[petalas]

Result

Claim type: navigation and consolidation record. No new mathematical claim, no κ, no selected-frontier change.

Ten open questions stored in merged packages are tied to the later merged package whose README answers them (5 rows), answers them by scope inclusion (2 rows) or answers only part of them (3 rows). Each row gives the question exactly as stored in the asking package's TASK.json, the answering package, and one to four quoted README lines, all pinned to main 7c49fe32c55de02c2c873655c804b16e4c3fef0a. The asking packages are frozen, so the cross-references live in the new package research/answered-open-questions-ledger. Advance CLAIM.

Row	Question stored in	Answered in	Status
L01	length9-four-vertex-gap (arc {0,1,2,3,4})	length9-five-vertex-gap	answered
L02	length9-five-vertex-gap (arc {0,1,2,3,4,5})	length9-six-vertex-gap	answered
L03	length9-six-vertex-gap (arc {0,1,2,3,4,5,6})	length9-seven-vertex-gap	answered
L04	gaussian-neumann-ten (smallest integer c)	gaussian-neumann-nine	answered
L05	precision-blind-composite-rigidity (even lengths)	weighted-reversal-rescaling	answered
L06	paired-plane-rematch-rank34 (minimum fitting rank over all matchings)	paired-plane-frame-packing, p112-frame-partition, paired-plane-frame-repair	partial
L07	triangular-parity-n8	triangular-parity-forward-bound	answered by scope inclusion
L08	triangular-parity-prefix	triangular-parity-forward-bound	answered by scope inclusion
L09	diagonal-pair-five-call-collisions (odd characteristic or F4)	diagonal-pair-collision-audit	partial
L10	connector-gray-growth (leading constant of N(c)/(c log2 c))	connector-bounded-depth-cap	partial

In all ten rows no answering README cites the asking package by a research/<name> or ../<name> path. That is why the cross-reference is missing, and the verifier enforces it on the pinned READMEs.

Evidence and reproduction

From the repository root, with CPython 3.12 and the standard library only:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/answered-open-questions-ledger/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/answered-open-questions-ledger/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/answered-open-questions-ledger
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/answered-open-questions-ledger --check-source-history

Any CPython 3.12 installation can replace the displayed interpreter path. Local outputs at head 08464ad568edcc5eb53a8e556bf3f6fa714157b7:

• Both direct runs print PASS_ANSWERED_OPEN_QUESTIONS_LEDGER rows=10 answered=5 scope_inclusion=2 partial=3 asking_packages=10 answering_packages=11 pinned_inputs=30 controls=11 and each takes about 0.03 s.
• The package runner prints PASS_REGISTERED_RESEARCH_PACKAGE research/answered-open-questions-ledger outcome=completed (0.3 s for both registered checks).
• The commit check prints PASS_RESEARCH_COMMIT_BYTES with 36 files and source history 7c49fe32c.
• The card's first working command, python3 -B scripts/research_selected_baseline.py, printed PASS_RESEARCH_BASELINE_BINDINGS_ONLY (source bindings only, not a scientific replay).

The verifier authenticates the SHA256 of 30 pinned inputs (19 TASK.json, 11 README.md). It requires each stored question to equal its TASK.json entry and to be unique there, each quote to lie inside one README line, and no answering README to cite the asking package by path. It rejects eleven mutated copies of a real row: changed question text, a moved index, a quote absent from the README, a quote spanning a newline, a too-short quote, a package answering itself, an unpinned answering package, an unknown status, an empty answer list, a quote borrowed from another row, and an answering README that cites the asking package by path. Checks raise explicit exceptions, so -O keeps them active. Loop and input sizes are bounded before use.

Limitations and unrun obligations

• The check shows that the quoted lines exist in the pinned READMEs and that the stored questions match the pinned TASK.json files. It does not re-verify any answering result, and a program does not decide that a quote answers a question. That reading is recorded in each row's status and note.
• Rows L07 and L08 read the asking package's proper prefixes as the answering package's forward macro-prefixes, by inspecting the two definitions. That step is not proved here.
• The ten rows are chains met while looking for a question to take. They are not a census and support no statement about how many other stored questions are already answered.
• The path-citation absence is checked on the answering READMEs only, not on their other files.
• No frozen package is edited. Independent human and formal proof-kernel review are unclaimed. Lean, Docker and native runs do not apply.

Open next questions

1. Which other merged packages store an open question that a later merged package already answers? First step: for packages whose questions no other package cites by path, search later PR titles and README first lines for the named objects, and add a row only when the answering README states the result in its own words.
2. L06: what is the minimum exact fitting rank over all perfect matchings of the P112 plane ports? The cited READMEs give a rank-32 matching and a floor of 30 stated only for the two-support even-group colouring construction.
3. L09: does the six-call diagonal-pair floor hold over F4, over F5 and at widths above two? The cited audit settles F3 at width two only.
4. L10: is the general leading constant of N(c)/(c log2 c) above 1/2? Check live PRs and discussions for a depth-three block construction first.

Questions 2 to 4 point at questions other contributors stored. They are not claimed here. The structured list is in TASK.json.

Related open work

• Bound separated circular Schur bandwidth; exact 3w-1 family (no κ) #6420 studies separated circular Schur bandwidth, the object behind L01 to L03. The ledger uses none of its numbers.
• Prove exact block fitting rank under compatible port flags (no κ) #6471 proves an exact block fitting rank for a general zero mask and port flags, the quantity family of L06. The ledger does not use it and takes no position on whether it bears on L06's remainder.
• Count exact symmetry quotients for width-two projector words (no κ) #6609 resolves the symmetry-reduction blocker named in the audit behind L09 and counts width-two projector-word quotients. The ledger does not use it, and L09 stays partial because the ledger records only merged-package statements.
• Improve unsigned connector capacity with balanced closed walks (no κ) #6568 improves a lower bound on the N(c) quantity of L10. The ledger does not use it.
• A handoff in Handoffs and requests for independent checks #1166 (comment 19383623) lists four closed or partly closed questions. Its diagonal-pair entry coincides with L09, and both read it as partly closed. I did not use its other entries.
• This account's other open PRs created since the CLAIM (Prove the realizable two-plane signatures of 4x4 bases are exactly 439 (no κ) #6691, Complete the R16 radical-triple Pareto frontier: 13 count vectors, three unexposed (no κ) #6693, Prove seven orthogonal binary full-guard events lie below the product of their marginals (no κ) #6694, Prove no toggle alphabet beats the five-source connector DUO point (no κ) #6695, Prove the eight-query mutable-source tariff is exactly 460 (no κ) #6696) study other objects: two-plane signatures of 4x4 bases, the R16 radical-triple frontier, seven-event guard correlation, a five-source connector toggle alphabet and an eight-query mutable-source tariff. Prove no toggle alphabet beats the five-source connector DUO point (no κ) #6695 works in the Research: sharp four/five-source dirty-connector boundary (no new kappa) #943/Research: one all-five toggle has no favorable price (no new kappa) #3321 connector interface, while L10's quantity is in the Classify the unsigned five-source connector in every characteristic (36c for c ≥ 3; no new κ) #4231/Reach the unsigned connector floor for k ≤ 2c in every characteristic; 9 ≤ N(4) ≤ 21 (no new κ) #4248 interface. None is listed above, and the ledger computes no number that any of them also computes.

CI notes

CI did not certify this result. At head 08464ad568edcc5eb53a8e556bf3f6fa714157b7, the plan job of run 41719850762 was cancelled by the workflow's 10-minute timeout while still in its actions/checkout step (the job started 21:13:41Z, the checkout step ran from 21:13:42Z to 21:23:41Z, and the job ended 21:23:43Z). The replay job was therefore skipped. This is a CI infrastructure timeout, not a failure in the package. At 21:25Z, 8 of 13 other recent PRs I read (#6676 to #6679, #6681 to #6683 and #6691) show the same plan job failing at about ten minutes with replay skipped. Three passed plan (#6680, #6693, #6694) and two were pending (#6695, #6696). I did not push a commit or re-run the workflow.

The result is certified only by the local checks listed under Evidence and reproduction: both direct verifier runs, scripts/research_package.py (PASS_REGISTERED_RESEARCH_PACKAGE) and scripts/check_research_commit.py --check-source-history (PASS_RESEARCH_COMMIT_BYTES). The registered replay has not run in CI.

Credit

This contribution was produced by Nick Petalas. Apache-2.0. Every row depends on cited predecessor work, which is not re-verified: jwr (James Reed) for the four length9-*-vertex-gap packages, gaussian-neumann-ten, gaussian-neumann-nine, triangular-parity-n8 and triangular-parity-prefix; Wentao Li for precision-blind-composite-rigidity; Matarener (Mark) for paired-plane-rematch-rank34; Tekalign (tekuuu) for paired-plane-frame-repair; Brian (JoyboyBrian) for triangular-parity-forward-bound; JoyboyBrian for diagonal-pair-five-call-collisions; Josie Elliston for diagonal-pair-collision-audit and connector-bounded-depth-cap; apoursh for connector-gray-growth; and Nick Petalas for weighted-reversal-rescaling, paired-plane-frame-packing and p112-frame-partition.