[unpaidmoon]

Change and mathematical scope

Exhaustive finite census, not a new κ. The selected exponent stays 781451/250000000.

The selected ordinary formula reads one thinned-controller field, ordinary_BIT.after_cover. Under that controller's one-weight stock contract the field is only 69/20000. The formula is strictly increasing in the cover, so exactly one rational cover would make it equal the recorded PR5679 component

C = 3507410738409/1000000000000000.

That cover is 3507256898809/996000000000000. It is not emitted. At the emitted cover the ordinary value remains the selected claim 8590884599/2500000000000, and C − ordinary = 71056898809/1000000000000000 > 0.

This is a formula identity on a one-element domain. It does not admit C as BIT. The pricing passes bit_saving = admitted = 17/5000, not ordinary. The outer ledger was not run. No selected-frontier file changes.

Task and overlap

Base: canonical main 7c49fe32c55de02c2c873655c804b16e4c3fef0a. Priority revision 8. Card supplier-boundary-audit, scope refined. Package: research/g20-source-bound-cover-census.

The card asks for one resolved gap on a latest BIT component. The gap is the cover field left open by the PR5679 stock-gate reading (discussion #1166 comment 19492491, fork draft PR 149). That reading compared C with the pinned ordinary value and did not enumerate the controller's cover field.

Overlap recheck on 2026-11-10 covered 885 open upstream PR bodies and the discussion cache. The preimage numerator appears in that open comment and in no open upstream PR. research/g20-component-stock-gate asks the odd-prime question for the different PR5708 preimage 3507565220149/996000000000000. This package does not answer that question and does not name a Gaussian caller outside this pricing assembly. No match is a novelty certificate.

Validation

Python 3.12, standard library only.

python3 -B research/g20-source-bound-cover-census/verify.py
python3 -O -B research/g20-source-bound-cover-census/verify.py
python3 -B scripts/research_package.py --package research/g20-source-bound-cover-census

Observed: PASS_G20_SOURCE_BOUND_COVER_CENSUS and PASS_REGISTERED_RESEARCH_PACKAGE with outcome negative-result. SHA256 and Git blob pins are checked before the scientific Fraction evaluation. Controls reject an unbound call, a second nested after_cover, and a duplicate JSON key.

Not run: the thinned-controller replay, scripts/research_selected_baseline.py, the outer ledger, either component caller, native maps, the odd-prime rule at the missing preimage, Lean, Docker, and make frontier6030-verify. The cover is the source literal Q('.00345'), checked against the pinned receipt.

Credit

The component is Ali Romman's PR #5679. The selected pricing and claim are DreamingOfClouds' PR #6030. The one-weight cover contract is Cinna Davis's research/query-thinned-controllers. The PR5708 preimage question remains with research/g20-component-stock-gate. The stock-gate reading that left this field open is the predecessor behind discussion comment 19492491.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Can a changed thinned-controller contract that emits a second after-cover make this formula equal C while keeping the one-weight delayed-cover proof? First step: name a second source assignment to after_cover and authenticate it before any arithmetic. Blocked by the single C1 sentence and the single writer. The odd-prime rule at the missing preimage was not run.
2. Can a Gaussian caller that does not use this pricing assembly consume C? First step: name that caller and the field it reads as bit_saving. This package does not take that question. Equality of ordinary with C would still leave this assembly's bit_saving equal to 17/5000.

Workflow feedback (optional)

The cover weight is a literal in the controller verifier, not a field of the physical BIT word. Reading that assignment before any replay avoided reconstructing the word.