Construct a P104 dyadic tensor code and price repeated Gram stages

[Clear1nsight]

This changes the representation premise behind #3961: one invertible Gaussian-dyadic code retains all 21,632 data fields across both logical P104 Gram stages. With U=[[I,B],[0,I]], L=U_r U_c^-t and (Xhat,Yhat)=(LX,L^-tY), the transformed coefficients are P_r M_c and M_r P_c, M=UU^t. The code is shared at the internal boundary, retains the kernel payload, and restores fixed X/Y slots without division by 13.

The package supplies literal scalar words with entry and exit charged. Against its specified uncoded reference, two repeated uncorrected Gram pairs save 110,592 unit additions and 33,280 halves/restoring doubles each; one pair loses 104,448 additions. This is a common-chart protocol comparison, not a full-caller or native-cost improvement. Other uncoded factorizations may amortize too.

The full identity caller still requires coded coefficients N_r M_c and M_r N_c, N=M^-1. Each omitted side term has rational rank 10,816; that is algebraic rank, not a native tariff lower bound. The proof derives the ordered physical chart conjugates and records the unresolved native code, actual repeated consumer, identity completion, helpers, ownership, routing, precision and complete gate. No actual adjacent completed P104 pair is claimed and no selected-frontier files change.

A separate ring obstruction distinguishes this construction from a free spectral split: A tensor A has rank 64 modulo 13, while the proposed product 169 P_r P_c vanishes. Thus bank-separate invertible Gaussian-dyadic codes cannot realize that particular normalization. General bank-mixing codes and changed alphabets are outside the obstruction.

Validation: registered Python3.12 replay; source-authenticated P104 reconstruction and full scalar word; independent Fraction evaluation on 50 basis columns with 7 ordering/negative controls; seven optimized tests covering typed/duplicate receipts, corrupt/missing sources, altered donor restoration and readonly Git-free replay. At exact head a8a1d744811cd7d1f9c43ec7ccbae85ef9695b61, the byte/history preflight passes 14 declared files, registered replay passes, and official export/check passes. All three commands also pass under -I -O -B from a Git-free export with empty PATH and all 15 files read-only; their bytes and modes remain unchanged. Export SHA256: 7ee61e6477be20673fdc7c6ba8795c9c9606c633fe8e4be2948d763ad4ee7de8. Hosted CI remains a separate pending check.

Scope: 11 new files under research/p104-tensor-code/, based on canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90; all three executable inputs are already on main. Outcome is partial. Next work must pin an actual repeated physical consumer and price the explicit N-P side maps before expanding native construction. Claim: #3954 (comment) . Live overlap refresh covered all 676 open PR bodies including drafts; main remained unchanged at publication checkpoint.

Credit: Chris R / Clear1nsight, with substantial OpenAI Codex assistance and coordinated agent review. #3961 supplies the preceding mismatch and reused source-authentication/root construction; #3882/#3940/#3943/#3954 retain the caller lineage. ToikY owns #3956's adapter comparison and #3966's phase gauge, context only. Original P104/E8/native/compiler sources retain the credits listed in README. No pending PR object is needed for replay.

[ToikY]

CLAIM — independent all-coordinate scalar-word audit of PR3979 at frozen head a8a1d74. I will authenticate and reuse its word builders only as the object under review, certify every literal operation on the actual104-port instance by exact disjoint-fiber maps, then verify the full21632-coordinate block identities by separate exact tensor/Frobenius contractions. This adds actual-instance compositional coverage beyond the small-grid basis and actual dense fixtures; it is not a new code or a claim that those finite checks are a defective proof. Semantic mutations will target axis/owner/order/restoration and undercharged invoices. No native expansion, new repeated caller, supplier or kappa claim. Stop with a scoped exact certificate or concrete counterexample/remaining-obligation finding. Canonical main20ecf289 / revision6 refreshed; all684 open PR bodies including drafts over seven nonempty pages plus empty eighth and the repository helper checked, live handoffs and current PR comments read; broader closed/diff/Discussion coverage partial. Science cutoff08:43:59UTC, expected handoff08:58:59UTC, 2026-10-19. Credit Chris R/Clear1nsight PR3979 and its retained P104/E8/native/caller lineage. ToikY with substantial OpenAI Codex assistance, including separate AI math/test contexts; no human/kernel review. No merge or frontier change.

[ToikY]

DONE — independent actual-instance word audit published in #3996 at b8dd4e0. All 763,392 events across the four words, 1,056 fibers/eight local maps and 32 global blocks on 21,632 data coordinates check exactly, with separately reconstructed geometry and no reused predecessor evaluator/invoice. Original construction, algebra and savings remain Chris R/Clear1nsight credit. Registered replay, actual CLI semantic controls, byte/history preflight and read-only Git-free normal/-O export pass; hosted run39222334496 remains separately in progress. Source head a8a1d74 unchanged; no discrepancy found in this scope, no complete predecessor/native or human/kernel review claimed. Physical repeated consumer, charts/helpers, identity completion and full bill remain open. Claim released, no reservation. Canonical artifact and handoff in PR3996 / Discussion1166; no merge or frontier change. ToikY with substantial OpenAI Codex assistance.