Certify actual P104 Newton producer and consumer interfaces

[Clear1nsight]

Why this is needed

PR #3382 proved a Gaussian Newton entrance for one literal P104 collector. It left three concrete implications open: whether the actual preceding producer supplies that entrance, whether the actual downstream consumer preserves the representation and requested map, and whether a complete implementation can improve the bill.

This focused package, research/p104-newton-interfaces, answers those assigned questions on the actual source paths. It follows the claim in Discussion #2750, pins canonical main 6f100d4bb5083f8c35d96fd95a539811c62f245c, and retains PR #3382's model/proof at 2834523b1cd4ea83ba7a043e2e2f5f3332cf9909 byte for byte. Task p104-side-correction has scope changed by the user’s explicit assignment to these three PR #3382 questions; the original card and decision are retained in TASK.json. The selected frontier is unchanged.

New results

1. Actual producer admission, with a reachable counterexample

The real precollector dependency cone has 257 events, 58 initial banks, 200 native transports of total rank 354, and 52 quarter ADDs. All six dirty D/Q entrances are supplied in B9 when the 52 named initial Y banks are in 4B9 and the initial D/Q banks are in B9. The stronger Y condition is necessary and sufficient for the stated prefix invariant; it does not classify extra final-cut admissions caused by cancellation.

The weaker initial B9 contract fails on Y27[0]=64, with every other initial component zero. All 358 initial banks lie in B9, and the actual full prefix through event 2024 remains arithmetically exact. The first membership failure in the entire 2,025-event prefix occurs at event 1090. At the collector entrance, D31[8]-D31[0]=-1, violating degree-one Newton divisibility. Separate valuation and full-prefix numerical implementations agree; amplitude 256 is the positive control.

2. Actual downstream restoration and explicit representation maps

The bounded open program has 63 persistent banks, 576 internal events and all 675 outgoing ADD ports, through event 4516. The producer cone is already included. Its initial contract is the 52 Y banks in 4B9 plus 11 arbitrary dirty D/Q/G banks in B9. External recipient histories are not executed by this projection.

A phase-sensitive certificate authenticates 392 native occurrences across 163 frames, including 230 redundant path equalities. It checks all 18 Pauli-generator images and an exact nonzero anchor, rejecting a changed global return phase that Pauli images alone cannot detect.

Writing A_H for the authenticated empty-to-frame operator, every persistent bank ends as A_F applied to its initial value, and private C is literally zero before erasure. The actual full-frame operator and its coefficient intertwiner are

$$ A_F=(C^{-1})^{\otimes9},\qquad E^{-1}A_FE=\begin{pmatrix}1&i\0&-i\end{pmatrix}^{\otimes9}. $$

The complete outgoing interface includes 348 Y→D, 171 Y→Q, 104 G→X and 52 initial-Q7→X reads. After normalising each X increment by its own source-frame operator, the 52-by-52 bank-coefficient matrix has rank one: each target receives a signed half-sum of the 52 initial Y banks, with 39 positive and 13 negative signs and cancellation of dirty D/Q/G coefficients. This is a frame-normalised port operator; a final physical X endpoint needs its omitted updates and transports.

The actual Q/F coefficient maps are reconstructed column by column. Their logical contract is E^-1 A E; an exact counterexample distinguishes it from applying A directly to arbitrary coefficients. Persistent compatible representations need no intermediate codec pairs, while exposed adapters and the 52 stronger Y admissions remain charged obligations.

3. Complete logical bill and conditional stopping decision

The independently reconstructed direct schedule includes 148,736 floor pairs, 784 actual wrappers, 425,230 Gaussian scratch swaps and 857 ADDs. It costs 2,067,456 real add/subtract operations plus 159,744 doublings, with 594,944 native floor halves and 1,382,400 exact quarter halves. Component traffic, setup, storage and cleanup are retained. Conservative bounds from initial component height H are 1568H for internal payload, 7840H for pair work and 1600H per outgoing increment; current recipient widths remain separate.

Physical admission, ownership, routing, control, adapters and recursive completion remain explicit unknown charges. Under exactly the inherited width-73, five-forward/four-dual profiles and coverage law,

$$ M_B(a)\ge1+\frac{1560}{73(832+B)}>1 $$

for 0<=a<1 and every finite number of fully paid auxiliary banks. At B=0, this is the credited 599/584 stop. It excludes expansion with that unchanged consumer, not arbitrary changed P104 profiles or coverage laws. This PR claims no complete supplier or improved κ.

Verification

The package combines written proofs, exhaustive finite operator certificates, dense signed fixtures and separately written source/count, full-prefix and scalar-row checks. Reproduction commands:

python3 -B research/p104-newton-interfaces/verify.py
python3 -B -O research/p104-newton-interfaces/verify.py

Local verification passed on CPython 3.12.14. Registered normal and optimised complete replays produce the same retained receipt, SHA256 fbc444897b13be5973c92ecfa5de67a8efae13b1aca0d8181bd430e2cffba1d3. A Git-free optimised replay also passes with Git unavailable. The public commit is 15d28c4de37dc47ea07cd7173c8b318fca7a4d75, tree 194bec3ab755726b686f4b9ba83f0d0835130c13, byte-identical to the tested tree. All 28 package/source files pass check_research_commit.py --check-source-history; the checked public export has those same 28 byte-identical inputs. The hosted Registered research packages run also passed both the plan and package replay jobs for this public head. These are automated checks and cross-review, not external human or formal proof-kernel review.

Open next questions

The package README and TASK.json retain two concrete handoffs: join all 675 ports to the actual external target histories and widths, or present a changed caller/profile with paid admission and a complete favourable cost screen. The first needs actual recipient continuation; the second needs a changed premise and full physical/recursive charges. The unchanged-profile supplier effort stops here.

Concurrent work and credit

The presubmission sweep covered 323 open PRs and 192 visible Discussion records, with incomplete Discussion pagination. It found Nick Petalas's complementary PR #3406, head 18a054fd585ab4b2010770ec83cba0c9f28184e3. That package classifies the whole-word independent-product entrance under inherited native covariance and explicitly links this active local-interface claim. Its broader theorem is credited pending context; it is not rerun or claimed as this package's result.

Clear1nsight, with substantial OpenAI assistance, including concurrent mathematical and implementation review agents. Credit remains with ywz65/PR #2586, Arham Tahir/PR #2665, Tekalign/PR #3025, Ross Richardson/PR #3068 and PR #3382. The inherited stopping insight is Jose Manuel's Discussion finding, source-audited by Vasek in PR #2744. Apache-2.0; predecessor notices and exact sources are retained.

Post-publication overlap and credit update

The live handoff on 2026-10-18 found Nick Petalas's PR #3416, published after our presubmission snapshot. At exact head f1112560883a5e81b1a29c37c81a79a20be31fe3, it reports a separate exhaustive certificate of all 1,245 archived native chart identities and all 2,070 occurrences, supplying PR #3406's inherited covariance premise. Its metadata and written proof were inspected; its suite was not rerun here. Our independently written 392-occurrence path certificate serves the bounded producer/consumer join and does not claim that broader canonical-chart audit. The Pauli-plus-anchor equality criterion is established predecessor mathematics, with explicit credit to Tekalign's PR #3218 and the original Clifford/native lineage.

Nick's separate correlated final-cut investigation has since produced PR #3426, exact head ce2221dddab6efd3027c09269765dd7eb45f2877, explicitly following this PR's distinction between a prefix invariant and final-cut cancellation. That follow-up reports an ideal correlated entrance and a reachable literal cancellation; its metadata was inspected, and its suite was not rerun here. This context update changes only the PR description; the tested scientific commit, receipt and source ZIP remain fixed.

Portable source export

The attached ZIP contains all 28 committed package/source files and the export integrity manifest. Its SHA256 is d2b9d67f4b2f73aa10e5f141b8f5fa64ba93ad95bf2605addb219650bd2b02af. Extract it and run the direct commands above from its root.

p104-newton-interfaces-source.zip