Research: independently audit PR #3131's first paired P104 collector at tensor multiplicity two

[commdata2338]

Change and mathematical scope

Independent finite audit of the first paired P104 collector from PR #3131 at actual tensor multiplicity two: n = 18, N = 262144, rank 14, events 2025–2039. The predecessor tested complete actual collectors only at N = 512 and left this larger actual payload unchecked. Two separately written exact evaluators agree on the entire outgoing value, promoted query and working grid on four deterministic signed fixtures. The five dirty source arrays remain unchanged and the private collector returns to literal zero.

All 524288 forward wrapper columns, plus their inverses, are checked against an independent strided-column implementation. Two fixtures have nonzero rounding error; cancellation and zero-sum cases test the grid boundary. The original pair/inverse and error policy are credited predecessor constructions. The new contribution is the actual tensor boundary check, source binding and discriminating controls, not a new lifting identity, fast implementation or multiplication exponent. This checks the collector's defined semantics with new code: PR #3131's own nested evaluator did not finish at this size in two 600-second attempts, so its implementation is not compared here (see Validation).

The package research/p104-tensor-collector-audit/ contains the README.md derivation, the complete receipt RESULT.json and the task card TASK.json. Fast physical execution, clean-stock hosting, the full supplier bill and all-size refinement remain open. The selected frontier and frozen predecessors are unchanged; the inherited unchanged-consumer screen 599/584 remains in force.

Task and overlap

Base: 463113d675af7410ac91d53a4fed51ec6494eb9a. Card p104-side-correction, priority revision 6, track complex-mechanisms, original scope key 72dfbf0708467ad34793; actual scope PR3131-first-paired-collector-lambda2.

Scope is changed, from realizing a named static endpoint collection to independently checking the explicitly unrun actual tensor boundary in PR #3131 PROOF section 7. This is one chronological restoration/precision component on the same P104 track. The static-collection and support-propagation questions already have separate investigations; this audit does not reconstruct them. The expansion-gate decision is to stop at the finite audit: no changed complete consumer or favorable new supplier bill is supplied.

The advance claim is in the existing collector thread. Handoffs #1166 and the canonical thread were checked before selection. The exact task card records the original catalogue card, existing checks, method, changed premise, stop rule and next obligations. Budget was one 60-minute session; bounded domain is four lambda = 2 fixtures, one lambda = 1 calibration and all addresses of the actual two outbound wrappers.

Dependency heads:

Predecessor	Exact head
PR #3131, Jose Manuel / dense paired collector	0c9e344d5a5295a218558fa4a51d867f39ff5311
PR #3025, Tekalign / signed pair and paired collector	a544ef068a46f4de3bc47d1d02149cbdc3ba547f
PR #3033, Tekalign / period split	b12bbaeb5ca2e83f15433fc2dd0ba3b766595281
PR #3072, Ross Richardson / conditional block evaluation	cd1bbd05251f9d8e15cbb0192f1bfe83dc138f5e
PR #3109, Jose Manuel / retained batched core	15eac811648182bdac7254a91fd9b841b1414ebc
PR #2250, Jose Manuel / affine compiler	d404b48a1e7b147556b309497d55089c837dddb2
PR #2586, ywz65 / actual collector recipes	7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1
PR #2287, Jose Manuel / selected C-layer	8c60765b5dea9d862b3b190d55da102a576031bf
PR #2899, Jose Manuel / physical ordinary interchange	2f0911ad735643a069b9790302fbf179e49f74f8

Tekalign's later PR #3134, head d8c0e3e88e501da6c19f858b7debf0c2e3e0be69, reduces wrapper-level lifting calls while retaining the same boundary. Its actual complete collectors remain at N = 512; its changed implementation is not replayed here. This account's PR #2654 error-growth audit and PR #2662 endpoint-fusion work have different objects. This account's concurrent PR #3214 (PR #3182's output support) and PR #3225 (the helper-13 cut for PR #3124's matching) are also distinct.

Overlap used the repository helper offline against complete-paginated snapshots, with the task card and targeted dense-paired-collector, actual lambda, tensor collector and multiplicity-two terms. Main packages, predecessor heads and the Discussions board were checked as well. These searches cover metadata and named sources, not every diff or unpublished work. Final fetch at 2026-10-17 18:08:57 UTC retained the same main head and revision 6, with no guidance or selected-record changes. Final metadata coverage was 253 open PRs at 17:49:11.608413 UTC and 2017 Discussion records at 17:52:04.322463 UTC, complete pagination. The optional path index was older (17:12:31.392684 UTC) with seven unverified head/base joins, so it is not a current changed-file novelty certificate. A closing recheck at 19:07 UTC found main still at 463113d675af7410ac91d53a4fed51ec6494eb9a and all nine dependency heads and PR #3134 unchanged; the snapshot of 18:44–18:46 UTC (277 open PRs, 2052 Discussion records, complete pagination) showed no other claim or PR on this boundary.

Validation

CPython 3.12.3, standard library only. From repository root:

python3 -I -B scripts/research_package.py --package research/p104-tensor-collector-audit --check-only
python3 -I -B scripts/research_package.py --package research/p104-tensor-collector-audit
python3 scripts/check_research_commit.py --package research/p104-tensor-collector-audit

Observed:

PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
PASS_P104_TENSOR_COLLECTOR_AUDIT cases=5 no_new_kappa
Ran 8 tests ... OK
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-tensor-collector-audit outcome=completed
PASS_RESEARCH_COMMIT_BYTES {"commit": "993e2d4ba993d9818c6d7c5ae1e35980d1ab3ebb", "files": 25, "package": "research/p104-tensor-collector-audit"}

The direct verifier compares complete arrays before digesting them. Exact Walsh ideal evaluation gives squared errors 5379503/8 and 2615337/4 in working-grid numerator units for the two rounding fixtures, at grids 3 and 5. The cancellation and zero fixtures use grids 25 and 3 and have zero error. The physical squared errors multiply these numbers by 2^(-2F). Exact forward and paired-inverse relative inequalities pass without floating point.

Controls include all 2401 signed pairs in [-3,3]^4, wrong layout, omitted tensor phase, reversed nonlinear stage order, wrong inverse, changed event/native binding, query promotion omitted, private return corrupted, source bytes corrupted, duplicate JSON keys and changed receipt values/types. The order witness has two different forward outputs but two successful paired cleanups. Eight behavioral groups run under -O, including the actual optimized CLI and four small comparisons with authenticated PR #3025 code.

Incomplete extended comparison. Two full retained PR #3131 nested-evaluator attempts each hit a 600-second cap (exit 124), with no completed receipt. Their explicit finite plans were (width,d,spacing,suffix,outer)=(160,2,2,1,3) and (160,157,1,2,14). Only the finite n<=10 guard was changed to n<=18 in an authenticated in-memory copy; the arithmetic and block-planning code stayed unchanged. These attempts are not successful evidence or arithmetic counterexamples. attempt_retained.py preserves them as optional follow-up commands outside the registered successful replay. The predecessor's unchanged N = 512 --suite consumers replay passed separately, in 2.47 seconds; it does not close the N = 262144 implementation comparison.

Registered replay, metadata/pins, all eight optimized controls and the original-return ideal fixture pass. The measured direct run took 32.36 seconds and 706984 KiB maximum RSS. The working tree is checked against the publication commit 993e2d4ba993d9818c6d7c5ae1e35980d1ab3ebb: all 25 package/input files match. The committed export passes inventory/hash validation, and the exact exported bytes also pass the complete direct replay and all eight controls with -I -O -B from a read-only directory outside any Git checkout.

No Lean, formal-kernel review, selected full cold replay, all-size fast implementation, lambda > 2 actual collector or PR #3134 implementation check was run. No independent human review is claimed. Finite success does not admit a complete supplier or prove a new kappa.

Credit

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.

Credit Jose Manuel / jmbarrancoml for PR #3131's actual dense field-major collector and explicit validation boundary; Tekalign for PR #3025/#3033's signed lifting pair, paired collector, grid policy and period split; Ross Richardson for PR #3072's conditional block construction. Retain Jose Manuel's PR #3109 and PR #2250/#2287/#2899 compiler and physical lineage, Douglas Colkitt's Fourier and workflow contributions, ywz65's PR #2586 actual native recipes, Arham Tahir (PR #2665, whose pinned copies of those recipes are the inputs read here), Vasek/flyingviper's consumer audit, and the retained Rohan Arun, Chafik Boukhalfa, Adam Gall, Josie Elliston and Ali Romman P104 lineage. Tekalign's PR #3134 wrapper refinement is credited adjacent work and is not imported as new here. Apache-2.0; frozen archives and notices are preserved.

The two new numerical evaluators were separately written within this contribution. The small predecessor calibration and the incomplete retained-evaluator attempts deliberately execute credited code; they are not separate human reviews.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

The package's README.md (Open next questions) and TASK.json give three follow-ups. First, retain the unfinished nested-evaluator comparison on this same fixture: allow a measured longer replay budget or establish its separate component equivalences. Next, bind an actual fast reversible backend trace to this finite boundary, accounting for source access, snapshots, cleanup, movement and clean stock. Finally, name a changed complete P104 consumer and price every rank and hosting term before further construction. This audit supplies no favorable changed full bill; the inherited 599/584 screen is unchanged.

Workflow feedback (optional)

Separating actual complete-collector tests from synthetic wrapper tests exposed a precise useful audit. Finite-model packages could make their executable size guard, tested actual multiplicities and replay times explicit in one small table. This would also make a bounded retained-evaluator comparison easier to plan.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG