Factor the restored P104 collector through one Newton query

[Clear1nsight]

Why this result matters

PR #3467 parametrized the larger stagewise P104 entrance, but its index did not establish what a restored caller can observe or whether the enlargement helps this collector. This package closes that logical interface and identifies exactly which coefficient directions reach Q.

Canonical investigation: #2750 (comment)

Established result

For the declared PR #3467 coefficient encoder K, append the actual 257-event producer cone, the actual 15-event first collector, a 252-event selective producer inverse, and K inverse. The core has 524 events; after the codec inverse, all 52 coefficient banks, all five dirty D banks, and all 58 public frames return, with private C erased at zero. Both codec directions are additional to the core inventory. The resulting update is

$$ Q_{\mathrm{out}}=Q_{\mathrm{in}}+E_9(a_2+a_9+a_{16}+a_{27}+a_{51}). $$

The return omits exactly the five inverse Q compensation ADDs. Full reversal would incorrectly add the initial dirty-D sum; the literal check verifies that adverse control on all 512 coordinates.

This answers three connected questions:

1. The larger entrance adds no five-readout range. With L the inherited stagewise entrance and S=(4B9)^52, both map onto B9^5 under the same five group-sum readout. A common explicit terminal-source section gives L/S isomorphic to ker(rho5|L)/(S intersect ker(rho5|L)), of size 2^86072. Every relative class has a kernel representative. rho5 itself does not descend to L/S, since rho5(S)=B9^5.
2. The source-derived caller can close with dirty restoration. The specified selective inverse supplies the exact returned-state contract and the Q update above. This is a newly appended logical return, not an assertion about an existing full-word return.
3. That caller factors through one Newton query. Two strict register schedules gather the five terminal coefficients, apply E9, add to Q, apply E9 inverse, and ungather. All 52 original coefficients remain returned outputs; invisible directions are not erased or released storage.

The five-readout map has Gaussian-array rank 2,560 and the final increment rank 512, with respective coefficient kernels of ranks 24,064 and 26,112. These are observation dimensions, distinct from the source program's native recipe rank mass.

Rank-nine strict real arithmetic	Owned zero Gaussian bank	Temporarily mutable terminal bank
ADD/SUB excluding doubling	43,520	41,472
Explicit doublings	2,304	2,304
Checked exact halves	4,608	4,608
Extra Gaussian banks	1	0
Separate real zero scratch words	1	1

If doubling is charged as one ADD, the ADD totals are 45,824 and 43,776. Both schedules restore their work storage. Conservative component bounds are 67,260H for non-query arithmetic and J+16,815H for Q. COSTS.md separates these strict schedules from the source core's incomplete native/component inventory; it does not infer a physical speedup from unlike tariffs.

Evidence and review scope

Public result commit: 9f225dd. Retained-source ancestor: 9e501ba. The public trees exactly match the locally tested trees. Only publication source-history pins and their receipt binding changed during publication; the scientific inputs, implementations, proof, costs, and original predecessor bytes stayed fixed.

• Two separately constructed literal executions each check 524 core events and 184,832 completed literal/ideal pairs. Full prepared/returned Y, coefficient, dirty-D, cut, and Q arrays are compared before hashing. The primary reuses authenticated predecessors; the independent implementation imports no predecessor executable and separately constructs the actual Y paths.
• Both direct schedules agree with those full returned coefficient and Q arrays. Signed arithmetic, width, alias/ownership, zero-exit, malformed-input, source-integrity, and typed-receipt controls are explicit and remain active under optimized Python.
• Three preparation/readout/direct fixtures distinguish a source-bound Y91/Y90 nonterminal kernel direction, a terminal difference, and a five-active strong representative. These are not three additional full 524-event replays.
• Registered normal and optimized Python 3.12 replays pass. The actual public commit passes committed-byte and source-history checks for all 31 exported source files. The exact committed export passes its transport-integrity gate. Actual Git-free replay and hosted CI results are reported in the publication comment rather than prospectively marked passed here.

Receipt SHA256: 27cf939d8766ac4baa120117d738045c80f8bde285f91446945f52b0f81188a1.

python3.12 -B scripts/research_package.py --package research/p104-restored-query --check-only
python3.12 -B scripts/research_package.py --package research/p104-restored-query
python3.12 -B scripts/check_research_commit.py --package research/p104-restored-query --ref 9f225dda71c45e2e6fea70e2ff5ef9f27192e1f9 --check-source-history
python3.12 -B scripts/export_research_package.py export --package research/p104-restored-query --ref 9f225dda71c45e2e6fea70e2ff5ef9f27192e1f9 --output /tmp/p104-restored-query.tar
python3.12 -B scripts/export_research_package.py check /tmp/p104-restored-query.tar

From the extracted Git-free export: python3.12 -I -O -B research/p104-restored-query/verify.py. The default verifier never rewrites its receipt.

Boundaries and next obligations

This is a closed logical coefficient caller. It does not supply a physical caller with those coefficient meanings, arbitrary raw-Y admission, the original full 2,025-event prefix, the whole 5,398-event word, or the 675 external-port contract. Physical routing/control, zero supply, access and ownership pricing, strict native/codec lowering, and the complete recursive bill remain open. The inherited 599/584 unchanged-profile stop and selected kappa remain unchanged. No human mathematical approval, formal kernel proof, or complete multiplication theorem is claimed.

TASK.json and README.md give two conditional next questions: name a real physical caller for this exact returned-state interface; or name an additional required, legally framed and fully priced readout that detects the source-bound kernel witness. Stop if no such consumer is justified. This package does not reserve a broader census or supplier construction.

The final canonical fetch at 05:29 UTC on 2026-10-18 remained main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. Relevant guidance, selected record, frozen inputs and replay tools were unchanged from the scientific base 6f100d4bb5083f8c35d96fd95a539811c62f245c. TASK.json records the handoff-first scope decision, complete open-PR checkpoint, subsequent bounded deltas, fresh canonical Discussion/hub checks and their coverage limits. No same-scope overlap was observed; this is not an exhaustive novelty claim.

Predecessor credit

PR #3467 supplies the exact entrance, codec and inherited index; #3423 already establishes the rank-one port map; #3382 supplies the Newton exactness application. Nick Petalas's #3416/#3426 provide phase-correct covariance and the correlated entrance; #3449, #3466 and #3469 address distinct calibration, full-prefix and adapter obligations. Credit ywz65/#2586 for the frozen word/native lineage, Arham Tahir/#2665 for retention, Tekalign/#3025/#3218 for signed-floor and phase-sensitive checks, Ross Richardson/#3068 for the exactness-domain question, Jose Manuel and Vasek for the unchanged-profile stop, and the retained geometry/native/compiler contributors. Ten selected predecessor files and their original notices are retained byte-for-byte with explicit provenance.

Clear1nsight, with substantial OpenAI assistance and three concurrent specialist agents for mathematical alternatives, independent execution, and source/overlap review. New work is Apache-2.0. Existing frozen sources and selected-frontier files are unchanged.

[Clear1nsight]

Exact public source and completed publication gates

Public head: 9f225dd. Retained-source ancestor: 9e501ba.

p104-restored-query-source.zip

The ZIP contains the exact 31 committed source files plus the export manifest. Every member's complete bytes and file mode were compared with the canonical committed tar export. It includes the six executable modules, written proof/cost ledger, deterministic receipt, all live inputs, retained predecessor sources/proofs and required notices. No Git checkout or dependency installation is needed for the direct replay.

After extraction, from the export root:

python3.12 -I -O -B research/p104-restored-query/verify.py

Actual results:

• Registered normal and optimized Python 3.12: PASS, same receipt.
• Public-head committed bytes and source-history checks: PASS for all 31 files, with both declared source commits in ancestry.
• Canonical committed tar export and transport-integrity check: PASS.
• Actual optimized Git-free replay on CPython 3.12.14: PASS in 17.191 seconds; all 32 files retain identical complete bytes and permission modes.
• Actual optimized CLI controls in separate disposable copies: missing WORD, a one-byte WORD corruption, and Boolean true substituted for integer receipt schema_version: 1 each exit 1 for the intended reason. The pristine export and archive remain unchanged.
• Hosted workflow 39101100427: success, including the plan, both registered scientific modes, and the unchanged-committed-input gate. The logs reproduce the same receipt and query hashes. Hosted CI ran GitHub's preview merge 3b340e68f356544862f558dadabbd86cf4337ed3, combining this public head with canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90; the public head itself was checked directly in the local committed and Git-free gates above.

Artifact	Bytes	SHA256
Source ZIP	232,282	f3e79f943d114b42168da9db70fabc8f9ada3e9cd7b953076c2ba33a940e16dc
Canonical tar export	849,920	71447820b1b65d42655fbc361bc9a635da816dfd02b9301f66dfecd5f28d93dc
Committed RECEIPT.json	94,393	27cf939d8766ac4baa120117d738045c80f8bde285f91446945f52b0f81188a1

The publication binding changed only the retained-ancestor metadata: the scientific receipt differs from the earlier tested receipt in exactly its authenticated SOURCES.json hash. The public tree 04928e0d6e76dae87dcdc2364908e1aae19d43e5 equals the final locally tested tree.

The final body/metadata delta at 05:39 UTC still had canonical main 20ecf289.... All seven new external PR bodies #3547–#3553 were checked, with no same-scope result observed. Adjacent #3548 is a distinct unbuilt centre-sharing relaxation. This supplements the coverage and limits in TASK.json; it is not an exhaustive novelty or scientific-acceptance claim.

The logical caller, quotient and scoped strict direct schedules are complete as an author-checked contribution. The named physical consumer, access/control/zero supply, complete supplier payment and independent mathematical review remain open as stated in the PR. Predecessor credit and the unchanged-profile 599/584 stop are preserved.