Classify and encode the exact correlated P104 producer entrance

[Clear1nsight]

Why this is needed

PR #3426 characterises ideal correlated admission at the first P104 collector cut, but leaves the actual stagewise integrality conditions open. Final cancellation alone does not ensure that the literal fractional ADDs and native pairs execute exactly.

This package, research/p104-stagewise-entrance, answers that handoff on the authenticated 257-event producer dependency cone. It follows the claim in Discussion #2750, task p104-side-correction, priority revision 6, with the explicit scope change retained in TASK.json. The base is canonical main 6f100d4bb5083f8c35d96fd95a539811c62f245c.

What this contributes

1. A necessary-and-sufficient stagewise entrance

All 58 initial banks belong to the Gaussian Newton lattice B9, with arbitrary admitted dirty D/Q inputs. Chronological partial sums separate the 52 Y banks into 32 intervals without a D transport, 15 intervals with one actual rank-one D transport, and five terminal coordinates.

Writing pi = 1+i, the two nonterminal weighted Newton profiles have exponents max(4-|S|,0) and max(4-|S\{0}|,0), pulled back through their actual frame histories. The terminal condition is 4B9. The complete entrance has index

2^(32*187 + 15*280 + 5*2048) = 2^20424

inside B9^52. It is strictly between (4B9)^52 and the predecessor's ideal terminal-only entrance, adding an index factor of 2^10184 beyond the latter. The full Gaussian quotient and the algebraic necessity/sufficiency proof are supplied.

The contract requires integral fractional-ADD increments, every literal native pair to equal its ideal complex-linear gate, and all six cut arrays in B9. It permits intermediate arrays outside B9. It does not classify genuinely rounded paths with later cancellation or execute the 1,768 omitted events of the full 2,025-event prefix.

2. A reversible parameterisation of the entire entrance

An explicit encoder maps 52 owned arbitrary Gaussian coefficient banks onto the complete admitted Y module. It executes each local Newton/diagonal profile, the actual inverse frame paths and extra inverse right wrappers, then groupwise backward differences. Its inverse reconstructs partial sums and rejects unavailable exact divisions. The six already admitted dirty D/Q banks remain separate inputs.

This changes the numerical source coordinates. A paid caller still needs an input/output intertwiner, a returned-source and frame contract, and ownership/restoration accounting. The Python references do not claim a measured physical in-place implementation.

3. An explicit logical cost and width bill

The preparation uses 158 native occurrences of total rank 281, 71,936 native pairs, 331 wrappers, and 159,020 direct Gaussian payload SWAPs.

Category	Encoder	Decoder
Real ADD/subtract subtotal before SWAP and phase lowering	1,133,456	1,123,216
Native real floor-halves	287,744	287,744
Additional exact real halves	0	270,224

All actual wrapper phases and movement are separately itemised. The optional fully lowered component-arithmetic schedule explicitly permits source-minus-target overwrites, so it is not the repository's stricter ADD tariff. Conservative work bounds are 612480H < 2^20 H for coefficient height H, and 98304J < 2^17 J for decoding admitted Y height J, plus signed storage.

These are constructive upper bounds. Physical copies, routes, control, owners, widths of the surrounding caller, and the full recursive bill remain unpriced. The conditional unchanged-profile 599/584 stop remains in force. No supplier or improved kappa is claimed.

Evidence and reproduction

The package contains the proof, explicit codec, primary literal evaluator, separately written independent evaluator, independent source-cost counter, strict receipt checks, retained sources, and three concrete next questions.

• Both implementations construct a dense signed 58-bank fixture through different actual paths, agree on initial and cut hashes, and each checks all six full-array cut formulae. All 90,624 literal/ideal native pairs and 52 exact quarter reads pass; all 52 codec roundtrips pass.
• Every one of the 512 basis directions in each nonterminal local profile receives an independent threshold check. The written proof supplies universal necessity/sufficiency; these finite checks do not substitute for it.
• Ideal-admitted negative controls fail first at the quarter at event 1087 and the native pair at event 1089, with matching module rejection and separately evaluated failure kinds. The credited PR Research: prove the correlated P104 ideal entrance #3426 paired-64 family passes the cone with zero cut.
• Normal and optimised registered Python 3.12.14 replays pass with the same complete typed receipt. Metadata and source pins pass. Separate optimised CLI processes reject a missing WORD, a corrupt WORD, and Boolean true replacing integer 1 in the receipt, each for its intended reason.
• The tested-tree read-only Git-free export passes with Git unavailable. All 26 exported files, including its manifest, retain their hashes, sizes, modes, inodes, and modification times.

python3 -B scripts/research_package.py --package research/p104-stagewise-entrance
python3 -B scripts/check_research_commit.py --package research/p104-stagewise-entrance --check-source-history

Public head 4e4b08c689242f7f3be2e5e08dc1ae8d728ff920, tree 908f3d09759d093df159d2fa8918e87f1aa72277, is byte-identical to the locally replayed tree. The public commit and strict source-history check pass for all 25 package/input files, and its portable export passes inventory verification. All 25 public exported source files match the Git-free replayed export byte for byte; only its commit-identifying export manifest differs. The four copied predecessor sources are retained byte for byte in public ancestor 091386d3632eb084eb264b293d6b7eb520fe2e3b.

Receipt file SHA-256 is 91b4f644189bacdd19952e360d55d3738a915e50cf98001baf7f47fda54bd561; its canonical scientific digest is f2ec5be0707ab21f9f7fae68ebb91e862c8ee8eff094fc2e62b37af39b9a0f49. Complete native covariance is inherited from PR #3416 and is not recertified here. No independent human or formal proof-kernel acceptance is claimed. Hosted CI is not yet claimed.

Coordination, concurrent work, and credit

The submission checkpoint completed all four open-PR pages, 368 records, with unchanged main. A final bounded delta check at 02:49:58 UTC, 18 October 2026, read the 11 new bodies #3455–#3465 through the unchanged #3454 boundary. Targeted Discussion #2750 and #1166 refreshes were read. This is incomplete for the full Discussion corpus, historical diffs, and unpublished work, and is not a novelty certificate.

Nick Petalas's concurrent PR #3449, head 5cb2ff187a27de1cbd1a37933f7228b35b15702b, independently proves the sharp index-280 profile for the particular Y27/Y26 rank-one window. Its exact proof was read at submission and agrees with our local profile. Credit is explicit, with no priority claim. This PR adds the general 58-bank entrance, all 52 independent partial-sum coordinates, the actual-path encoder/inverse, and their direct invoice.

Hiroki Kumazaki's PR #3446 recipient closure, Nick Petalas's PR #3448 all-depth product entrance, and the newer PR #3462 normalised omitted-endpoint completion are complementary. Their full proofs and executables were not replayed here; their physical and caller obligations remain separate.

Clear1nsight, with substantial OpenAI assistance from four concurrent mathematical, implementation, and coordination agents. Credit remains with ywz65/PR #2586, Arham Tahir/PR #2665, Clear1nsight/PR #3382/#3423, Nick Petalas/PR #3416/#3426 and concurrent #3449, Tekalign/PR #3025/#3218, Ross Richardson/PR #3068, and Jose Manuel and Vasek W for the inherited unchanged-profile stop. Apache-2.0 and predecessor notices are retained.

Open obligations

The next useful steps are a named caller with proved coordinate and return equations, admission for its additional histories outside this cone, and a changed fully charged supplier screen. The selected frontier is unchanged. This contribution releases its scoped claim without reserving any of those follow-ups.

[Clear1nsight]

Portable source export and hosted verification

The registered package workflow passed for head 4e4b08c689242f7f3be2e5e08dc1ae8d728ff920, including the bounded package replay and unchanged-input check.

The attached ZIP contains all 25 committed package/input files plus the export integrity manifest, so review needs no full repository clone. Extract it and run from its root with Python 3.12:

python3 -I -B research/p104-stagewise-entrance/verify.py
python3 -I -O -B research/p104-stagewise-entrance/verify.py

ZIP SHA-256 is b7ff1d3058b224db9266ebd7a922a8b7e44e0d19a58df2258c091e49faf9ff9a. Its 25 source files match the tested public tree byte for byte. The scientific receipt digest is f2ec5be0707ab21f9f7fae68ebb91e862c8ee8eff094fc2e62b37af39b9a0f49.

The canonical claim is DONE/released. A newly observed complementary PR #3466, head 5b240fb98ae187f336b247fb45e59037af131c17, resolves full-prefix admission for the fixed two-source family. Its PR body was read after publication; its proof and executable are not imported evidence here. This contribution retains the general 58-bank/257-event cone scope, with caller, omitted-history and paid-profile obligations stated in the package.

p104-stagewise-entrance-source.zip