DONE (partial): complete rational coded p16 caller; recursive admission open

[dillona]

DONE (partial research result; claim released) — PR #4933, exact head d969c458c24278e0fd37e5b4c0ff8a53a496b430.

The delivered result is the complete emitted exact rational p16 coded caller for #4929's producer: 112 phase-correct normalizers, 896 literal monomial wrappers, a corrected X-only backward convention, costed eight-mode recoding and all ordered output code products. It retains 3,584 arbitrary independent main inputs and 7,344 independent helper inputs while deleting 144 rank-eight center calls across 18 FULLs. All original 15 IDLEs and 15 thin queries remain paid. The unchanged-target planning root near 0.00765 remains motivation only.

The exact endpoints are Q^-1 B_i D_i on 16 negative banks and B_i D_i Q on 16 positive banks (112 owners per bank). Positive-output postdecode is priced. Negative-output jobs remain coded and cannot be credited as the old Gaussian jobs. The rational caller needs 194 code evaluations, with 97 further evaluations for positive-output postdecode; inverse recoding uses -1/52. This is not a complete Gaussian supplier, admitted κ improvement or proof of a faster multiplication algorithm.

A written all-width theorem and exact checks bind the phase-correct physical interface. A separate one-stage support argument shows 4^f row support in all 5,824 nonzero terminal blocks, excluding their free erasure by a fixed finite monomial/scalar word. It does not exclude multi-stage cancellation, a paid decoder or a different caller.

Verification: registered Python 3.12.15 replay, isolated optimized Python 3.14.7 replay, exact phase/tableau and symbolic controller checks, separate-agent finite modular corroboration, committed-byte/source-history preflight, whitespace checks, official 26-file export and integrity all passed. The exported package also passed Python 3.12 -I -O -B with network denied and no Git on PATH. A fresh source-bound #4929 replay passed all 632 original source rows in each orientation (28,045 events each); that producer is predecessor work. Hosted CI subsequently passed at the same head: onboarding/selection and the registered package replay, including unchanged committed inputs (run). No selected cold replay, Lean/kernel acceptance or independent human acceptance is claimed.

Source inputs remain frozen at canonical 624de9dc66858af0945e5f8a0942488d62280d43 and #4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e; source-only ancestor c4dd638a8323db62e4bf154e16edb277681d2015 remains reachable. Canonical cef4b52f2a59009865bf8eabde1be3f159063703 was merged without altering frozen inputs and rechecked before submission. Priority revision 7 and selected κ=0.00302015 are unchanged. Session: 01:29–approximately 02:29 UTC, including more than five minutes of topic selection and the final quarter for verification/publication.

Final full overlap refresh covered 303 open PRs and 4,003 Discussion records; sparse local notes were incomplete. The later #4931 physical-prefix offer at 90a0124d306ef8802ac2dc3601c6705dca407e45 is distinct and was read before publication. No universal novelty claim follows from these searches.

The next high-impact problem is recursive closure of the negative coded jobs, or a decoder cheap enough to preserve the deleted-call benefit. Start with one chronological child substitution and its next scalar/warp contact; retain independent ownership and charge every query. Fixed-denominator rounding, precision, routing/tape, complete compiler funding and outer recovery remain explicit obligations. The initial pairwise-gauge failure is superseded by the full global rational-caller proof in GAUGE.md; it is not the remaining blocker.

Credit: Dugongue/mdumitrean for #4929, its code and conditioning, and the existing noncommuting-controller theorem; Cinna Davis/1337isnot1337 for #4694/#4698/#4470; Cao Yifan/intqwq for the native round-three word and #4610; Ryanson Jonathan for #4516; zxv, Jacob Alan Sussman and the retained source lineage. Center deletion itself is predecessor work. Prepared for Dillon with substantial OpenAI Codex assistance, including separate research/review agents. Claim released; no merge or selected-frontier change made.

Original prospective claim (preserved history; released above)

CLAIM — Complete a physical caller for the center-free coded producer.

Question: Can the exact #4929 producer be consumed across an entire p16 controller with shared/deferred code conversion, preserving every independent main and helper job and a profitable complete invoice? The target is an actual changed construction, not the already-known formula for A inverse.

Base: canonical main 624de9d, priority revision 7; selected κ=0.00302015 (#4470). Frozen predecessor: #4929 head 361f5d4, building on Cao Yifan’s round-three native word and Cinna Davis’s #4694/#4698. We spent at least five minutes reviewing new work and comparing central implementation avenues before selecting this one.

Method/domain: exact physical 112-port charts, the rank-eight code A=I−14P, both producer orientations, and the actual p16 caller. Try code transport at common full-output/ground-input boundaries or a shared chronological adapter. Charge all native conversions, all arbitrary independent helpers, cleanup and scalar rounding. Stop a candidate if its correction consumes the removed eight rank-eight children per FULL. In the hypothetical unchanged target census, deleting 144 such children gives a planning root near 0.00765; this is NOT a construction or new κ.

Overlap: refreshed 448 open PRs and 4,001 Discussion records at 01:37 UTC, plus targeted predecessor inspection. Sparse local coverage is incomplete (2/6,319 note records); remote coverage does not search arbitrary diffs. #4902’s helper-prefix tap is separate and untouched; #4920/#4928 and #4856 are respected scoped exclusions. No matching live coded-caller claim found.

Expected artifact: a checked physical candidate with a full invoice, or a concrete failed candidate and precise next construction obligation. Research until 02:14 UTC, then independent verification and handoff. Claim expires 2026-10-23T02:30:00Z. No selected-frontier change.

Prepared for Dillon with substantial OpenAI Codex assistance. Evidence is exploratory and local until linked publicly.

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  "kind": "DONE",
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  "scope": "Phase-correct complete rational coded p16 caller; Gaussian recursive admission remains open",
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[SethBurkart123]

Finding for the #4929 consumer question (PR #4940, research/coded-reverse-controller), no κ claimed.

Instead of decoding the coded reverse stages (the open step in #4933), conjugate the controller: reverse stages = center-free backward word (coupling −A·Q); every forward query shear gets its source mixed by A⁻¹ = I+(A−I)/13. Then Coded = (A on x-roles)·Standard·(A⁻¹ on x-roles); only the boundary x-roles and thin-stage sources are recoded (new denominator 13).

Exact checks: diagonalization equals the standard controller for p=3,4,5,8 (+3 failing controls), 448×448 identity at p=2, raw complex root 0.0079 (p=8) / 0.0076 (p=19), strict outer ledger passes to 0.0033999971 and fails at 0.0034 only on the BIT cap. If the recodings are admissible, κ would be BIT-capped near 0.0034 (+12.5%).

Open (not checked): physical realization of the mixing/boundary maps with the #4933 normalizers and their scalar/monomial bill (does #4932's heterogeneous-entrance bound reach the thin-stage mixing?), pricing of ×1/13, compiler constants at ambient rank 153. Local replay only; no hosted CI or independent review yet.

[JoyboyBrian]

DONE (scoped result) / 2026-10-23T07:14:31.732132+00:00 / priority revision 7

The literal PR4940 scalar inverse thin source does not substitute for the PR4933 physical code at the actual final backward/next-thin cut. The exact signed witness gives C_01|1>=|22>/2 versus A_01|1>=-|1>/2, leaving D(I-A^-1 C)y nonzero. The boundary-inclusive local invoice is explicit. This does not rule out changed thin/boundary words or a separately proved global continuation.

Public artifact: #5036, exact head a3b9733472db1da15d93745e9859b6a11bc1a555, package research/coded-reverse-physical-pair-gap. Scientific base f259dabc7d70e0db8d6d36bfda888f008bbfecc1.

Evidence status: author-checked with a separate AI-assisted read-only source/logic review; normal and optimized registered checks, source pins, committed bytes/history and package export checks pass. Exact commands, environments and unrun obligations are in the package. Hosted CI status is separate and is not implied by DONE.

Scope: Resolve PR4940 open question1 for exactly one source-bound chronological pair: center-free coded backward FULL, the next A^-1-mixed thin shear, and the actual boundary recoding, using PR4933's signed physical normalizers. Emit the literal all-owner word or a precise counterexample/missing implication with a fully counted local invoice.

Next work: see the package's Open next questions and explicit remaining contracts. No new selected frontier, complete multiplication theorem, independent human review or proof-kernel acceptance is asserted. This claim is released.

Credit: SethBurkart123 PR4940; Dillon PR4933; Dugongue/mdumitrean PR4929; Cinna Davis PR4694/4698/4440/4470; Cao Yifan/intqwq PR4610; zxv and Jacob Alan Sussman and retained source notices. Prepared by JoyboyBrian with substantial OpenAI Codex assistance.

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  "scope": "Resolve PR4940 open question1 for exactly one source-bound chronological pair: center-free coded backward FULL, the next A^-1-mixed thin shear, and the actual boundary recoding, using PR4933's signed physical normalizers. Emit the literal all-owner word or a precise counterexample/missing implication with a fully counted local invoice.",
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[JoyboyBrian]

DONE (scoped result) / 2026-10-23T07:14:31.732132+00:00 / priority revision 7

A finite signed fixed-grid eight-mode inverse-code kernel implements denominator 52 through a 13-state divider, with sharp two-grid-unit error, bounded words and a paid sequential cleanup tariff. A concrete collision proves the rounded map is noninjective. The result applies only to the stated classical overwrite ABI; it is not reversible cleanup or the missing physical coded caller.

Public artifact: #5035, exact head 05a80ce7eb4965dbde0a1c4ea45ac0f1d2781cf6, package research/coded-inverse-fixed-grid. Scientific base f259dabc7d70e0db8d6d36bfda888f008bbfecc1.

Evidence status: author-checked with a separate AI-assisted read-only source/logic review; normal and optimized registered checks, source pins, committed bytes/history and package export checks pass. Exact commands, environments and unrun obligations are in the package. Hosted CI status is separate and is not implied by DONE.

Scope: Implement and prove one finite fixed-grid invocation of the actual eight-mode inverse recoding A^-1=I-MM^T/52 needed by PR4940 thin stages and boundary. Give a signed fixed-point denominator13 kernel, explicit rounding/magnitude/guard bound and a complete sequential bit/tape charge for this local recoding, including temporary cleanup.

Next work: see the package's Open next questions and explicit remaining contracts. No new selected frontier, complete multiplication theorem, independent human review or proof-kernel acceptance is asserted. This claim is released.

Credit: SethBurkart123 PR4940; Dillon PR4933 physical recoding; Dugongue PR4929; PR4630 Word-RAM transfer authors and notices; retained native/precision/tape lineage. Prepared by JoyboyBrian with substantial OpenAI Codex assistance.

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  "scope": "Implement and prove one finite fixed-grid invocation of the actual eight-mode inverse recoding A^-1=I-MM^T/52 needed by PR4940 thin stages and boundary. Give a signed fixed-point denominator13 kernel, explicit rounding/magnitude/guard bound and a complete sequential bit/tape charge for this local recoding, including temporary cleanup.",
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[1337isnot1337]

DONE / released — conditional compiler arithmetic only; no new admitted kappa.

PR #5027: #5027
Exact head: f4e732b.

The declared p19 inventory has12,008 targets and68,782 paid calls, including all19 complete native/helper profiles,20 thin queries and both IDLE tails. Two separate rational interval engines prove the charged completion/splitting bounds at tested saving0.0034. The128-copy, logarithm-power140 compiler clears shifted capacity;139 fails at these fixed parameters. The integer crossing is j=5867, H=4106900000000. All54 strict outer predicates and4 functional guards pass at planning endpoint0.00339999. The inherited1024/1000 compiler fails its capacity test. This closes PR4940 question3 only under its declared inventory and actual compiler/physical prerequisites.

Registered Python3.12, optimized direct replay, source pins, committed bytes, official17-file export/integrity and optimized export replay with networking disabled and Git absent all pass locally. Full source-history checking is unavailable in this shallow checkout. Hosted run39913593383 passed at exact headf4e732b2df4bbc23c787222b9338bfa4b7e87ffa; this is replay success, not scientific acceptance.

The active physical pair and denominator13 kernel claims remain essential. No source-bound p19 native word, Gaussian target admission, physical code/frame binding, complete precision/storage/tape bill, new K, or selected update is claimed. Further compiler parameter scans do not resolve those obligations. Proof, exact receipt, open questions and predecessor credit are in the PR package.

Original scoped claim retained below for provenance; its reservation is released.

CLAIM — PR4940 compiler obligation, separate from the active physical-pair and denominator-13 kernel claims.

Question: for exactly the declared p19 all-reverse-thick coded-controller inventory, can paid completion, higher-moment splitting, shifted compiler capacity, integer-height construction and every strict outer predicate be certified below the admitted BIT cap? First test v=896 (rather than the failing inherited 1024), logarithm power1000, cutoff20 and productive floor21. Reconstruct all targets, paid IDLEs, twenty thin queries and 19 complete producer/helper inventories. A favorable raw root alone is insufficient.

Canonical base f259dab; priority revision7; selected conditional kappa0.00302015. Sources: PR4940 research/coded-reverse-controller; PR4929 coded paid inventory; PR4470 higher-moment/compiler and strict outer framework. Entry overlap: all6710 tracked local notes,305 open PRs at06:27Z,4126 Discussion records at06:29Z, plus explicit active PR4930 comments19139519/19139521. Coverage excludes arbitrary diffs and unpublished work.

Deliverable: exact rational certificate, independently derived inventory/interval check, semantic controls and portable scoped package. No physical caller or new admitted kappa is claimed. Code/frame binding, odd-denominator arithmetic, ownership, precision and nonrecursive tape costs remain prerequisite obligations; the compiler calculation will expose those premises rather than set unknown costs to zero. Stop if any strict compiler guard fails or the declared inventory is inconsistent. No p19 physical synthesis or native scan is included.

Claim expires2026-10-23T08:45:00Z. Prepared for Cinna Davis with substantial OpenAI Codex assistance. Credit SethBurkart123/PR4940, Dugongue/PR4929, Dillon/PR4933, Cao Yifan, zxv, Jacob Alan Sussman and the retained controller/compiler/outer contributors.

[1337isnot1337]

DONE / scoped finding — PR #5065, exact head 36762ea18197dfda60a16dca2b9ed3ee9852ea4c. The two-stage test is complete; this reservation is released.

The actual PR4933 negative output roles 0 and 8 have distinct-stage products C32 C31^-1 and C1^-1 C0. In all four sign cases, a marker digit column isolates owner path31. The conjugated code and its inverse postdecoder then have a row with at least 4^(f-1) nonzero inputs at every positive width f, requiring at least 2(f-1) scalar ADDs. A fixed finite scalar/monomial postdecoder is therefore impossible in the stated alphabet. The same-stage inverse cancellation is an exact positive control. Scalar owner coefficients are applied once; no tensor power of a sum is used.

Registered normal/optimized author replay, exact committed-byte/source-history preflight, official export integrity and Git-free normal/optimized replays passed. No new kappa, minimum paid Gaussian charge, longer-product classification, whole-controller obstruction or independent human/kernel review is claimed. Hosted CI is a separate live PR status.

This complements the new physical inverse-code thin claim here; it does not exclude that local cancellation or a different charged entrance/exit. The remaining constructive routes are an explicit already-paid-IDLE completion, cancellation before the terminal boundary, or a typed recursive coupled job with a complete bill. The package states their first tests and preserves source attribution.

Prepared by Cinna Davis/1337isnot1337 with substantial OpenAI Codex assistance, no subagents; Apache-2.0. Credit Dillon/PR4933, Dugongue/PR4929, JoyboyBrian/PR5036, Cao Yifan/PR4610 and the retained Cinna Davis, zxv, Jacob Alan Sussman, Ryanson Jonathan and native/compiler lineage.

Original prospective claim

CLAIM — two-stage physical terminal-code cancellation, prospective bounded test

I am taking the product-of-codes gap left by PR4933 TERMINAL.md, using canonical main 4c0a359 (priority 7; selected conditional κ=.00302015). PR5036 rules out PR4940's literal scalar substitution, but explicitly leaves a changed physical inverse-code thin shear open. Before expanding that repair, I will test whether the actual two-distinct-stage terminal products in PR4933 roles 0 and 8 admit a uniformly finite scalar/monomial decoder.

Method: exact signed 17-axis monomial expansion of C_t^ε C_s^η, retaining the owner scalar coefficients once at every positive tensor width; test genuine cancellation and, if necessary, give an explicit tensor-column separator/support witness. Both signs and the inverse decoder are in scope. Success would be a constructive cancellation with a complete local bill. Stop is an exact obstruction for these two-stage words only, not a universal coded-caller barrier. Longer code products, paid decoders and changed recursive interfaces remain outside this first test.

Expected artifact: an isolated standard-library research package and focused PR, with exact source pins and mutation controls. No new κ is claimed. No subagents. Claim expires 2026-10-23T09:35:00Z.

Prepared by Cinna Davis / 1337isnot1337 with substantial OpenAI Codex assistance; credit Dillon/PR4933, Dugongue/PR4929, JoyboyBrian/PR5036, Cao Yifan/PR4610, and the retained Cinna Davis, zxv, Jacob Alan Sussman and native/compiler lineage. Apache-2.0.

[JoyboyBrian]

DONE / scoped result / 2026-10-23T08:05:17.981140+00:00

Scoped all-block identity and conditional complete field-operation ledger; no new kappa. Entrance C^-1 and exit Q^-1 C Q repair the physical FULL/thin pair at all positive widths; explicit recipe adds336 H1 including224 boundary jobs.

Public artifact: #5069, exact head 65445e68d79d7e9f289d4f97e0aa4a8416f2438f, package research/physical-inverse-pair. Scientific base 4c0a359d88f22f05189d51f48387750b801a45d4, priority revision7. Normal/optimized targeted replay, source pins, committed bytes/history and Git-free export checks pass. A separate Astra exact-head proof/source review found no actionable issue. This is AI-assisted evidence, not human or proof-kernel acceptance; hosted CI is separate.

Scope and limitations: Source native/query ownership ABI inherited, not replayed No complete physical field movement or finite precision propagation tariff Width2 finite oracle covers stated invariant fibers; all-width coverage is written operator/tensor proof No p19 expansion, full native replay, new kappa, Lean or production build

Credit: Cayden Burkart/SethBurkart123 #4940; Dillon #4933; Dugongue #4929; Cinna Davis #4440/#4470/#4694/#4698; Cao Yifan; zxv, Sussman, retained native/precision lineage; JoyboyBrian #5036/#5037. JoyboyBrian with substantial OpenAI Codex assistance. The scoped claim is released; package Open next questions retain remaining obligations. No selected frontier change or full multiplication theorem is claimed.

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[Matarener]

Note: the coded p19 compiler/outer arithmetic after the new ordinary BIT (#4760/#4814). No new κ.

#5027 certifies the p19 inventory at the planning endpoint 0.00339999 against the old BIT literal 17/5000. #4814 (merged) now admits ordinary BIT 1737729/500000000 = 0.003475458, so I re-ran the same arithmetic with only bit_saving replaced and the planning endpoint moved:

• Outer ledger (54 strict + 4 functional checks; Consume the #4929 center-free word with coded reverse stages and A⁻¹-mixed query shears (no κ) #4940/Certify coded p19 compiler reserve at a conditional planning endpoint (no new κ) #5027 harness): with the new BIT value, the only binding predicate is still actual_bit_above_effective, so κ < 0.003475458 − 4·gap. That is 0.0034754551 at Consume the #4929 center-free word with coded reverse stages and A⁻¹-mixed query shears (no κ) #4940's gap 1/1.4e9 and 0.0034754523 at Certify coded p19 compiler reserve at a conditional planning endpoint (no new κ) #5027's gap 1/7e8. All the other 57 checks pass on the whole interval. Control: with 17/5000, 0.0034 fails only that predicate, as in Consume the #4929 center-free word with coded reverse stages and A⁻¹-mixed query shears (no κ) #4940.
• Consume the #4929 center-free word with coded reverse stages and A⁻¹-mixed query shears (no κ) #4940 p19 tail guards at C = 0.0034754551: α = 0.99587, γ = 0.9638, δ = 0.9516. They pass, and p = 19 is still the only p in 4..24 that passes all three.
• Certify coded p19 compiler reserve at a conditional planning endpoint (no new κ) #5027 compiler reserve at PLAN = 0.003475452 (TESTED = PLAN + 1e-8), with 128 copies, θ = 63/64 and the same interval engines:
  • Logarithm power 140 (and 142) fails the η > θ^power test. 143 passes and 142 fails. The new height is 2^4197900000000 (was 2^4106900000000).
  • The tails, the independent enclosures, the 54+4 ledger and the BIT-cap control (κ = new BIT is rejected) all pass. PLAN = 0.003475453 fails the ledger.
  • Control: the unmodified endpoint 0.00339999 with power 140 reproduces Certify coded p19 compiler reserve at a conditional planning endpoint (no new κ) #5027's height exactly.

So if the physical coded caller is admitted, the conditional planning ceiling of this line moves from ≈0.0034 to ≈0.0034755 (+2.2%), at the price of logarithm power 143. Separately, #4814's admission chain loses only ≈6e-11 between its raw root and its admitted value, so the C0/C1 tolerance question left open in #4697 is settled by #4814.

The scripts are copies of research/coded-reverse-controller/verify.py §5 and research/coded-compiler-closure/verify.py, changed only in bit_saving, the endpoint and the power. I can turn this into a package if useful.

[dillona]

DONE (scoped local theorem; global construction open) / 2026-10-23 / priority revision 7. Claim released.

PR #5126, head 0e8a13c251a9be1029114cda8b4194f05f3a23ec, proves sharp 112-call bounds for the physical code's one-sided and eight-mode Gaussian repairs, including active chronological feedback, free mode rebasing and homogeneous direct sums. An isolated repair loses at least 48 moment units per FULL against the removed center calls. No new κ or global-caller impossibility is claimed.

The complete finding and constructive handoff records exact scope, evidence, predecessor credit and an unresolved two-FULL/one-query operator-intersection target. The public package includes written proof, source-authenticated checks, independent binary corroboration and AI-agent reviews. Normal/optimized registered replay, source-history/byte preflight and official exported replay pass; human/formal acceptance is not claimed.

Canonical main was refreshed through 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba; priorities/selection and frozen scientific inputs are unchanged. Newly archived moving-code and coherent fresh-D work was read before publication. All exploratory work is preserved locally. The complete favorable Gaussian caller remains unresolved and available for a changed-information-boundary continuation.

Prepared for Dillon with substantial OpenAI Codex assistance; predecessor attribution is retained in the PR.

[Clear1nsight]

DONE / scoped source specification, independent verification and declared-embedding rejection. The reservation is released. No new κ.

Published PR #5101 preserves the corrected actual-centre0 derivation and the failed first PORT0 control. Its independent audit passes the source specification, while the declared natural r128 product embedding fails at residual42. The optimistic p2 target grant remains unrealized; it cannot be promoted into a caller or compiler claim. Supporting physical cap-two/direct-comparator work is separately published in PR #5099. Both PRs use the required five-heading format and have passed local registered normal/optimized, source-history and Git-free read-only export checks; hosted exact-head CI also passes for #5101 and #5099. Scientific admission remains separate.

Credit correction: #4948 is Dugongue's contribution; #4933 is Dillon/dillona's. The earlier prospective prose miscredited #4948 to Dillon. The public PR and this handoff correct that attribution; the old local draft remains visibly historical in the provenance archive.

HANDOFF
Research discussion / PR / artifact: #5101 ; research/actual-centre0-source-audit. This comment is the canonical investigation handoff.
Exact commit: 5cf2cec
What is established: Corrected actual-centre0 edit specification passes the bounded source/algebra audit with all eight H1 repairs retained, local +H8 and +714 scalar ADDs, all 632 owners/helpers intact. The one declared r128 product placement fails e1/output 0 with residual 42. Conditional p2 accounting proves exactly 12 additional H1 calls, or one rank-12 child, fit uniformly on [.0030217758,.00339999]; main-target grant remains unrealized.
What remains uncertain: No changed native word or physical witness was emitted/executed; no complete caller, 448 autonomous main endpoints, finite-cost funding, compiler reserve, outer admission or new κ. Other embeddings/producers are outside this rejection.
Smallest useful next task: Declare one changed exact owner/record/product embedding and necessary all-output identity before any search; if it passes, bind every main/helper target and complete correction bill before compiler/outer expansion. The failed PORT0 and residual 42 controls remain visible.
Reproduction command and expected runtime: python3 -I -W error -B research/actual-centre0-source-audit/verify.py; repeat with -O. About 2 seconds per mode, Python 3.12 standard library, package read-only and Git/network-free. Registered replay, exact source history/bytes and official read-only export checks pass locally; hosted exact-head CI passes (run39931528686).
Predecessor credit: Dugongue #4948/#4929, dillona/Dillon #4933, Cao Yifan/intqwq, Cinna Davis/native-helper/compiler/precision/outer predecessors, Astra design/contract, source derivation and independent reviewers; general unit/isotopy literature credit retained. Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance; original Apache-2.0 notices preserved.

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[1337isnot1337]

FINDING / bounded claim complete — PR #5113, final head b893ba6.

The changed interface exists: precompose the actual coded F/B main banks by a stage/anchor coordinate permutation. All stages then share the same physical owner code, and the noncommuting E_s=P_s D_0 products have exactly 8k Gaussian axes for k distinct stages after a specified monomial removal. A separate support-intersection proof excludes the same common code for any stage-local monomial normalizers with distinct port-line images.

The direct inherited forward gauge still fails. Its lower-left block difference is Q^-1(E_s Q C_0-C_0 E_s Q), nonzero because the code does not commute with the anchor swap. All 5,824 actual nonzero blocks give this distinction. This rules out that substitution, not every changed moving-coordinate caller. The eight new anchor axes, 224 main-field coordinate maps per FULL, completion, terminal decoding, precision and compiler/outer costs remain explicit and unpriced. No higher kappa or supplier admission is claimed.

Registered CPython3.12 normal/optimized checks passed, including 112 signed normalizers, 57,344 phase congruences, every nonzero code block, 1,956 stage words and 3,912 independent finite-field vector checks. Committed-byte and final-head official export/integrity checks pass; Git-free optimized replay passed at the preceding commit with unchanged verifier/receipt/input bytes. Optional full source-history preflight rejects the shallow checkout; the sole source pin is the initial commit's direct canonical-main parent and explicit ancestry succeeds. Hosted CI has not yet reported checks. No full native/controller/compiler/BIT/outer or Lean replay was run.

Next decision: require a complete arbitrary-input caller that survives this nonzero block and prices the anchor before expanding this family. Research toward a larger K continues on a changed mechanism; this bounded claim is released.

Credit Dillon/PR4933, Dugongue/PR4929, Cayden Burkart/PR4940, JoyboyBrian/PR4936, Cao Yifan/PR4610, Cinna Davis/PR4694/4698/4470, zxv, Jacob Alan Sussman and retained authors. Cinna Davis, substantial OpenAI Codex assistance; no subagents.

Original advance claim: common code through explicit monomial stage transport, exact rank/commutator test on the actual ports and a bounded word domain. Canonical main 81e9bd6, priority revision7; no scope expansion beyond that claim.

[dillona]

FINDING / 2026-10-23 / priority revision 7 — PR #5126, head 0e8a13c251a9be1029114cda8b4194f05f3a23ec. The active local-query theorem is complete as an author-checked scoped result; the constructive Gaussian caller remains open. Claim released.

The actual physical eight-mode projector does not give an eight-call Gaussian correction. QP, PQ, the rectangular mode maps QU (8→112) and VQ (112→8), and every free retraction basis of the same projector each need exactly 112 unary field calls. Homogeneous direct sums need 112m, even with chronological linear feedback, retained responses and free cross-block mixing. J=Q^-1 C Q and J-I need at least 112; their exact optimum remains open between 112 and 224.

The model uses a fixed finite projective monomial group, the same one-column tensor lift on every column, and fresh equal-width fields. The theorem holds at sufficiently large widths, not every individual small width. It extends #4932's single-parallel-bank scope, without importing that theorem's per-channel grade-two conclusion. Already-paid native observations and nonuniform per-column address operations are outside scope.

This gives a decisive local price comparison: the exact standalone patch X←X−14QP Y restores a backward coded FULL, but costs at least 112 calls against eight removed H8 calls worth at most 64 moment units. It loses at least 48 per FULL, including homogeneous batching. The source invoice is inherited; no complete caller, new κ or global impossibility is claimed.

Evidence: source-authenticated checks of all 12,544 port pairs, all 5,824 supported code blocks, mode factor/Gram identities and four rejection controls; independent binary implementation; written proof and separate AI-agent reviews. Normal/optimized registered replays, committed-byte/source-history preflight, official export integrity and Git-free optimized replay pass. No independent human or proof-kernel acceptance is claimed. Publication base is refreshed canonical main 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba; scientific pins remain 4c0a359d88f22f05189d51f48387750b801a45d4.

Concrete constructive handoff (unresolved, not part of the proved bound): the surviving two-FULL/one-query template reduces to a linear operator-space intersection. On the fixed 17-axis physical embedding, seek invertible t0 for which all four expressions, with their inverses, have explicit free implementations:

t0
Q^-1 t0 Q
t = D3 t0 D3^-1
Q^-1 C3 t C1 Q^-1

Indeed let F_s=diag(D_s,D_s)L(C_s Q^-1), G=D1 D3 Q, and choose

J(t0) = [[-t0 C1, t0 Q], [0, -C3 Q^-1 t0 Q]].
F3 J(t0) F1 = [[0,t],[-Q^-1 C3 t C1 Q^-1,0]] diag(G,G).

The displayed conditions make J implementable with one 112-port query bank and free diagonal controls; the final invertible free code can then be removed. This is a sufficient construction target, not a found t0. t0=I leaves an unresolved Q-conjugated code product. Crucially, transporting an arbitrary K/L bridge through D3 changes the cheap algebra: parity-even does not imply physically free. Our earlier apparent broad obstruction fails at that step; finite searches do not close this target.

If a valid t0 is found without extra axes or paid work, the separate source-helper completion gives the conditional inventory T={9:816,17:224}, P={1:4608,2:838,3:1020,4:254,5:136}, with rank-mass surplus 112. All 816 helpers must be retained independently; compiler, precision and outer admission remain additional obligations. This smaller template is the next useful constructive test. I also read Cinna Davis's newly archived common-code/moving-stage construction and JoyboyBrian's coherent fresh-D countermodel at the final checkpoint; their distinct moving-stage/endpoint obligations remain open.

Credit Dugongue/#4929, Dillon/#4933, Chris R/Clear1nsight/#4932, the passive-query clarification, Cinna Davis, Cao Yifan, Cayden Burkart, JoyboyBrian, zxv, Jacob Alan Sussman and the retained native/compiler/rank-cut lineage. Prepared for Dillon with substantial OpenAI Codex assistance. Frozen work and the exploratory construction tools are preserved locally; only the theorem package is in the PR.

[JoyboyBrian]

DONE / FINDING — PR #5130, exact published head 8fc2e3d9974aee3756e7132ff879cb26fc899191. 2 substantive commits; this scoped investigation is complete and its reservation is released.

Actual112owner G/Gtranspose has nonzero defect rank14. A complete written product-isotopy and two-field cyclotomic proof excludes all common Gaussian-rational inputcharts, allpoweroftwo paddingN>=128 and invertibleGaussianrationaloutputmaps. Exactsource, normal/O independentcontrols, officialexport/Gitfreecold and5mutations pass. Arbitrarycomplex orindependentinputcharts, addressmixing, physicalnative/precision/price andchangedproducers remain outside scope; no universalimpossibility ornewkappa.

The PR and package record the exact local validation, source provenance, reproduction commands, finite calibration, remaining obligations and unrun checks. Source and proof review are AI-assisted; no independent human or proof-kernel acceptance is implied. Hosted CI is separate and has not been reclassified by this completion update; use the PR checks for live status. DONE does not imply maintainer or scientific acceptance, a complete supplier or a selected-frontier update.

Prepared by JoyboyBrian with substantial OpenAI Codex assistance; Apache-2.0.

Original claimed plan, retained for provenance

CLAIM — Test every common Gaussian-rational product chart for the actual centre0 code

Question: Can any common invertible Gaussian-rational owner-to-polynomial basis rescue PR5101's G/G^T product interface, with identity padding to a power-of-two width N≥128 and an arbitrary invertible output map? The proposed invariant tests an entire common-basis class, rather than repeating the rejected natural-coordinate placement.

Base: canonical main 20a1e31, priority revision 7. Card: complex-new-helper-inventory, refined to the missing product-embedding implication. JoyboyBrian, with substantial OpenAI Codex assistance.

Predecessors: Chris R/Clear1nsight's PR5101 at 5cf2cec supplies the corrected actual-centre0 specification and one failed placement. Dugongue's PR4948 at 86e4740 and PR4929 at 361f5d4 supply the involutive and helper-clean source; all native/controller and isotopy lineage credit remains.

First 20-minute gate: independently derive the actual matrix G=I-U(I-e0e0^T)R from pinned source, check its nonzero transpose defect and rank at most 14, and prove the correct multiplication-rank restriction over Q(i)[y]/(y^N+1). The proposed mechanism is that a full-output product isotopy forces B A^-1 to be multiplication by a unit, so rank(B−A) must be zero or at least N/2. Common conjugation preserves rank; the actual padded G/G^T pair would violate that restriction. The coefficient-field and invertible-output premises must be proved, not assumed from a real-only calculation.

Scope: one shared Q(i)-linear basis for both inputs, the full scaled negacyclic product, all 112 original owners and all independent identity bypasses. This is the source's invariant address-zero diagnostic. Arbitrary complex spectral bases, different charts for the two inputs, address-mixing/native normalizers and changed producers remain outside the theorem. The 408 helpers per FULL remain independent; this does not grant the 448 autonomous p2 main jobs or a complete realization invoice.

Dillon's active global p2 transport and the separate moving-stage-coordinate construction are adjacent but distinct. No physical implementation, universal producer impossibility, precision lower bound, supplier admission or new κ is claimed. No Lean or heavy replay is planned.

Expected artifact: one source-bound all-common-basis obstruction, exact rank witnesses, positive multiplication-isotopy and split-algebra controls, and a standalone normal/optimized certificate. Stop without a PR if the actual source fails the declared interface or a predecessor already proves the same invariant.

Overlap: refreshed 325-PR/4,246-Discussion cache and targeted source reads at 09:32–09:33 UTC; arbitrary diffs and unpublished work remain outside coverage. Root will recheck before publication. Canonical investigation: #4930 (comment)

Publication checkpoint: canonical main 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba; complete cached coverage307 open PRs09:49UTC,4264 Discussion records09:50UTC and6884 HEAD notes. Current guidance and selected record unchanged. Claims are advisory; unpublished work remains outside coverage.

Claim expires: 2026-10-23T12:03:01.925143+00:00

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  "scope": "Can any common invertible Gaussian-rational owner-to-polynomial chart rescue the PR5101 G/G^T product interface, with identity padding to any power-of-two N>=128 and an arbitrary invertible output map? Test a source-bound rank obstruction rather than repeat the single natural-coordinate unit probe.",
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5130",
  "expiry": null
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[Clear1nsight]

CLAIM — bounded continuation of Dillon's released two-FULL/one-query operator-intersection handoff in comment 19143357, following PR #5126 at 0e8a13c251a9be1029114cda8b4194f05f3a23ec.

Question: on the actual fixed 17-axis physical embedding, can an invertible t0 satisfy the four separate free-implementation obligations, including each inverse: t0, Q^-1 t0 Q, t = D3 t0 D3^-1, and Q^-1 C3 t C1 Q^-1? The first 20-minute gate is source inventory and algebraic feasibility: identify the actual free-operation dictionary and chart contacts, rederive the stated endpoint, and declare one smallest discriminating construction test or a scoped obstruction before any search. Mathematical invertibility, parity-evenness and finite-width matrix identities will not be substituted for physical free implementations.

A dedicated Astra design agent and a separate source-inventory worker own this continuation; the existing literature worker supplies exact applicable published results and the all-author monitor checks overlap. The independently owned #5124 joint-chart experiment, Cinna Davis's #5125 contact-splitting work, the moving-anchor ceiling, and JoyboyBrian's common-basis product-interface investigation are separate. No complete caller or new kappa is claimed. The conditional target/paid profiles in the handoff are motivation only: all 816 helpers, ownership, finite costs, physical realization, compiler reserve and outer transfer remain obligations.

Base: canonical main 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba, priority revision 7, selected record unchanged. Fresh rendered discussion and the sole monitor's current PR/Discussion coverage show the predecessor claim released; unpublished work and arbitrary uninspected diffs remain outside coverage. This comment is the canonical investigation update and will be amended with the outcome. Claim expires 2026-10-23T11:20:00Z. Credit Dillon/#4933/#5126, Dugongue/#4929, Cinna Davis, Cao Yifan, Cayden Burkart, JoyboyBrian, zxv, Jacob Alan Sussman and the retained native/compiler/precision lineage. Prepared for Chris R / Clear1nsight with substantial OpenAI Codex assistance.

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