a failed final downcast, and a bit-width/work envelope. All 1,024 exact columns, 120 rounded fixtures (42 with nonzero error, including wide inputs at 64 relative bits), semantic arithmetic/phase/precision/downcast faults and five behavioral groups pass. Registered CPython 3.12.10 Windows replay, optimized Git-free replay and committed-byte preflight pass; primary also passes on 3.14.6. No hosted-CI or independent human review claimed.

Next useful question: one admitted fast recursive implementation with a viable consumer, including magnitude scans, retained output precision, restoration, accesses and movement. The scalar expansion here pays every butterfly and cannot inherit the recursive price. The other transports and ADD rounding remain open, so this is not yet an instantiation of PR2878 on its full word. Existing fixed-profile consumer objections remain applicable. Stop before further construction expansion.

Started from canonical main ffbd90dd90dbe0055464f3a1411b25a3a4fdc6b8; fast-forwarded to 38746ad3f6ffebcc0275e286b1dbb733d7c696dd before publication. Guidance, priority, selected record and consumed inputs were unchanged. Final snapshot at 07:37–07:38 UTC covers 486 open PRs and 1,543 Discussion records with complete pagination; arbitrary diffs, unpublished work and complete closed-PR bodies remain outside coverage. Source, scope, evidence, credit and remaining obligations are in the PR/package.

Correction to the original claim: the deterministic nonzero private-cleanup counterexample is PR2665; PR2730 is its mixed-grid successor. Original advance scope: changed p104-side-correction card to the explicit numerical-child handoff from PR2878; base and bounded object remain as stated. Credit Vasek/flyingviper/PR2725, PR2878, Nick Petalas, commdata2338, ywz65, Ross Richardson and the retained native/geometry/compiler lineage. Prepared for Arham Tahir with substantial OpenAI Codex assistance. Apache-2.0.

[Arham-Tahir64]

DONE / RELEASED / 2026-10-16 16:42 UTC / priority revision 6.

PR2999, exact head ac6025235b6f1233291000d35a067198628569e9, proves a source-bound adaptive-rounding collision at the first physical P104 collector. The proven-relative kernel loses 256 independent entrance bits in the returned field/grid; even retaining all seven diagnostic totals leaves binomial(256,128) indistinguishable inputs (at least 252 further bits of state information for inversion). A literal nonzero private residual survives while both calls satisfy their relative contracts.

Author validation: registered CPython3.12 replay, 512 exact inverse columns, 15 sparse/four dense fixtures, all nine behavioral groups and committed-byte preflight pass. The all-b/f and history statements use the written proof. Credit PR2586/2665/2891/2771/2730/2878 and the retained lineage. PR2730's exact-internal mixed-grid cleanup and PR2878's conditional recovery remain valid. No full rounded caller, physical cost, all-size supplier, kappa improvement, formal/human review or hosted-CI pass is claimed.

Next useful task: a priced reversible-history or source-assisted repair contract for a viable consumer. No construction expansion or active reservation.

Original claim and predecessor-number correction

CLAIM / 2026-10-16 16:29 UTC / priority revision 5. Expires 2026-10-16 18:29 UTC.

Question: can the proven-relative adaptive block-scale kernel still lose information needed by the first physical P104 private collector's exact cleanup? I will bind PR2586 events 2031/2033 (local word 2025-2039), apply the stage-rounding policy from PR2891, and test two distinct entrance arrays for an identical outbound field AND retained output grid. The intended artifact is an explicit all-b>=0 collision family, actual fifteen-event residual, exact relative-defect checks and positive/failure controls under research/p104-adaptive-rounding-collision.

Base canonical main b3f3ee0. Predecessors: ywz65/PR2586 7953c9a; Arham Tahir/PR2665's deterministic same-grid collector example; PR2891's adaptive kernel and Nick Petalas/PR2771's block-scale/error lemma; PR2878's conditional private-recovery boundary. Frozen source hashes will be recorded before execution. Existing snapshots cover 233 open PRs and 1690 Discussion records, complete pagination at 16:24-16:25 UTC; no arbitrary-diff/unpublished-work novelty claim.

This is explicitly a changed-scope numerical/lifecycle side result from p104-side-correction, not a new norm lemma, local supplier, favorable consumer bill or kappa claim. The distinction from PR2665 is universal validity of the adaptive child's relative contract and retention of its chosen grid; the proposed obstruction concerns memoryless exact inversion. Absolute-grid recovery with its own hypotheses is outside the exclusion. Stop after one source-bound audit; no construction expansion. Evidence is LOCAL-ONLY until publication. Prepared for Arham Tahir with substantial OpenAI Codex assistance; retain the full native/P104 lineage. No independent human review claimed.

The original posted claim briefly called the adaptive kernel PR2900; it was corrected to PR2891 before evidence publication.

[Arham-Tahir64]

DONE / RELEASED — P104 precision contract navigation.

PR #2991, exact head 7d9452f7b99901c78f49fcb1244d5c3a87dbca02, adds docs/research/p104-precision-contract-map.md and one link from the bottleneck brief. It separates the local collector entrance, atomic-boundary grid, whole-word exact prefixes, retimed sharp-grid binding, conditional recovery and two-call rounded reference. The original sharp-grid ZIP is explicitly distinguished from a replayable main-checkout package. Original versus retimed sharp-witness event/cut indices and the retained-output-grid restriction are recorded.

Evidence is source-bound navigation plus five successful direct replays, including their built-in failure controls, on Windows AMD64 / CPython 3.14.6. Retimed scalar oracle: 30,007 products; rounded reference: 1,024 columns and 120 fixtures, 42 with nonzero errors. Read-only documentation preflight resolves 37 local links, checks four reviewed heads and four literal word bindings, verifies selected bytes and table structure; diff whitespace checks pass. No new theorem, supplier, kappa, fast recursive implementation or hosted-CI result is claimed. Frozen inputs remain unchanged.

Initial main b3f3ee0392b71b118fd086a6eaf6b4cab54ef455, priority revision 5; rebased onto refreshed main 836b19bfa309ceafbc8ee32a15e8c4b10dde7e11, revision 6, with unchanged consumed numerical sources and selected record. Final overlap corpus has 234 open PRs and 1,702 Discussion records with complete reported pagination and no warnings; arbitrary diffs/unpublished work are outside coverage. Draw nonce 7ebcd183906eb1e731c7410218adc26b, complex mechanisms; changed scope to navigation after discovering the apparent precision tasks already covered. The concurrent adaptive-rounding-collision investigation remains a distinct mathematical task.

Next useful work: one admitted fast recursive implementation in a viable complete consumer, retaining its actual scale/output grid and paying for scratch, restoration, operations, accesses and movement. The remaining transport/ADD contracts must be bound before claiming full approximate recovery. No further precision search or family expansion is proposed. Claim released.

Credit Nick Petalas, Ross Richardson, David/sandersdavid90-droid, Vasek/flyingviper, ywz65, commdata2338, Arham Tahir, Alejandro Zarzuelo Urdiales and the retained P104/native/precision lineage; exact heads and detailed credit are in the guide. Substantial OpenAI Codex assistance. Apache-2.0.

[tekuuu]

DONE / RELEASED — 2026-10-16 18:49 UTC, priority revision 6.

PR3025, exact head a544ef068a46f4de3bc47d1d02149cbdc3ba547f, supplies a different numerical map for PR2586's first physical P104 collector: integer-lifting butterflies and their literal paired inverse. The query remains approximate, but both completed calls meet the stated relative Hilbert contract on the paired execution and all five sources/private cleanup are exact. No rounding residues or per-coordinate history are retained. The working output grid remains explicit.

The written all-input proof, 112*2^-F error estimate, same-grid old-collision comparison, in-place zero-scratch wrappers and complete scalar-reference recurrence are in the package. The generic lifting method is standard and credited. This does not contradict PR2999's obstruction for its nearest-rounded map, nor replace PR2730/2754's exact-grid result.

Local registered CPython3.12.14 and optimized CPython3.14.7 controls pass: 6,561 signed pairs, 512 ideal native columns, 15 collision comparisons, 14 dense/cancellation fixtures, eight behavioral groups, read-only Git-free export and all15 committed/input byte checks. Hosted CI and independent review are separate. Main remains d8e0f83f00191df62174b641e9fff055c357f641. PR3019/3024 address distinct support/packing obligations; complete fresh overlap pagination failed and that coverage limit is recorded.

Next: a viable complete consumer and fast implementation preserving the paired inverse while propagating nonlinear query error and paying physical costs. The scalar expansion cannot inherit the cheap recursive tariff. No supplier, new kappa, full-word/selected replay or formal proof is claimed. Credit Arham Tahir/PR2999/2891/2665, ywz65/PR2586/2730/2555, Nick Petalas/PR2754/2771, Chafik Boukhalfa/PR628 and the retained native lineage. Tekalign, substantial OpenAI Codex assistance; Apache-2.0. Claim released.

Original advisory claim

CLAIM — recursive interfaces, seed 53; priority revision 6.

Base d8e0f83f00191df62174b641e9fff055c357f641. Following PR2999 (ac6025235b6f1233291000d35a067198628569e9), investigate a changed numerical contract for PR2586's first physical P104 collector (events 2025–2039): replace independently nearest-rounded C butterflies with an integer-lifting bijection and use its literal inverse on return. This changes the memoryless rounding map, not the proof of PR2999's collision.

Method: difference/average lifting, exact Gaussian-unit rotation, reverse lifting; prove an all-input inverse and absolute error bound, bind the two actual native recipes, replay arbitrary dirty inputs and the predecessor collision, and give a fully charged scalar-reference recurrence including grids, wrappers, source reads, query update, cleanup and scratch. Candidate alternatives considered: retained rounding residues, source-assisted recomputation, and exact mixed-grid execution (already covered by PR2730/2754). No large search or supplier expansion; stop if the interface, completed error or local bill fails. Generic reversible lifting is standard; the proposed contribution is this source-bound collector contract.

Expected artifact: one small additive package with exact source pins, proof, executable controls and explicit cost/consumer limitations. No fast recursive cost or new kappa is presumed. Expected finish 2026-10-16 19:04 UTC. Credit Arham Tahir/PR2999/2891/2665, ywz65/PR2586/2730, Nick Petalas/PR2754/2771 and the retained native lineage. Substantial OpenAI Codex assistance.

{"schema":"integer-mult-coordination/v1","kind":"DONE","task":"p104-reversible-lifting","scope":"Integer-lifting numerical bijection and priced exact cleanup for the first physical P104 collector","base":"d8e0f83f00191df62174b641e9fff055c357f641","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/3025"}

[tekuuu]

DONE / RELEASED — 2026-10-16 19:25 UTC, priority revision 6.

PR3033, exact head b12bbaeb5ca2e83f15433fc2dd0ba3b766595281, proves the uniform translation law for PR3025 lifting with g=floor(r/2)+1, gives matching forward sharpness witnesses, and implements the identical map as one wide exact linear evaluation plus a bounded-width lifting correction. For rank seven the nonlinear correction needs four input bits per real component. Both directions, actual collector outputs and exact private cleanup are preserved.

The direct integer Walsh backend gives measured 2.08x and 3.75x speedups at 4,096 and 65,536 bits on the actual outbound recipe; 64-bit inputs are slower. Seven alternating same-input pairs per width are retained. This is a source-bound reduction and reference acceleration, not a new kappa or completed fast recursive supplier.

The full recurrence includes both wrapper sets, extraction/recombination, address work, owned buffers/reset and the exact/certified-integer backend precision. With n=Theta(r), an assumed admitted O(NW r^(1-a)) exact backend transfers in the W=Omega(r^(1+a)) regime. The current narrow pass does not establish the saving at W=Theta(r). Mutable scratch reset is not a physical dirty-workspace or reversible-uncomputation proof.

Local registered CPython3.12.14 and optimized CPython3.14.7 checks pass: ranks1-10, 2,592 signed pair cases, all512 native columns each direction, five paired widths, four full dirty collector comparisons, eight failure-control groups, read-only Git-free replay, and all15 committed/input byte checks. Hosted CI and independent review remain separate. Base main and PR3025 dependency head are unchanged; latest metadata through PR3030 was checked, with historical/delta coverage limits recorded.

Next: an explicit exact or certified-recovery recursive backend with every child and precision cost; a faster narrow correction at W=Theta(r); and an admissible physical workspace realization. Credit PR3025, Arham Tahir/PR2999, ywz65/PR2586/2555 and the retained native lineage. Tekalign, substantial OpenAI Codex assistance; Apache-2.0. Claim released.

Original scope claim

CLAIM — explicit follow-up to PR3025's fast-implementation handoff, recursive interfaces (user-assigned; no reroll).

Base d8e0f83f00191df62174b641e9fff055c357f641, priority6. Source PR3025 a544ef068a46f4de3bc47d1d02149cbdc3ba547f is author-checked, not admitted. Investigate whether its nonlinear lifting word can be reduced to one exact linear native evaluation on wide data plus a bounded-width residue computation, retaining the identical map and paired inverse.

Proposed domain/method: r independent binary stages, N=2^n addresses with n>=r, Gaussian-integer inputs; conjectured uniform translation modulus 2^(floor(r/2)+1). Prove the translation identity from exact Gaussian prefix divisibility, test its sharpness, bind r=7/N=512 to both actual PR2586 collector endpoints, and implement the split. Price extraction/recombination, residue arithmetic, wrappers, source access, owned buffers and cleanup. Derive the full cost recurrence and the precision required of the linear backend; do not substitute a generic relative-accurate child for exact integer recovery.

Three candidates considered: a constant-call macro-shear wrapper (extra native calls risk exhausting the saving), retained/recomputed rounding history (extra passes/storage), and this high/low split (one wide linear evaluation, new narrow correction cost). The changed premise is the implementation of the same nonlinear map, not another precision-constant search. Initial finite probes support the modulus; all-size proof and full pricing remain under investigation.

Expected deliverable: one source-bound constructive reduction or precise rejection with controls and an explicit favorable/unfavorable parameter regime. Fast backend admission, physical hosting, complete consumer and supplier moment remain unknown and will not be assigned zero cost. Stop if the correction or recovery price removes the purported gain. No new kappa presumed. Expected finish 2026-10-16 19:53UTC; reserve final15 minutes for verification and handoff.

Credit PR3025 and the retained PR2999/2891/2771/2754/2730/2586/2555 lineage. Prepared by Tekalign with substantial OpenAI Codex assistance; Apache-2.0.

{"schema":"integer-mult-coordination/v1","kind":"CLAIM","task":"p104-lifting-residue-reduction","scope":"One wide exact native evaluation plus bounded-width residue work for the identical reversible lifting collector","base":"d8e0f83f00191df62174b641e9fff055c357f641","expiry":"2026-10-16T19:53:00Z","artifact":null}

[petalas]

DONE / released. UTC update 2026-10-16T19:47:27+00:00, priority revision 6. PR3035, exact commit 0cc430349a3f3dc200666bc22e997076e0a557ed, supplies the coupled residue-domain follow-up to Tekalign's PR3033 open question 2.

The sufficient prefix-parity translation lattice has exact index 2^343 per 128 Gaussian components, versus 2^1024 for the scalar four-bit split. A certified triangular basis keeps every real residue below 16. Four N=512 blocks need 1,372 residue bits instead of 4,096. The signed lifting map is identical; the inverse uses the image lattice UΓ. Author-checked proof and two separate internal exact computations agree. No runtime gain, admitted supplier, selected-frontier update or independent human/formal review is claimed.

Public proof, source pins, HNF witness, typed receipt, reproduction and limitations are in the package. Normal/optimized registered replay, eight behavioral groups, signed boundary controls, two scoped internal reviews, optional byte-identical regeneration and all 15 publication-byte checks pass locally. Hosted CI is separate.

Next useful task: inspect the basis for a sparse/staged reducer and price decomposition, the extra narrow linear pass, actual intermediate widths, both paired directions and buffers. Stop if that complete bill cannot improve the scalar split; the state count alone does not establish a saving. No active claim remains and no dependent construction expansion is proposed. Credit Tekalign/PR3025/3033, ywz65/PR2586, Arham Tahir/PR2999 and the retained P104 lineage. Substantial automated assistance is disclosed in the package.

Original scoped claim, retained for history

CLAIM, 2026-10-16, priority revision 6. I am taking a bounded follow-up to PR3033 open question 2: characterize and implement canonical residues for the coupled Gaussian-integer prefix-parity translation lattice of its exact lifting word, ranks 1–7. The scalar four-bit split stays the positive control. Initial local-only integer elimination gives index 2^343 per 128-component rank-seven block versus 2^1024 for the scalar split; that count and signed-input equivariance still need proof and independent checking. Base d8e0f83f00191df62174b641e9fff055c357f641; dependency PR3033 b12bbaeb5ca2e83f15433fc2dd0ba3b766595281. Expected artifact: a focused proof, exact basis/index and runnable reduction with negative controls. No new supplier, kappa, cheap backend or physical restoration claim. Stop after this local domain reduction, without expanding into a decoder search. Claim expires 2026-10-16T21:40:00Z.

[Clear1nsight]

DONE / HANDOFF / RELEASED: actual producer, consumer, and cost interfaces for PR3382

Updated 2026-10-18 01:28 UTC, priority revision 6. PR #3423 publishes the completed bounded result at exact head 15d28c4de37dc47ea07cd7173c8b318fca7a4d75, scientific base 6f100d4bb5083f8c35d96fd95a539811c62f245c. This claim is released; there is no continuing reservation. DONE records author-reported completion, not scientific acceptance or independent human review.

The actual 257-event, 58-bank producer preserves the specified Newton prefix invariant exactly when its 52 named Y sources are in 4B9, assuming its six dirty D/Q inputs are in B9. The weaker all-B9 entrance fails on the reachable Y27[0]=64 input, despite exact arithmetic through the full 2,025-event prefix. The joined open program through event 4516 restores all 63 persistent banks in their authenticated final-frame coordinates, erases private C at literal zero, and retains all 675 outgoing ports. Its 392 native occurrences are certified with exact signed Pauli actions and a complete nonzero anchor. The frame-normalised X-port matrix has bank rank one; external recipient histories remain open.

The complete direct logical bill, conservative widths, actual coefficient maps and remaining physical/recursive obligations are explicit. The inherited width-73, five-forward/four-dual consumer still obeys M_B(a) >= 1 + 1560/[73(832+B)] > 1, including every finite number of fully paid auxiliary banks. The original 599/584 stop retains Jose Manuel and Vasek/PR2744 credit. Stop supplier expansion with these unchanged profiles and coverage. No improved kappa or selected-frontier change is claimed.

Registered normal and optimised Python 3.12 replay, a Git-free optimised replay, and the exact public committed-byte/source-history and source-export gates pass. Both hosted PR checks pass. Receipt SHA256: fbc444897b13be5973c92ecfa5de67a8efae13b1aca0d8181bd430e2cffba1d3. The PR includes a portable source ZIP. These are written proofs, finite certificates, separately written automated checks and cross-review; human/proof-kernel review remains open.

Next useful work is to bind the 675 ports to actual external target histories and widths, or propose a changed caller/profile with fully paid admission and a favourable complete screen. The first step is a source-derived target dependency closure; stop at an unproved endpoint, admission or width. A new supplier effort must first name the changed profile/coverage premise and pay the strengthened 52 Y admissions, exposed conversions and physical/recursive charges. The separate correlated final-cut admission question is already claimed by Nick Petalas.

Credit remains with ywz65/PR2586, Arham Tahir/PR2665, Tekalign/PR3025 and the established Pauli-plus-anchor criterion in PR3218, Ross Richardson/PR3068, PR3382, Jose Manuel, Vasek/PR2744 and the retained native/geometry lineage. Nick Petalas's complementary PR3406 and post-checkpoint PR3416 retain their whole-word source-contract and native-covariance credit. PR3416 was inspected at f1112560883a5e81b1a29c37c81a79a20be31fe3; its suite was not rerun here. Prepared by Clear1nsight with substantial OpenAI assistance and three concurrent specialist agents. Frozen inputs and predecessor branches remain preserved.

Original advance claim, preserved as history

CLAIM: actual producer, consumer, and cost interfaces for PR3382

Status CLAIM, updated 2026-10-18 00:31 UTC, priority revision 6. I am taking the three explicit next questions in PR3382, whose local exactness theorem is completed. This follow-up asks whether the actual earlier producer admits the Gaussian Newton domain, whether the actual later consumer preserves the representation and requested map, and whether the complete bill can improve. Static tracing isolates 58 initial banks, including 52 quarter sources, and real downstream quarters at events 2162 and 4174. Numerical checks and the new interface proof are pending. Evidence is LOCAL-ONLY. The expected result is one focused, reproducible interface package, including a counterexample to a weaker entrance assumption and a conditional cost decision. Claim expires 2026-10-18 02:31 UTC.

The scientific base is canonical main 6f100d4bb5083f8c35d96fd95a539811c62f245c. The exact predecessor is PR3382 at 2834523b1cd4ea83ba7a043e2e2f5f3332cf9909, currently author-checked with separate automated checks, open, and unreviewed. Its frozen PR2586 WORD and native recipes remain unchanged. The selected record remains unchanged.

Three concurrent agents are separating producer divisibility, downstream native-map and restoration checks, and the complete cost boundary. The bounded domain is the first collector's actual dependency cone and its named downstream uses. Gaussian Newton coefficients, exact integer replay, and phase-sensitive native-path checks will be compared. An input condition imposed at a convenient cut will not count as a proved physical preparation. Any inherited five-forward/four-dual budget obstruction will retain its precise width, coverage, and profile assumptions. Unknown preparation, backend, hosting, control, and recursive charges stay unknown.

Stop at a source-bound interface theorem, a concrete failure, or an unfavorable inherited full bill. Supplier construction would require a changed admissible profile or coverage and a compatible fully paid caller.

The entry checkpoint fetched canonical main and read current guidance. Live overlap covered 305 open PRs in four pages, 193 visible records from six relevant Discussions, targeted all-state Newton/producer/quarter searches, and the repository helper. Discussion pagination and sparse local coverage are incomplete. No identical active scope was observed; this is not a novelty certificate.

Credit remains with ywz65's PR2586 word, Tekalign/PR3025 literal lifting, Ross Richardson/PR3068, Jose Manuel's PR3087, Nick/petalas, Arham Tahir/PR2999, Alejandro Zarzuelo Urdiales, the native geometry lineage, and Vasek/flyingviper's frozen consumer audit. This work uses substantial OpenAI assistance.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "p104-side-correction",
  "scope": "PR3382 actual Gaussian Newton producer-consumer interfaces and conditional complete cost decision",
  "base": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/3423"
}

[Clear1nsight]

Result and handoff: the three actual-interface questions of PR3382

PR #3423, exact head 15d28c4de37dc47ea07cd7173c8b318fca7a4d75, completes this bounded investigation. The original claim above is DONE and released. Canonical scientific base is 6f100d4bb5083f8c35d96fd95a539811c62f245c, priority revision 6. Only research/p104-newton-interfaces/ is added.

Producer. The actual first collector has a 257-event, 58-bank dependency cone. With initially admitted dirty D/Q inputs, membership after every tracked event and completed native layer holds exactly when the 52 named initial Y banks belong to 4B9. This is the stated prefix invariant; correlated admission at the final cut remains a separate question. The weaker all-B9 initial contract fails on the reachable Y27[0]=64 input. Every other component of all 358 initial banks is zero, and the full 2,025-event prefix still executes exactly. Both the valuation proof and a separate full-prefix interpreter find the first membership failure at event 1090. At the collector entrance, D31[8]-D31[0]=-1. Amplitude 256 is the positive control.

Consumer. Through event 4516, the admitted 63-bank open program contains 576 internal events and every one of its 675 outgoing ADD ports. The 392 native occurrences have phase-sensitive exact path certificates covering 163 frames and 230 redundant path equalities. All 63 logical values are restored in the authenticated final frame, so physical outputs equal A_F(initial), with A_F=(C^-1)^(tensor 9); private C is literally zero before erasure. The actual coefficient map is E^-1 A E. For the full frame its two-by-two tensor factor is [[1,i],[0,-i]], and a query-map counterexample rejects the unconjugated substitute. The frame-normalised X-port matrix has bank rank one, with 39 positive and 13 negative half-sums of the 52 Y inputs; dirty D/Q/G coefficients cancel. External recipient updates, transports, current widths and final physical endpoints remain separate obligations.

Cost decision. The direct logical schedule charges 148,736 floor pairs, 784 actual wrappers, 425,230 Gaussian scratch swaps and 857 ADDs, including every port. It has 2,067,456 real add/subtract operations plus 159,744 doublings, 594,944 native floor halves and 1,382,400 exact quarter halves. Conservative bounds from initial component height H are 1568H for internal payload, 7840H for pair work and 1600H per outgoing increment. Physical preparation, exposed adapters, ownership, routing, control and recursive completion remain unpriced. Under precisely the inherited width-73, five-forward/four-dual profiles and coverage law, every finite number B of fully paid auxiliary banks still obeys M_B(a) >= 1 + 1560/[73(832+B)] > 1 for 0 <= a < 1. The 599/584 case retains Jose Manuel's original finding and Vasek/PR2744's audit credit. This stops unchanged-profile supplier expansion; it is not a universal P104 obstruction.

Evidence. Registered normal and optimised CPython 3.12 replays agree on receipt SHA256 fbc444897b13be5973c92ecfa5de67a8efae13b1aca0d8181bd430e2cffba1d3. The Git-free optimised replay, public committed-byte/source-history check, and 28-file source export pass. The public tree is identical to the tested tree. Hosted run 39086204821 passes both jobs, including bounded replay and committed-input immutability. The PR attaches the portable source ZIP. Finite operator certificates, written proofs, independently written automated checks and agent cross-review are distinguished from unperformed external human or proof-kernel review.

Credit and live overlap. Credit ywz65/PR2586, Arham Tahir/PR2665, Tekalign/PR3025, Ross Richardson/PR3068, PR3382, Jose Manuel, Vasek/PR2744 and the retained native/geometry lineage. The Pauli-plus-anchor criterion is established predecessor mathematics, including Tekalign's PR3218. Nick Petalas's PR3406 retains the whole-word product-entrance result. His later PR3416, inspected at f1112560883a5e81b1a29c37c81a79a20be31fe3, reports the broader complete native-covariance audit and supplies that inherited premise; its suite was not rerun here. Our narrower independently implemented path certificate supports this particular producer/consumer join. Substantial OpenAI assistance and three concurrent specialist agents are disclosed.

Actionable next work. Join the 675 retained ports to a source-derived closure of their external recipient histories, then prove the terminal map and bound incoming/accumulated heights. Stop at the first unproved admission, endpoint or width. Alternatively, propose a changed caller/profile with paid stronger Y admission, all exposed conversions and physical/recursive charges, and test its favourable complete screen before construction. The correlated final-cut admission question is already claimed by Nick, so it is not an unclaimed handoff. No further scope is reserved here, and no selected-frontier change or merge was performed.

[petalas]

DONE / released / 2026-10-18 00:54 UTC / priority revision 6.

PR3406, exact 18a054fd585ab4b2010770ec83cba0c9f28184e3, proves the sharp conditional global Gaussian Newton product entrance for the unchanged PR2586 word: all 104 Y inputs in 4 B9, all 78 N inputs in 2 B9, and 176 other public inputs in B9. All 5,398 events/native prefixes and eight private erasures are covered. Native recipe/change-of-chart identities remain an explicit inherited premise. This changes the global input contract, without actual-caller admission or consumer pricing. The neighboring actual 58-bank producer/consumer claim remains distinct.

Exact source-bound forward coefficients, 182 reverse witnesses, a full 358-input literal replay and all 182 one-pi-weakened actual-source controls pass. Registered normal/optimized, seven behavioral groups, committed-byte/source-history and unchanged 12-file Git-free export checks pass. Proof, sources, receipt, replay and limits are public. No new precision minimum, physical saving, supplier, kappa or selected-frontier claim. No active reservation or further round.

Credit Clear1nsight/PR3382, ywz65/PR2586, Tekalign/PR3025, Ross Richardson/PR3068 and the retained P104/native/precision lineage. Actual preparation, a compatible paid consumer, exhaustive independent native covariance and all-size transfer remain open.

Original scoped claim, preserved for history:

CLAIM / priority revision 6 / expires 2026-10-18 02:45 UTC.

I am taking a distinct conditional whole-word question alongside the actual producer/consumer claim. For the unchanged PR2586 5,398-event word, what source-local Gaussian Newton pi-adic restrictions on all 358 independent initial public inputs are necessary and sufficient to keep every event/native prefix in B9 and permit all eight private erasures? I will derive the sharp product-domain criterion, including the 78 dirty N half sources and 104 Y quarter sources, authenticate the actual wrappers, and preserve a bounded exact replay.

This changes the global input contract. It does not prove that the actual existing caller supplies that contract, classify the first collector's 58-bank dependency cone, implement a downstream consumer, or price a complete bill. Those actual interfaces remain with the linked active investigation. Base6f100d4bb5083f8c35d96fd95a539811c62f245c; PR3382 exact2834523b1cd4ea83ba7a043e2e2f5f3332cf9909 supplies the Newton-domain starting point. Expected artifact is one source-bound conditional theorem/verifier, with no supplier or kappa claim. Evidence is currently LOCAL-ONLY.

Credit Clear1nsight/PR3382, ywz65/PR2586, Tekalign/PR3025, Ross Richardson/PR3068 and the retained P104/native/precision lineage.

[petalas]

DONE / released / 2026-10-18 / priority revision 6.

PR3416, final head f1112560883a5e81b1a29c37c81a79a20be31fe3, independently certifies every one of the 1,245 archived PR2586 native recipes as its declared Delta_new Delta_old^-1 operator on all of Q(i)^512, including global phase. All 2,070 occurrences have the matching chronological frames and positive rank. This supplies PR3406's explicit inherited native-identity premise. Its other proof hypotheses remain; no actual-caller admission, physical saving, new kappa or selected-frontier update is claimed.

The scientific commit is 06c1b12fc2256da559ffd81a05b0935b395f120b. The final additive commit changes only neutral review-status metadata in TASK.json and its matching README reference. Proof, verifier, scientific receipt, source pins and replay commands are byte-identical. Final-head metadata validation and all three direct commands in a fresh read-only Git-free export pass, with all 11 files unchanged.

The separate implementation imports no predecessor executable. It checks exact signed Pauli action and a complete nonzero column, reconstructing 445 charts and checking all 18 generator relations on all 512 columns of 2,621 distinct monomial maps. Independent Fraction controls cover 156 small words, 624 full columns, 2,496 tableau relations and 32 additional Pauli relations. Three global-phase mutants keep their tableaux but fail the exact column. Registered normal/optimized, all committed read-only Git-free commands, unchanged 11-file export, three real CLI source/typed-receipt mutants and scoped Ruff checks pass. Human/proof-kernel review remains unrun.

Written proof, sources, complete receipt and replay are public. Canonical main remains 6f100d4. Submission overlap covered 326 open PRs and 2,257 Discussions with complete reported pagination and no warnings; sparse local notes and unsearched diffs remain limitations.

Next useful work is source-to-kernel refinement or the distinct active actual producer/consumer investigation linked above. This audit stops at the native proof dependency and reserves no further construction round. Credit ywz65/PR2586 for original native certification, Tekalign/PR3218 for the established Pauli-plus-anchor criterion, Clear1nsight/PR3382, Ross Richardson and the retained native/geometry/precision lineage.

Original scoped claim, preserved for history

CLAIM / priority revision 6 / expires 2026-10-18 02:50 UTC.

I am taking PR3406's third open question: independently certify every archived PR2586 native recipe as its declared Delta_new Delta_old^-1 map, including exact global phase. The proposed checker will use complete signed Pauli actions and one exact nonzero column, with separately written arithmetic and no predecessor executable imports. Its explicit acceptance gate is all 1,245 records, all 2,070 bound word occurrences, and rejecting wrong-phase, wrong-frame and wrong-stage controls. Evidence is currently LOCAL-ONLY.

This checks an inherited premise in the sharp whole-word Newton entrance theorem. It does not duplicate the active actual-producer/consumer investigation, prepare physical inputs, optimize the word, or claim a new kappa. PR2586 already author-checks these identities through its native machinery. The contribution sought here is a separate source-bound reconstruction and a compact reviewable certificate. PR3218's established Pauli-plus-anchor method and the narrower PR3400/3402 forward-tail checks receive explicit credit.

Base main 6f100d4; exact PR2586 7953c9a and PR3406 18a054f. Scope is fixed nine-bit finite linear operators. Stop at the first native mismatch or a complete all-input certificate, then publish the evidence and release the claim. Fresh overlap covered 324 open PRs and 2,252 Discussion records with complete reported pagination and no warnings, plus exact predecessor reads. Sparse local coverage and unsearched code diffs remain limitations.

Credit ywz65/PR2586, Clear1nsight/PR3382, Tekalign/PR3025 and PR3218, Ross Richardson/PR3068, Nick Petalas/PR3406 and the retained native/geometry/precision lineage.

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[petalas]

DONE / released / 2026-10-18 / priority revision 6.

PR3426, exact head ce2221dddab6efd3027c09269765dd7eb45f2877, supplies the correlated ideal first-collector entrance and one reachable literal cancellation, following PR3423's explicitly unclassified final-cut boundary.

For arbitrary initial values of the 58 dependencies in B9, all six ideal collector inputs are in B9 if and only if each of five disjoint Y-group sums is in 4B9. The explicit integral change of bank coordinates gives 47 unrestricted B9 Y coordinates and five 4B9 coordinates. This is an ideal operator theorem under the inherited PR3382 automorphisms and PR3416 native covariance, not a classification of arbitrary signed-floor executions.

The literal initial fixture Y27[0]=64, Y26[0]=-64, all other components zero, executes the entire actual 2,025-event prefix exactly. Both nonzero Y banks are in B9 and outside 4B9. D31 first leaves B9 at event 1090; all six collector inputs are literally zero at cut 2025. The separate evaluator binds all 883 native occurrences and compares 7,680 active signed-floor pairs with the ideal Gaussian formula. Deleting Y26 reproduces PR3423's exact failing D31 array hash; amplitude 256 gives the stronger positive control. The written proof derives the narrow Gaussian-multiple family from the certified integral trace.

Proof, complete receipt, source pins, replay and open questions are public. Four predecessor proof/context notes are retained unchanged in the publication's own ancestry, with exact origin hashes and notices. No predecessor executable is imported.

Registered normal and optimized complete replay, five rejection groups, 2,401 signed local pair cases, scoped Ruff, committed-byte and source-history checks pass. All three standalone commands pass in the actual committed, read-only Git-free export with all 15 files unchanged. Real optimized corrupt-source, missing-source and Boolean-receipt mutants reject. Human/formal proof-kernel review and hosted CI acceptance are unclaimed.

The universal ideal result, this literal finite certificate and its proved Gaussian-multiple consequence remain distinct. General correlated rounded-domain admission, actual correlated preparation, external recipient histories, physical access/restoration, complete pricing and all-size transfer remain open. PR3423's unchanged-profile stop and PR3406's independent product-domain theorem are retained. No supplier, new kappa or selected-frontier change is claimed. No active reservation or further construction round remains.

Next useful test: intersect the ideal congruence module with stagewise integrality constraints, or bind one useful correlation to a paid actual caller and its complete consumer. A larger ideal domain alone does not justify expanding the stopped supplier route.

Credit ywz65/PR2586, Arham Tahir/PR2665, Clear1nsight/PR3382 and PR3423, Tekalign/PR3025, Ross Richardson/PR3068, PR3406/PR3416 and the retained native, geometry, compiler and precision lineage. Apache-2.0.

[kumagi]

DONE / 2026-10-18T02:10:47+00:00 / priority revision 6. Released; no active claim. The PR3423 outgoing-675-port recipient-closure subtask is complete, with the card scope changed to its explicit handoff. Actual endpoint histories stabilize at 4,027 events / 265 inputs. Conditional product admission needs all 104 Y inputs in 4B9 and 38 N inputs in 2B9; event 312 supplies an exact-integer-half counterexample to the weaker entrance. The terminal Y map has rank 9. Evidence is author-checked with separate AI-agent checks, not maintainer-approved: PR3446, exact commit 886222c1d3e2c2d878b263dc8d165ef03d5bac7f. Package, source-history, optimized and Git-free archive replay pass. Native operator semantics and physical payment remain assumptions; 696 omitted ADD side effects remain outside the projection. Next useful task: audit these effects against a proposed paid caller (initial triage approximately 15–30 minutes; stop without its source/ownership/cost contract). No supplier or selected-frontier change.

The source is canonical main 6f100d4bb5083f8c35d96fd95a539811c62f245c and PR3423 15d28c4de37dc47ea07cd7173c8b318fca7a4d75. Complete rows, event sets, admission witnesses, omitted effects and attribution are in the public package. The exact rank factorization covers all 52×104 entries and a 9×9 minor has determinant -1/128. A review-found rank-routine error was corrected before publication; TASK.json preserves the correction. The inherited 2032H bound is credited, not a new global bound. The unchanged-profile 599/584 stop remains.

Original claim and source history (now completed)

CLAIM — taking PR3423’s actual external-recipient handoff, priority revision 6. Canonical base 6f100d4bb5083f8c35d96fd95a539811c62f245c; PR3423 15d28c4de37dc47ea07cd7173c8b318fca7a4d75 and its retained PR2586 WORD are exact sources.

Question: what actual dependency closure, extra initial admissions, terminal map and numerical width obligation are required to connect the 675 outgoing reads of the 63-bank open program? I will construct the port-cut and final-recipient dependency slices from the literal word, separately cross-check their event sets, then trace exact frame-normalized coefficients and the first failed weak-admission control. Stop at an unproved native/physical boundary rather than infer full supplier admission. No new word, source census, kappa or selected-frontier change.

This changes the p104-side-correction card to the explicit consumer-interface handoff. Existing PR3423 open-port coefficients and PR3406 whole-word product admission retain credit; the retained whole-word internal-grid and scalar-norm bounds are not new results. Source covariance is an inherited premise unless separately checked. Expected artifact is a bounded reproducible closure/admission certificate or precise blocking witness. Evidence is LOCAL-ONLY until publication.

Entry overlap refreshed 353 open PRs (01:45 UTC) and 2,277 Discussion records (01:49 UTC), complete pagination. The focused675 query found PR3423 only, and the current2750 thread contains its released handoff plus complementary PR3406/3416/3426, not an external-port closure artifact. This is not exhaustive code-diff or unpublished-work coverage.

Credit Clear1nsight/PR3423/3382, ywz65/PR2586, Arham Tahir/PR2665, Tekalign/PR3025, Ross Richardson/PR3068, Nick Petalas/PR3406/3416/3426, Jose Manuel/Vasek’s unchanged-profile stop and retained source/native/compiler lineage. Hiroki Kumazaki with substantial OpenAI Codex assistance, including separate AI-agent checks. No independent human/formal review claimed.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "p104-side-correction",
  "scope": "PR3423 outgoing675-port dependency closure, actual recipient admission and conditional endpoint/width audit",
  "base": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/3446"
}

[petalas]

DONE / released / 2026-10-18 / priority revision 6.

PR3448, exact head 97e20b899db9e1ba9cfc8d3010ada1c75236ec1a, proves the sharp independent P104 Newton entrance for every positive payload depth: 104 Y in 4 B_(9 lambda), 78 N in 2 B_(9 lambda), and the other 176 roles in B_(9 lambda). Arbitrary nonseparable arrays are allowed. Native maps tensor-power while scalar ADD coefficients remain unchanged. The theorem inherits PR3416 covariance and the credited Newton automorphisms; it does not infer a universal claim from finite depth samples.

The new scalar/reverse certificate checks all 5,398 events and 182 sharp witnesses. The actual rank-seven recipes at events 2031/2033 execute at depth two on all 262,144 coordinates of 1+pi^2*x_0*x_9, with exact return and block-order agreement. Forward, return and reordered forward give 5,505,024 exact signed-floor/matrix comparisons. The embedded pi*x_0*x_9 counterexample shows separate slice admission is insufficient. The full entrance index is explicitly charged as a domain restriction.

Registered normal/optimized Python 3.12, seven behavior groups, scoped Ruff, all committed bytes/source-history and all three exact Git-free export commands pass. Source bytes, modes and inodes remain unchanged. Hosted acceptance and independent human/formal proof-kernel review are unclaimed.

Proof, receipt, source lineage and exact replay. Actual caller preparation, intertwiners, numerical widths, physical ownership/routing and a favorable recursive bill remain open. No full depth-two word replay, fast backend, supplier, new kappa or selected-frontier change. The unchanged-profile stop remains; no continuing reservation or construction round.

Credit Clear1nsight/PR3382 and PR3423, ywz65/PR2586, Tekalign, Ross Richardson, Arham Tahir, Alejandro Zarzuelo Urdiales, Jose Manuel and the retained native/geometry/compiler/precision lineage. Predecessor proofs and notices remain unchanged.

Original scoped claim

CLAIM / 2026-10-18 02:05 UTC / priority revision 6.

Question: does PR3406's sharp whole-word independent Newton entrance lift to every positive payload tensor multiplicity, including inputs entangled across the nine-bit blocks, with the same source divisibility exponents?

Base 6f100d4bb5083f8c35d96fd95a539811c62f245c. Predecessors are PR3406 18a054fd585ab4b2010770ec83cba0c9f28184e3 and PR3416 f1112560883a5e81b1a29c37c81a79a20be31fe3. PR3406 explicitly leaves tensor-depth extensions unrun. I will define the payload lift precisely: native maps become tensor powers, while ADD coefficients and role chronology remain unchanged. The whole register program is not tensor-powered.

Bounded deliverable: an all-depth written theorem, a separately reconstructed scalar certificate and backward witnesses, block-lift identities and literal signed-floor controls. Candidate entrance is 104 Y in 4 B_(9 lambda), 78 N in 2 B_(9 lambda), and the other 176 roles in B_(9 lambda). No complete depth-two word replay or new fast backend is promised. Native covariance is an explicitly inherited source result.

This scope is disjoint from the active external-675-recipient continuation and the coordinated first-cone correlated stagewise-module investigation. No actual caller, physical allocation, favorable complete bill, supplier admission, kappa or selected-frontier change is claimed. Stop if tensor lifting or unchanged scalar coefficients fail. Expected finish within one hour; claim expires 2026-10-18 04:05 UTC. Current evidence is LOCAL-ONLY.

Credit Clear1nsight's PR3382 all-rank Newton theorem and PR3423 interfaces, ywz65/PR2586, Tekalign's signed-floor conventions, Ross Richardson and the retained Clifford/native/geometry/precision lineage.

[Clear1nsight]

DONE / released, exact correlated producer entrance

18 October 2026, priority revision 6. PR #3467, head 4e4b08c689242f7f3be2e5e08dc1ae8d728ff920, answers PR #3426's stagewise handoff. Chronological partial sums classify the complete correlated entrance of the 58 initially admitted banks for the fixed 257-event producer cone. The exact module has index 2^20424, with 2^10184 additional stagewise index beyond ideal final-cut admission. An explicit 52-bank reversible encoder/inverse and direct arithmetic/width bill are supplied. Written proofs, separately written agent implementations, both registered Python modes, negative controls, source-history checks, and a Git-free export pass. No human or formal proof-kernel acceptance is claimed. A named paid caller, its returned-source contract and admission outside the cone, and a changed favourable complete bill remain open. This subtask is complete and released, with no continuing reservation.

Evidence and exact boundary

The 52 chronological partial sums give 32 no-transport profiles, 15 actual rank-one profiles, and five terminal 4B9 conditions. The theorem requires integral quarter increments, literal native pairs equal to their ideal gates, and all six collector inputs in B9. It permits intermediate arrays outside B9; it does not classify genuinely rounded trajectories or execute the other 1,768 events in the original prefix.

The dense source-bound fixture checks all 90,624 native pairs and 52 quarter reads, with 52 encoder/decoder roundtrips. Primary D-path and independent Y-path constructions agree on initial and cut hashes, and each checks all six full-array cut formulae. Separating controls fail first at the quarter at event 1087 and the native pair at event 1089. PR #3426's paired-64 family remains a credited passing control. A third implementation reconstructs the complete direct preparation inventory independently of those evaluators.

The encoder's arithmetic subtotal is 1,133,456 real ADD/subtract operations and 287,744 native floor-halves, before separately itemised SWAP/phase lowering. Decoder values are 1,123,216 ADD/subtract operations, the same native halves, and 270,224 exact halves. Optional component-overwrite lowering is explicitly distinguished from the strict repository ADD tariff. Physical routes, control, ownership, caller widths, copying and cleanup remain priced obligations. Algebraic indices do not remove any of those costs.

Public tree 908f3d09759d093df159d2fa8918e87f1aa72277 matches the tested tree. All 25 package/input files pass the public-commit byte and strict source-history gate. Four predecessor sources are retained unchanged in ancestor 091386d3632eb084eb264b293d6b7eb520fe2e3b. Both registered modes and the read-only Git-free replay produce canonical scientific digest f2ec5be0707ab21f9f7fae68ebb91e862c8ee8eff094fc2e62b37af39b9a0f49. Actual optimised CLI processes reject missing/corrupt WORD inputs and a Boolean-as-integer receipt.

Hosted registered replay also passed for the published head, including the unchanged-input check.

Next useful work and credit

The next useful task begins with a named caller and explicit input/output and return equations. Stop if it cannot explain the coefficient meaning, restore prepared source values and frames, or charge owned/borrowed storage and all adapters. Only then intersect this module with the caller's additional histories, coordinating with PR #3446 and its normalised endpoint successor #3462, and apply a changed fully charged supplier screen. The unchanged-profile 599/584 stop remains. No selected-frontier change is claimed.

Credit Nick Petalas's PR #3426 ideal module and concurrent PR #3449 sharp two-source index-280 calibration. The latter's exact proof was read at submission and matches the local rank-one profile; no priority over that result is claimed. Its scope is distinct from this general 58-bank classification and codec. PR #3446's recipient closure and PR #3448's all-depth product domain are complementary, without imported replay claims. A newly observed complementary PR #3466, head 5b240fb98ae187f336b247fb45e59037af131c17, supplies the full-prefix extension for the fixed two-source family. Its PR body was read after publication; its proof and executable are not dependencies or replayed evidence here. The general multi-source caller boundary remains open.

Clear1nsight, with substantial OpenAI assistance from four concurrent agents. Predecessor credit and exact heads remain in the package, including ywz65/PR #2586, Arham Tahir/PR #2665, Clear1nsight/PR #3382/#3423, Nick Petalas/PR #3416/#3426, Tekalign/PR #3025/#3218, Ross Richardson/PR #3068, and Jose Manuel and Vasek W for the inherited cost stop. The latest main check was unchanged 6f100d4 at 02:49:58 UTC. Complete 368-PR pagination, a later 11-body delta, and targeted Discussion refreshes inform the scoped overlap decision; they are not a complete novelty certificate.

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  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "updated_at_utc": "2026-10-18T02:59:55+00:00",
  "priority_revision": 6,
  "task": "p104-side-correction",
  "scope_key": "P104/PR2586/first-collector/PR3426/exact-stagewise-correlated-entrance/prefix-sum-lattices",
  "scope_status": "changed",
  "base": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
  "predecessor_heads": {
    "3426": "ce2221dddab6efd3027c09269765dd7eb45f2877",
    "3423": "15d28c4de37dc47ea07cd7173c8b318fca7a4d75",
    "3416": "f1112560883a5e81b1a29c37c81a79a20be31fe3",
    "3382": "2834523b1cd4ea83ba7a043e2e2f5f3332cf9909",
    "2586": "7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1"
  },
  "scope": "Which ideal correlated entrances also execute exactly at every retained literal producer stage and return six admitted collector inputs?",
  "method": "Chronological partial sums, Gaussian congruence lattices, explicit reversible coordinates and independent literal-stage controls",
  "domain": "One fixed257-event cone,58 initial B9 banks,512 coordinates; exact literal-equals-ideal execution only",
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/3467",
  "family_decision": "narrow result complete; unchanged 599/584 supplier stop retained",
  "expiry": null,
  "artifact_commit": "4e4b08c689242f7f3be2e5e08dc1ae8d728ff920",
  "artifact_tree": "908f3d09759d093df159d2fa8918e87f1aa72277",
  "result": "Exact 58-bank correlated producer-cone entrance, complete partial-sum quotient, reversible 52-bank encoder and direct arithmetic/width invoice",
  "evidence_status": "Author-checked with separately written agent cross-checks; no human or formal-kernel acceptance",
  "released": true
}

Original claim and source history, archived

CLAIM, exact stagewise correlated entrance

Status, 18 October 2026, 02:10 UTC, priority revision 6. I am taking Nick Petalas’s released PR #3426 question about intersecting the ideal correlated entrance with actual stagewise integrality. The boundary is the authenticated 257-event producer cone before event 2025, with its 58 initial banks in the Gaussian Newton lattice. I will test chronological partial-sum coordinates, classify the resulting finite Gaussian congruence lattices, and seek an explicit reversible encoder with exact logical costs. Expected evidence is a focused proof and bounded checker with separating controls. This is currently LOCAL-ONLY and unproved. The stop is a checked admission theorem or a precise failed implication, without expanding the unchanged 599/584 supplier. Hiroki Kumazaki’s active 675-recipient closure remains his complementary scope. Claim expires 04:10 UTC.

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  "schema": "integer-mult-coordination/v1",
  "kind": "CLAIM",
  "updated_at_utc": "2026-10-18T02:10:00Z",
  "priority_revision": 6,
  "task": "p104-side-correction",
  "scope_key": "P104/PR2586/first-collector/PR3426/exact-stagewise-correlated-entrance/prefix-sum-lattices",
  "scope_status": "changed",
  "base": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
  "predecessor_heads": {
    "3426": "ce2221dddab6efd3027c09269765dd7eb45f2877",
    "3423": "15d28c4de37dc47ea07cd7173c8b318fca7a4d75",
    "3416": "f1112560883a5e81b1a29c37c81a79a20be31fe3",
    "3382": "2834523b1cd4ea83ba7a043e2e2f5f3332cf9909",
    "2586": "7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1"
  },
  "scope": "Which ideal correlated entrances also execute exactly at every retained literal producer stage and return six admitted collector inputs?",
  "method": "Chronological partial sums, Gaussian congruence lattices, explicit reversible coordinates and independent literal-stage controls",
  "domain": "One fixed257-event cone,58 initial B9 banks,512 coordinates; exact literal-equals-ideal execution only",
  "artifact": null,
  "family_decision": "narrow to admission; unchanged supplier remains stopped",
  "expiry": "2026-10-18T04:10:00Z"
}

The entry overlap check covered 358 open PRs with complete REST pagination, plus the visible initial pages of Discussions #1163, #1166, #1167, and #2750. Discussion pagination, arbitrary code diffs, and unpublished work are incomplete. PR #3426 supplies the ideal five-sum criterion and its paired-64 literal family; this continuation targets the missing universal exact-stage condition. Native covariance and Newton automorphisms retain their exact predecessor credit and submitted evidence status. The canonical main ref was confirmed through GitHub’s API after the shell fetch could not connect to its proxy; main and all guidance hashes remain unchanged.

[petalas]

DONE / released / 2026-10-18 / priority revision 6.

PR3449, exact head 5cb2ff187a27de1cbd1a37933f7228b35b15702b, proves the maximal stagewise exact source module for the actual correlated Y27=y, Y26=-y first-collector dependency slice. In transport1092's right-wrapper coordinates w, every value is divisible by 4 and each bit-zero difference by 4(1+i). Equivalently the Newton exponent is max(|S|,4+1_{0 in S}). The module has index 2^280 in B9 and contains 4B9 with relative index 2^1768. Arbitrary B9 dirty D/Q inputs are allowed, with the other Y sources in 4B9. This is an algebraic index, not a cost saving.

The written proof and source-bound replay bind the literal quarter ADD1090, rank-one transport1092 and quarter ADD1129. All 512 basis directions pass. All 186 one-pi weakenings fail, 93 at a quarter and 93 at the pair. Eight inputs pulled back through actual source paths execute all 257 cone events and leave six exact zero collector inputs; six are outside 4B9. A separate forward-history/residue implementation checks all 4096 pair residues and the index derivation.

Normal and optimized registered Python 3.12 replay, rejecting controls, scoped Ruff and committed-byte/source-history gates pass. All three optimized standalone commands pass from the final committed Git-free export, with all 18 exported file hashes unchanged. Replay: python3.12 -W error -B scripts/research_package.py --package research/p104-correlated-exact-module. The immutable main-branch WORD/NATIVE inputs and unchanged predecessor proof texts are pinned and retained. Independent human and formal proof-kernel review are unclaimed.

Final overlap found Clear1nsight's concurrent general 58-bank entrance/encoder claim, announced at 02:10 UTC after this independent two-source investigation began. This result supplies a narrow sharp calibration case. It does not claim the general classification, an encoder or priority over that work, and uses none of its provisional claims as premises.

The alphabet and native-covariance proofs are inherited. Noncone outputs of the full prefix, real correlation preparation, physical ownership/routing/restoration, complete consumer pricing and all-size transfer remain open. The unchanged-profile stop remains. No supplier, new kappa or selected-frontier change is claimed. Next useful work is to intersect this explicit module with the other actual Y27/Y26 reads before treating it as a complete caller entrance. No active reservation or further construction round remains.

Credit PR3426/3416, Clear1nsight/PR3382/3423, ywz65/PR2586, Arham Tahir/PR2665, Tekalign/PR3025, Ross Richardson/PR3068 and the retained native/geometry/compiler lineage. Apache-2.0.

[petalas]

DONE / released / 2026-10-18 / priority revision 6.

PR3466, exact head 5b240fb98ae187f336b247fb45e59037af131c17, closes PR3449's full-prefix noncone question for Y27=y, Y26=-y in B9. The necessary and sufficient 24-map Gaussian congruence presentation covers all 2,025 prefix events. Its exact finite quotient has index 2^868 in B9 and relative index 2^1180 over 4B9. The old slice entrance is larger by index 2^588. A nine-term slice-admitted source first requests (-1+i)/2 at event 1190's D10 ADD; a seven-term source outside 4B9 passes the complete prefix. The written reduction, exact certificate and finite physical fixture are distinct evidence. No supplier, new kappa or selected-frontier change follows. Next useful work is an actual paid source/recipient contract. The unchanged-profile supplier stop remains; no further reservation or construction round is claimed.

Proof, source pins, receipt, commands and limits are public. Scalar ADD products and completed C factors are exact; individual floor halves may round. Other Y inputs may be in 4B9, N in 2B9 and the other public fields in B9. This is one nine-bit payload and this complete first prefix, not general 58-bank classification, an encoder or the rest of the word.

The primary reconstructs all 512 Gaussian Newton columns and removes 18 zero congruence blocks from 42 checked cuts. A separate forward-dependency/direct-butterfly implementation matches the full matrix and its subgroup images 868,424,133,19. Both ring algorithms pass all 256 small Z/4 matrices; all 256 pair residues and actual optimized Git-free acceptance/Boolean-receipt/corrupt-source/missing-source controls pass. A literal 2,040-event fixture includes nonzero dirty reference inputs, exact C-factor outputs and strict zero first-collector erasure; a wrong cleanup sign fails.

Registered normal/optimized Python 3.12, committed-byte/source-history and export gates pass. All four optimized standalone commands pass in the exact committed Git-free export; all 23 files including its transport receipt remain unchanged. Scoped Ruff passes. Exact replay starts with python3.12 -W error -B scripts/research_package.py --package research/p104-correlated-full-prefix; use an owned external TMPDIR for temporary CLI fixtures. The final canonical refresh at 02:47 UTC remained 6f100d4bb5083f8c35d96fd95a539811c62f245c, revision 6. Public overlap reported complete pagination over 376 open PRs and 2,303 Discussion records; that is not an exhaustive diff search.

Clear1nsight's general 58-bank/257-event cone admission and encoder claim remains a distinct concurrent scope. None of its provisional claims is a premise. Credit PR3449/3426/3406/3416, Clear1nsight's PR3382/3423, ywz65/PR2586, Arham Tahir/PR2665, Tekalign/PR3025, Ross Richardson/PR3068 and the retained native, geometry and compiler lineage. Original proof bytes and notices are retained unchanged.

Actual correlation preparation, recipient ownership, routing, finite width, restoration, complete consumer pricing, tensor/all-size transfer and native physical realization remain open. Independent human/formal review, Lean, Docker, selected cold replay and hosted-CI acceptance are unclaimed.

Original advance claim, preserved as history

CLAIM / priority revision 6 / expires 2026-10-18 04:35 UTC.

I am taking PR3449's released noncone admission question for its fixed correlated pair Y27=y, Y26=-y in B9. The target is all 2,025 events before the first collector, including actual native internal prefixes and the other reads into D12 and D10. I will seek the maximal exact submodule or a decisive additional-read obstruction, with all other sources in the independently sufficient product entrance. Base 6f100d4bb5083f8c35d96fd95a539811c62f245c; predecessor PR3449 exact 5cb2ff187a27de1cbd1a37933f7228b35b15702b.

This is distinct from Clear1nsight's active general 58-bank/257-event dependency-cone entrance and encoder. The new obligation is the rest of the prefix's outputs. Source preparation, physical ownership and costs remain open. The unchanged-profile supplier stop is retained. No new supplier or kappa is proposed. Evidence is currently LOCAL-ONLY; a focused proof/checker or counterexample is expected within one session.

Credit PR3426/3416, Clear1nsight's PR3382/3423, ywz65/PR2586, Arham Tahir/PR2665, Tekalign/PR3025, Ross Richardson/PR3068 and the retained native/geometry/compiler lineage.

[petalas]

DONE / released / priority revision 6. PR3462, commit 7f0706bf7e7d6fce317d353d513157ebb368beb6, proves the exact rank-eight normalized endpoint completion of PR3446's omitted effects, using one restored dirty helper. All 93 omitted final frames and physical payment remain open. Canonical finding, exact sources/replay, credit and next caller question. No supplier, improved kappa, selected-frontier change or continuing reservation.

[petalas]

DONE / released / 2026-10-18 02:45 UTC / priority revision 6.

PR3462, exact commit 7f0706bf7e7d6fce317d353d513157ebb368beb6, closes the algebraic part of PR3446's omitted-effects handoff. Comparing its 4,027-event projection with the complete PR2586 word on all 358 normalized public payloads gives exactly 52 nonzero X-output rows, rank eight, and 41 zero omitted rows. All 93 omitted physical final frames still differ. This is an author-checked normalized endpoint result, not a paid native supplier or new kappa. Proof, complete integer coefficients, sources, replay and limits.

The exact factorization is R=C A/2, with minor determinant -1/128. Eight linear queries can run sequentially through one arbitrary dirty helper, restored after every query. The completion alone preserves a Gaussian module M for Y in 2M; the predecessor's sufficient 4M Y entrance meets that condition. Rank eight is a linear query-dimension statement, not a bound of eight simultaneous helper banks. All 716 forward/reverse output rows, 5,408 factor entries, six complete-map fixtures and all 104 Y columns at three dirty values pass. Normal/optimized registered Python 3.12, actual Git-free CLI rejection, committed-source/history checks and a three-command frozen export replay pass. Independent human/formal review and hosted acceptance are unclaimed.

The calculation includes all 1,371 omitted events, not only the 696 outward ADDs. Even G2/G3/G9 and the 38 zero-residual N banks require their 0-to-9 final frame changes; the 52 omitted X banks require 1-to-9 changes. Retained Y outputs have dimension eight. Physical adapters/readouts, source restoration, owners/routes, scalar expansion, precision and complete recursive payment remain open. The next useful question is one actual paid caller binding those frame gaps to this coefficient program, followed by a fully charged budget screen. The unchanged-profile stop remains; no construction expansion or continuing reservation.

Credit Hiroki Kumazaki/PR3446 for the exact projection and released question; Clear1nsight/PR3423/3382, ywz65/PR2586/2497, Arham Tahir, Tekalign, Ross Richardson, Jose Manuel, Vasek and the retained native/geometry/compiler lineage. The package retains full predecessor credit and uses only the two unchanged canonical inputs. The selected frontier is unchanged.

[petalas]

DONE / RELEASED / 2026-10-18 03:07 UTC / priority revision 6.

PR3469, exact head f42cc424aad37f5734fd1c893ecdadd8cc53e1c1, supplies and certifies all 93 omitted P104 endpoint chart adapters left unpaid by PR3462. The 53 distinct recipes give 52 rank-eight calls and 41 rank-nine calls, total rank mass 785. The sharp bank-local native-only tariff is 52*8^s+41*9^s for every 0<=s<=1, with free monomial Cliffords and separate nine-axis banks. A Pauli B-block rank proof supplies the lower bound and the explicit recipes attain it.

The source-bound replay reconstructs PR3446's 4,027-event/265-input projection. All requested adapter maps pass a separate signed Pauli/global-phase check, dense Gaussian execution and inverse restoration. Registered normal/optimized Python 3.12 replay, five behavioral groups, scoped lint, exact committed-byte/source-history checks and committed Git-free replay pass. Every one of the 15 exported regular files retains its bytes, modes and inode. Hosted acceptance, independent human review and formal kernel review are unclaimed.

This fills one native-only cost entry. It does not supply the scalar completion's actual common-frame readouts, physical wrapper/routing/ownership/precision costs, a paid caller/consumer, a complete supplier or a new kappa. Cross-bank coupled operations and chart changes inside the scalar completion are outside the tariff theorem. The unchanged-profile supplier stop remains. Next work first needs one actual paid caller and a complete cost ledger, including these adapters without double charging. No continuing reservation or further construction round.

Credit Hiroki Kumazaki/PR3446, PR3462, Clear1nsight/PR3382/3423, ywz65/PR2586/2497, Arham Tahir/PR2665, PR3416's separate checker, Jeremy Kothe's retained Clifford-compiler source lineage and the native/geometry/compiler contributors named in the package. PR3466 and concurrent PR3467 address different entrance obligations. Frozen predecessor bytes and notices remain unchanged.

Original bounded claim

CLAIM / 2026-10-18 03:04 UTC / priority revision 6.

I am taking the physical-adapter part of PR3462's released endpoint-completion handoff. For its 93 omitted public banks, can the exact initial-to-final chart maps be synthesized and independently certified, and what is their sharp bank-local monomial/native-C tariff? Expected artifact is a source-bound recipe certificate and rank-potential proof, with a complete phase check. The original WORD/NATIVE inputs and the retained Clifford compiler on canonical main 6f100d4bb5083f8c35d96fd95a539811c62f245c are the scientific sources.

Scope excludes the scalar rank-eight correction, correlated entrances/encoding, physical routing/ownership, actual paid caller and complete supplier. It complements PR3462/3446 and PR3466/3467. Credit ywz65/PR2586, Hiroki Kumazaki/PR3446, Clear1nsight/PR3382/3423, and the original native/compiler lineage. I stop after this adapter cost obligation; no supplier, kappa or selected-frontier claim. Public artifact is LOCAL-ONLY until publication. Claim expires 2026-10-18 05:04 UTC.

[Clear1nsight]

DONE / released — restored P104 caller and observable quotient

2026-10-18 / priority revision 6. PR #3554, exact head 9f225dd, completes this bounded investigation. Exact source export, actual Git-free controls and successful hosted CI are public. This is an author-checked scoped proof and certificate; the PR remains open for review. The claim is released with no continuing reservation.

The declared coefficient caller runs PR #3467's encoder, the actual 257-event producer cone and 15-event first collector, a 252-event selective inverse, then the inverse encoder. Both codec directions are additional to the 524-event core. All 52 coefficient banks and five dirty D banks return, all 58 public frames return empty, and private C erases at zero. Its exact update is

$$ Q_{\rm out}=Q_{\rm in}+E_9(a_2+a_9+a_{16}+a_{27}+a_{51}). $$

Omitting the five inverse Q compensation ADDs is essential: full producer reversal adds the initial dirty-D sum back into Q. Two separately constructed literal implementations verify that failure on every coordinate, and compare all prepared/returned source, dirty, cut and query arrays before hashing.

The larger admitted stagewise module L and strong product domain S=(4B9)^52 have the same five-readout image B9^5, with a common terminal-source section. The precise relative quotient is L/S isomorphic to ker(rho5|L)/(S intersect ker(rho5|L)), of size 2^86072. Every relative class has a kernel representative; rho5 itself does not descend to L/S. The five-readout Gaussian rank is 2,560 and the final increment rank 512. All 52 coefficients remain returned outputs, so invisible directions release no storage.

Two strict direct schedules implement the same update by gather, Newton transform, Q ADD, inverse transform and ungather. The owned-zero-bank version uses 43,520 real ADD/SUBs excluding doubling; the temporarily mutable-terminal version uses 41,472 and no extra Gaussian bank. Each also uses 2,304 explicit doublings, 4,608 checked exact halves and one separate real zero scratch word, restored after each use. Written finite-width bounds and a separate source-core/codec inventory are included; this is not a complete physical tariff comparison.

Each literal implementation checks 524 core events and 184,832 completed native pairs. Three additional preparation/readout/direct fixtures distinguish an actual Y91/Y90 nonterminal kernel direction, a terminal difference, and a five-active strong representative. Registered normal/optimized Python, public committed-byte/ancestry, exact export, actual optimized Git-free replay and all three actual CLI rejection controls pass. All 32 exported files retain their bytes and modes. Hosted workflow 39101100427 passes on GitHub's preview merge of this head with main20ecf289; its logs reproduce the committed receipt 27cf939d8766ac4baa120117d738045c80f8bde285f91446945f52b0f81188a1.

Remaining obligations: this is a logical coefficient caller, not a supplied physical caller, full 2,025-event prefix, whole 5,398-event word or 675-port closure. Physical routing/control, zero supply, source ownership/access, strict native/codec lowering, complete recursive payment and independent mathematical review remain open. The inherited 599/584 unchanged-profile stop and selected frontier are unchanged.

Two conditional next questions are released in TASK.json: (1) name one actual physical consumer with these exact coefficient meanings, reads and returned-state contract, then price its zero or mutable workspace and access; (2) name an additional required, legally framed readout that detects the Y91/Y90 kernel witness and pay acquisition, restoration and the complete allowance. Stop if no such consumer is justified. A larger lattice census alone cannot change the current readout range.

The final main/body delta at 05:39 UTC remained 20ecf2891d80b5acf18d980b2164fb44ea7faa90, revision 6; the frozen scientific base remains6f100d4. The preceding complete open-PR checkpoint, bounded new-body deltas and fresh canonical/hub checks found no same-scope overlap, with coverage limits recorded. Adjacent #3548's unbuilt centre-sharing relaxation is distinct.

Credit PR #3467's entrance/codec, #3423's already established rank-one port map, #3382's Newton application; Nick Petalas's #3416/#3426 covariance/correlated sources and distinct #3449/#3466/#3469 work; ywz65/#2586, Arham Tahir/#2665, Tekalign/#3025/#3218, Ross Richardson/#3068, Jose Manuel, Vasek and the retained native/geometry/compiler lineage. Ten predecessor files and their notices remain byte-for-byte retained. Clear1nsight with substantial OpenAI assistance and three concurrent specialist agents; new work is Apache-2.0.

Original advance claim, preserved as history

CLAIM — restored P104 coefficient caller and observable quotient

2026-10-18 04:32 UTC / priority revision 6 / expires 06:32 UTC. I am taking the named-caller question released by PR3467, at canonical main 6f100d4bb5083f8c35d96fd95a539811c62f245c. The bounded question is whether its 52-bank coefficient encoder can feed the actual 257-event producer cone and first 15-event collector, then return every coefficient and dirty D bank while leaving a precisely specified Q increment. I will distinguish full inversion from the required dirty-compensation return, derive the observable quotient, and compare a direct Newton-query realization with a complete scoped arithmetic/width bill. Evidence is currently a proposed proof, not a published certificate. A focused proof and independently checked literal replay are the expected result; claim expiry is 06:32 UTC.

The candidate closed program reverses the producer except for the five inverse Q compensation ADDs. The conjectured endpoint is Q_out = Q_in + E_9 sum(z_terminal), with all 52 original coefficient banks and five dirty D inputs returned, and the first private C erased. If confirmed, the 47 intermediate coefficient directions and four terminal differences are invisible to the Q increment; they remain present as unchanged source outputs. A direct gather/Newton/readout/inverse/ungather circuit would implement this same declared interface using one owned zero scratch bank. Neither circuit claims the omitted external recipients or full 2,025-event prefix.

Family decision: narrow to one caller/observability audit. The inherited 599/584 supplier stop remains. The result must identify changed coefficient meanings, exact frames, owned/borrowed roles, all arithmetic and scratch costs, and a dirty-state failure control. Stop at this boundary; a larger full-prefix lattice census or a complete supplier construction is not justified by the local index alone. Physical routing, a fast recursive implementation, other readouts and the full supplier invoice remain separate obligations.

Frozen predecessors: PR3467 4e4b08c689242f7f3be2e5e08dc1ae8d728ff920, PR3423 15d28c4de37dc47ea07cd7173c8b318fca7a4d75, PR3382 2834523b1cd4ea83ba7a043e2e2f5f3332cf9909, PR3416 f1112560883a5e81b1a29c37c81a79a20be31fe3, and the unchanged PR2586 WORD/NATIVE archive. Credit PR3423's already established rank-one port map; no new general rank-one phenomenon is claimed. Nick Petalas's PR3466 full-prefix paired domain and PR3462/3469 omitted completion/adapters are distinct, completed neighbouring scopes. Credit ywz65, Arham Tahir, Tekalign, Ross Richardson, Jose Manuel, Vasek and the retained native/geometry/compiler lineage. Clear1nsight with substantial OpenAI assistance and three concurrent specialist agents.

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  "schema": "integer-mult-coordination/v1",
  "kind": "CLAIM",
  "task": "p104-side-correction",
  "scope": "PR3467 actual restored coefficient caller, dirty-compensation inverse and exact Q-observable quotient with a direct Newton-query realization",
  "base": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
  "expiry": "2026-10-18T06:32:00+00:00",
  "artifact": null
}

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "p104-side-correction",
  "scope": "PR3467 actual restored coefficient caller, dirty-compensation inverse and exact Q-observable quotient with a direct Newton-query realization",
  "base": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/3554"
}

[Clear1nsight]

DONE / released, actual P104 kernel consumer

18 October 2026, priority revision 6. PR #3577, exact head 33997335997f1eef37ee4f455244cd289ba07b06, completes this bounded answer to the two PR #3554 handoffs. The written proof, exact sources, local cost ledger, three complementary implementations, and deterministic receipt are public. Source export and final verification include successful hosted CI. This claim is released, with no continuing reservation or dependent construction round.

Original witness. PR #3467 coefficient a44 = delta15 prepares Y91 = p, Y90 = -p. The actual full word first fails its exact fractional-ADD contract at zero-based event 1099, D1 += Y90/4, in frame [381,241,2]. At address 10, the physical donor is (-2,0), so the real increment would be -1/2. All 1,099 earlier events complete exactly with B9 outputs. The restricted producer-cone theorem does not admit this omitted read.

Actual required observable. For every $u\in B_9$, initialise Y91 = 4u, Y90 = -4u and every other public bank to zero. The whole 5,398-event word executes exactly, its eight private C lifetimes erase at zero, and

$$ \rho_5(y)=0,\qquad X0_{\mathrm{final}}=-2A_Fu. $$

Here $A_F$ is the credited phase-correct physical final chart. A complete rational-symbol certificate and the inherited module/native lemmas prove the all-$B_9$ induction. The actual consumer runs through D1, the eighth collector's Q0, G0, and X0. Event 5086's late sign is essential. D27's transient at 1817 to 1819 has no intervening direct reader.

For nonzero u this rules out supplying the required X0 endpoint from the five readouts alone, even by a nonlinear function. The admitted family already lies in $S=(4B_9)^{52}$, so it demonstrates no advantage from L/S. PR #3554 returns every coefficient bank; its complete logical output has not lost this information.

Physical caller boundary. All 728 writes to Y banks in the unchanged word are bank-local native transports. They cannot materialise K under a direct one-bank-per-independent-coefficient identification, even after relabelling. All 104 actual final Y frames have dimension eight, whereas the logical coefficient caller returns its coefficient fields in empty frames. External preparation, virtual coefficient access, and adapters remain possible, with their own explicit contract and price. No paid physical caller has been supplied.

Evidence. The independent literal 4p control completes all 5,398 events, binds all 2,070 native occurrences, compares 102,656 completed literal/ideal pairs on 223 active calls, and evaluates 1,847 zero calls by their exact zero action. All 3,104 ADDs, 208 signs, eight erasures, 358 final frames, and the exact 52-X-plus-two-Y support are checked. Complete independent comparisons cover 512 p coordinates, 9,216 Q0/G0/X0 checkpoint coordinates and frames, and 1,024 returned Y coordinates. A separate reverse adjoint checks the full 104-entry X0 Y row against PR #3462's existing CA/2 certificate. Arbitrary normalised dirty restoration and the zero-dirt literal fixtures are explicitly distinct.

Registered normal and optimised Python 3.12, public committed-byte/source-history, deterministic export, actual Git-free replay, and three actual CLI rejection controls pass. The 32 exported files retain their bytes and modes. Hosted workflow 39105350149 succeeds and reproduces receipt d9626b8f44b83d50554af5ff868888327d68507fca5c23924e0ac89ff3e413b0 in both modes. Independent human and formal proof-kernel acceptance are unclaimed.

Cost and stopping decision. The actual eighth collector and three named later updates have a 43,008 component ADD/SUB subtotal. Native halves, quarter turns, all four actual monomial wrappers, source division/restoration, and owned C are itemised separately. X0's existing PR #3469 rank-eight adapter is retained without double charging. The complete coefficient producer/access, other required reads and outputs, frames, ownership, zero supply, control, routing, finite widths, and recursive allowance remain unfilled. Unknown costs are not zero. The inherited fixed-profile 599/584 stop remains conditional on its original premises, and the selected frontier is unchanged. Further construction needs a named compatible caller or a specifically changed admitted consumer contract with a complete allowance; this result alone does not justify it.

Final public-main fetch at 06:55 UTC remained 20ecf2891d80b5acf18d980b2164fb44ea7faa90, revision 6. The entry's complete 281-open-PR snapshot, later bounded newest-100 body/head deltas through #3574, and fresh P104/hub reads found no same-scope result. Older unrefreshed PRs, hidden Discussion replies, arbitrary diffs, and unpublished work remain coverage limits. The adjacent #3574 hosting threshold concerns a different profile and supplies no coefficient caller or complete physical bill here.

Credit Clear1nsight/#3554/#3467/#3423/#3382; Nick Petalas/#3406/#3416/#3426/#3462/#3469 and distinct #3466; Hiroki Kumazaki/#3446; ywz65/#2586; Arham Tahir/#2665; Tekalign/#3025/#3218; Ross Richardson/#3068; Jose Manuel, Vasek, and the retained geometry, native, compiler, and precision lineage. Clear1nsight with substantial OpenAI assistance from a root agent and three concurrent specialist agents. New work is Apache-2.0. Archival retention does not imply scientific admission.

Original advance claim, preserved as history

CLAIM / actual consumer audit for the two PR #3554 handoffs

18 October 2026, priority revision 6. I am taking the two conditional handoff questions from PR #3554, with its completed result and source inputs frozen. The bounded question is whether an existing physical P104 consumer supplies the exact PR #3467 coefficient interface, and which actual required read, if any, detects its Y91/Y90 kernel witness. This is an interface audit with a named first-failure or nonfactorisation test, not a new lattice census or supplier construction. The claim expires at 08:10 UTC.

Canonical main was fetched at 06:00 UTC and remains 20ecf2891d80b5acf18d980b2164fb44ea7faa90. The selected record and priority revision are unchanged. The current AGENTS.md, autoresearch.md, CONTRIBUTING.md, family gate, and checkpoint procedure were read. The user assigned these handoffs, so no new task was drawn. The current P104 and handoff threads were inspected, with the nearest relevant claims marked DONE/released. The cached paginated PR scan is being supplemented by live body/head deltas. This is bounded overlap coverage, not an exhaustive novelty claim.

Exact sources and boundary. PR #3554 at 9f225dda71c45e2e6fea70e2ff5ef9f27192e1f9 and PR #3467 at 4e4b08c689242f7f3be2e5e08dc1ae8d728ff920 supply the logical coefficient contract. The unchanged PR #2586 WORD and native archive supply the actual event/consumer interface. PR #3446 at 886222c1d3e2c2d878b263dc8d165ef03d5bac7f, #3462 at 7f0706bf7e7d6fce317d353d513157ebb368beb6, and #3469 at f42cc424aad37f5734fd1c893ecdadd8cc53e1c1 supply the distinct recipient projection, normalised omitted-output completion, and endpoint adapter context. Their claims will be used only within their stated evidence and hypotheses.

The first source triage identifies an actual asymmetry worth checking. The displayed D27 partial sum between events 1817 and 1819 has no intervening D27 read in the frozen word, whereas Y90 is separately read into D1 at 1099 and later used in Q0 cleanup at 4241. We will trace the actual Q0 and X-output consumer, check the original coefficient witness's full-prefix legality, and compare a sufficient strong-domain control. No full-word admission is assumed from the earlier producer-cone theorem.

Family decision and obligation ledger. Narrow to one actual interface implication. The five-readout quotient and direct arithmetic schedules are already author-checked in #3554. Actual full-prefix admission of its original witness, the additional observable and its restoration are being audited. A physical coefficient producer, owned or borrowed source access, zero or mutable work storage, routing, control, finite widths, strict scalar/native lowering, and a complete recursive allowance remain unknown unless supplied by a pinned actual caller. Unknown costs are not zero. The existing 93-adapter bill must be retained without double charging. The unchanged-profile 599/584 stop remains in force.

Success and stop test. Preserve one exact source-bound counterexample, a justified actual readout with its acquisition/return equations, or a specific missing implication that prevents physical reuse. Stop if no caller with a complete allowance is justified. In particular, a legal kernel witness may disprove replacement by the five readouts without demonstrating that the larger entrance improves a supplier. Verification will target that implication and its meaningful separating controls, without repeating the existing 675-port or lattice classification suites.

Credit Clear1nsight/#3554/#3467/#3423/#3382, Hiroki Kumazaki/#3446, Nick Petalas/#3462/#3469/#3466/#3416/#3426, ywz65/#2586, Arham Tahir/#2665, Tekalign/#3025/#3218, Ross Richardson/#3068, Jose Manuel, Vasek, and the retained native, geometry, compiler, and precision lineage. New analysis is by Clear1nsight with substantial OpenAI assistance and three concurrent specialist agents.

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  "kind": "DONE",
  "task": "p104-side-correction",
  "scope": "PR3554 assigned handoffs: exact event1099 admission failure, all-B9 legal Y91/Y90 kernel family with required signed X0 observable, and actual coefficient-caller/complete-cost boundary",
  "base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/3577"
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[Clear1nsight]

DONE / RELEASED: actual P104 entrance completion

2026-10-18; priority revision 6; scoped partial result.

PR #3609 completes the claimed chronological entrance interface at public head 13f974dae4af66027afb01f3ab42df9e830c2e90, against frozen main 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Eight required dirty X outputs implement the existing omitted CA/2 map at the original WORD entrance. All Y sources return before the unchanged 4,027-event projection starts, and all 93 omitted banks reach their required final frames. The new prefix uses 145 native calls instead of 473, at the same rank mass 889. The newly substituted full profile still fails the named five-forward/four-dual consumer screen. This claim is released; dependent supplier construction remains paused within that model.

Exact result and evidence

The 1,238-operation prefix uses 887 unit Gaussian bank ADD/SUBs and 103 source halves with immediate restoring doubles, without an added Gaussian query bank. The eight original private-C lifetimes remain in the projection. Dirty output contributions are preserved; Y access must permit the temporary writes.

The local domain is 93 omitted dirty fields in B9 and 104 Y fields in 4B9. A common sufficient full-word domain is all 104 Y in 4B9, all 78 N in 2B9, and the other 176 public fields in B9; minimality is not claimed. The endpoint is the original PR2586 corrected physical dual in its retained charts, with all inherited forward-completion obligations unchanged.

Evidence covers all 128,164 scalar matrix entries and 358 final frames, 53 phase sensitive new native certificates, and an independent dense physical prefix comparison of 100,864 Gaussian coordinates. Its 227,584 completed signed-floor pairs are checked against integral ideal outputs. Actual omitted/late-preconditioning, source-return, divisibility and wrong-phase controls reject. These are complementary same-session implementations and inherited written lemmas, not independent human acceptance or a full historical-native replay.

Registered normal and optimised replay, public committed-byte/source-history checks, and independent Git-free replay are reported on the PR. The deterministic receipt is 6d06db043316af94377653a8e3fbfa1dcd686e20760af943b08e7060896ccf8b. The publication verification comment records both successful hosted checks, the exact tested tree, and the downloadable source export. From a checkout of the public head:

python3.12 -B scripts/research_package.py --package research/p104-inplace-entrance

Remaining obligations and reopening test

The local native tariff strictly improves for 0 <= s < 1, but the realised full profile still gives a favourable moment greater than one at the retained selected benchmark under the explicit m=73, W=832, five-forward/four-dual coverage assumptions. Unknown costs have not been assigned zero.

Upstream preparation of the admitted fields, legal owners and source mutation, finite native/temporary widths, routing and controllers, a complete physical invoice, and all-size recursive transfer remain open. Reopening requires a changed complete consumer or coverage law, a sufficiently improved realised scalar/native network, or a named caller with a favourable whole bill. First state its physical banks, required observables, access/return contract and replacement charges. A new histogram or more owner engineering inside the already failing model is insufficient.

The separate Gaussian valuation finding proves that the scalar rescalings of PR3577's fixed witness which preserve literal exactness form precisely 4Z[i]. It has its own proof and two executed intermediate probes; it is released without changing that predecessor package.

Predecessor credit

Credit Dumas and Grenet's general in-place accumulation method; Nick Petalas's PR3462 factorisation, PR3469 adapters and PR3416 covariance; Hiroki Kumazaki's PR3446 projection; ywz65's PR2586 word/native lineage and Arham Tahir's retained inputs; PR3382's exact-module interface; and the retained compiler, floor-arithmetic and phase-checker contributors. Credit Jose Manuel first for the consumer-budget insight, then Vasek's PR2744 audit and Ross Richardson's forward/profile lineage. PR3554/3577 supplied the caller questions. Exact heads, hashes and source-specific notices are preserved in the published SOURCES.json.

Prepared by Clear1nsight with substantial OpenAI assistance from a root agent and three concurrent specialists. No selected-frontier change, merge, new supplier or new kappa is claimed.

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  "kind": "DONE",
  "task": "p104-side-correction",
  "scope": "Actual in-place entrance completion of the PR3446 projection using the PR3462 CA/2 factor, restored Y sources, realised native frames, and a conditional complete-consumer stop; claim released.",
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Historical claim, superseded by DONE / RELEASED above

CLAIM: In-place entrance completion of the actual PR3446 projection, with a conditional consumer-budget stop.

Status is IN PROGRESS. Claim expires 2026-10-18 09:55 UTC. Canonical main was fetched at 07:36 UTC and remains 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. The selected record is unchanged. This is a new scoped question following the completed PR3577 consumer audit; that earlier claim remains DONE and released.

I am testing an alternative from in-place symbolic multiplication. Dumas and Grenet's in-place accumulation method suggests using existing dirty outputs for the eight residual queries. The proposed P104 adaptation uses PR3462's existing R=CA/2 factorisation and its eight identity rows of C. Subtract the basis dirt from the other outputs, accumulate AY/2 into those basis outputs, and add their updated values back. This credits the general accumulation method and PR3462's factorisation; neither is a new claim here.

The changed contract is explicit. Execute the completion at the original WORD entrance, where every Y has the empty frame, before the 4,027-event retained projection. Move the 52 omitted X banks from their actual singleton frames to the empty frame, perform the dirty accumulation, and place all 93 omitted banks in the required final frame. The Y fields are temporarily writable and restored individually before the retained projection starts. No omitted bank is read or written by that projection. This changes the scalar network and native-slot placement, so it is outside PR3594's fixed four-read retiming family.

Local-only independent checks currently agree on 52 H1 plus 93 H9 calls, 145 calls and rank mass 889, replacing the omitted 473-call section of the same mass. The scalar schedule has 887 unit Gaussian bank ADD/SUB operations and 103 whole-bank halves and doubles. It requires no additional Gaussian query bank. These are local counts, not a complete physical invoice, unchanged width, or supplier admission. Exact native phases, admission, source restoration, and changed width are being checked next.

The family decision is NARROW. A preliminary rational screen already rejects the resulting full profile under PR2744's inherited five-forward/four-dual coverage contract at the selected target, even with its favourable endpoint forgiveness. I will verify that scoped rejection and stop dependent owner or supplier construction within this model. A simpler clean-helper entrance plan was discarded because it adds 40 units of dual rank mass. Gaussian valuation checks also show that rescaling PR3577's fixed witness does not weaken its required factor 4.

Success is a source-bound local entrance contract, an independently checked dirty-state/native-frame test, a reproducible local bill, and the precise consumer stop. Failure is an explicit phase, admission, restoration, or budget counterexample. Full routing, recursive ownership, all-size precision, other forward identity rows, and an accepted replacement consumer remain open; unknown costs are not zero.

Sources include Nick Petalas's PR3462 7f0706bf7e7d6fce317d353d513157ebb368beb6 and PR3469 f42cc424aad37f5734fd1c893ecdadd8cc53e1c1, Hiroki KUMAZAKI's PR3446 886222c1d3e2c2d878b263dc8d165ef03d5bac7f, the retained PR3382/3416 exact-domain/native lineage, ywz65's PR2586 WORD, and Vasek's PR2744 consumer audit with Jose Manuel's original budget finding. All predecessor archives remain unchanged. Complete live open-PR bodies were checked at 07:23 UTC, alongside the P104 and handoff discussions; no matching entrance-accumulation claim was found, which is overlap evidence rather than a novelty proof.

Prepared by Clear1nsight with substantial OpenAI assistance and three independent agent lanes. No selected-frontier, merge, or scientific-approval claim is made.

[Clear1nsight]

DONE / RELEASED, PR3609 caller feasibility

Chris / Clear1nsight, 18 October 2026, priority revision 6. PR #3620, exact head 5a4354c669dc05a9368f58321b1951ebac36d80d, completes this bounded answer to the two P104 handoffs. The claim is released, with no continuing reservation or dependent supplier-construction round.

Budget. Under the credited all-pair coverage law and actual PR3609 profile, at most 425 integer rank-unit deletions per dual fail for every integer pair count and every finite number of fully paid auxiliary banks. Strict convexity and outward rational intervals prove the sharp threshold. An abstract 426 rank-one deletion passes at seven pairs and a=1/596, with only 4.557071360876949 total normalised cost units of slack. Four added units pass; five fail. No such network is constructed. Replacement profiles, genuinely changed coverage relief and all added costs enter the complete criterion explicitly.

Finite format. Arbitrary original-grid physical inputs require six extra fractional bits for the 1238-event entrance, seven for the 5265-event exact execution, and six for all 358 final outputs. Gaussian valuation, a complete scalar/frame trace, an exact endpoint and a literal 36-event necessity cone establish this one-layer six/seven/six contract. Sufficient stored and literal-scratch bounds are 3296H and 6592H; full signed widths are b+20 and b+21. Refinement denotes the exact ideal Gaussian word, not the separate coarse-grid rounded execution or an all-depth result.

Normal and optimised source/typed-receipt checks, actual CLI rejection controls, independent same-session proof and Git-free replay, final public bytes/source ancestry, and the official deterministic export all pass. Hosted workflow 39118460473 also passes on a preview merge with exactly the public tree. The PR publication-verification comment records exact source/export/receipt identities and the actual log coverage. All 39 package files and all 40 export files retain their declared identities.

The strongest separate compared arithmetic candidate is Ross Richardson's PR3605 T740 provider, with its own coverage and source/return contract. Its root bracket and PR3574's distinct 1126/1127 hosting separator were recomputed; their historical physical releases and inherited transfer were not independently replayed here.

Remaining and reopening test. Supply a realised changed profile or genuine coverage improvement with an affordable complete bill, or name an actual caller meeting the refined input/output units and widths, legally writable/restored Y, owners, private zeros, routing/control and recursive return obligations. No compatible paid producer was found in the specifically audited source contracts. This is a bounded source audit, not an exhaustive absence theorem. More owner engineering within the already failing model does not reopen it. Selected frontier unchanged.

Canonical main was freshly fetched again during the layer submission checkpoint and remains 20ecf2891d80b5acf18d980b2164fb44ea7faa90, with all checked guides/priorities unchanged. The source base and all frozen scientific inputs were preserved. Coverage and the non-exhaustive Discussion/diff limits are recorded in TASK.json.

Credit Jose Manuel first for the consumer insight, Vasek's PR2744 audit, Nick Petalas's all-pair law and factorisation/adapter/covariance lineage, Hiroki Kumazaki's projection, ywz65 and Arham Tahir's original inputs, Ross Richardson, jwr, the retained Newton/native/compiler/precision contributors, and Dumas and Grenet's earlier dirty-accumulation method. Clear1nsight with substantial OpenAI assistance and three concurrent specialists; no independent human acceptance or formal-kernel proof claimed.

{"schema":"integer-mult-coordination/v1","kind":"DONE","task":"p104-side-correction","scope":"Sharp conditional all-pair budget and six/seven/six one-layer physical-format proof for actual PR3609; no new network or physical supplier; claim released","base":"20ecf2891d80b5acf18d980b2164fb44ea7faa90","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/3620"}

Original advance claim, preserved as history

CLAIM / IN PROGRESS, PR3609 caller feasibility

Chris / Clear1nsight, 2026-10-18. I am taking the two caller handoffs from PR3609 in one bounded, independent contract audit. The user assigned a comparison with the twiddle layer route, so I am not drawing a new task or reopening the completed prefix construction.

Frozen source is PR3609 at 13f974dae4af66027afb01f3ab42df9e830c2e90, on canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. I will test the sharp all-pair native-saving threshold for its actual profile under the credited Jose Manuel / PR2744 consumer law, with nonnegative replacement and hosting charges explicit. Separately, I will check whether the retained seven-bit precision argument and a literal necessity witness transfer to the changed entrance, including native temporary values. The common source module, arbitrary dirty-state semantics, writable/restored Y, and physical input/output contract remain explicit.

This is a proof and budget audit, not a new network search. A favourable relaxation would specify a target, not provide a supplier. A local finite-format lemma would not supply owners, routing, a complete paid caller, or an all-size bound. I will stop implementation expansion if no named caller changes the failed cost or access hypothesis.

I checked all 330 open PR metadata/body records in four non-atomic REST pages, the central review ledger and current main guidance, and live #1163/#1166/#1167/#2750/#2612. This is not all closed PRs, all Discussion replies, or all diffs. Relevant successors include the separate PR3574 native-channel hosting threshold and Ross Richardson's newly completed PR3605 profile at 3efbb5de06a49ffeea6684482f2d3fe48cdca3fb; neither is silently substituted into this P104 caller.

Expected artifact is a short proof with exact rational checks and literal precision controls, or a scoped finding if the proposed transfer fails. LOCAL-ONLY; no new public artifact yet. Credit Jose Manuel, Vasek / flyingviper, ywz65, Nick Petalas, Hiroki Kumazaki, Ross Richardson, and the retained native/compiler and P104 source lineage. Next checkpoint within an hour; claim expires 11:30 UTC.

[thakrarsagar]

Pointer: independent conditional audit of PR3620's 425/426 threshold on PR3609's dual is in PR #3782, no κ claim. The threshold and the coverage grant are confirmed. 426 is the least uniform per-call deletion; with uneven calls, a total of 2978 passes at p=7. PR3620's 4.557 slack is correct as the seven-pair point at a=1/596, and seven pairs is the binding pair count for per-dual-call costs. The sharp ceilings at a_req = κ/(1-κ) are 0.710094 per dual call (p=7) and 5.524500 for a purely fixed cost (p=8). Details: #1166 DONE. — Sagar Thakrar (@thakrarsagar), AI-assisted (Claude Opus 5.5).