Quarter-integral ternary bit frames: nine-call floor with dirty registers

[Maximooch]

Result and scope

Extends Tuafo #1604 (head c5f5bef) from the 338 half-integral ternary frames to the union of half- and quarter-integral frames (676 frames). Exactly nine paid rank-one-idempotent calls are still necessary and sufficient for three identity targets with any finite restored dirty workspace.

The 776 relevant eight-call multisets include 111 new mixed-denominator cases. Coefficient rank removes 770; exact singleton-odd characters remove the same six physical survivors as the predecessor. README gives the group-algebra argument, exhaustive-coverage reduction, and nine-call upper witness. No new kappa, selected-frontier modification or universal rational-frame obstruction is claimed.

Evidence

• Registered package replay: PASS_REGISTERED_RESEARCH_PACKAGE.
• Primary exact census under python3 -I -O -B: PASS, including eight corrupt-certificate controls and formal upper witness.
• Adapted code-disjoint DFS census: agrees on every decomposition/candidate list; independently generated character solutions and two more corruption controls.
• python3 -B -m unittest discover -s tests -p 'test_research_*.py': 29 tests passed. Assertion tracebacks are intentional invalid-fixture tests.
• git diff --check: passed; package metadata/pins passed.
• CPython 3.12.8, standard library only.

Limitations and attribution

The orientation-only research_baseline.py failed because research/community-frontier1094-audit/ASSEMBLY.json is absent from this checkout. No selected cold replay, Lean proof, physical admission or independent human review is claimed. The result is about the explicit finite alphabet only.

Both checker implementations are adaptations of Tuafo #1604, not newly independent authorship. The package pins original-file hashes and retains credit; README also credits Ali Romman #468 / eumemic #288 / huxint #203, woklerx #1456 and Cinna Davis #1541. Prepared for Maximooch with substantial OpenAI assistance.

Coordination: discussion #1594, claim comment 18916871. Fresh overlap snapshot on October 14, 2026 covered 439 open PRs and 326 discussions with complete pagination. The nearest overlap is the explicitly credited predecessor and its proposed quarter-integral next question.

Replay

python3 -B scripts/research_package.py --package research/bit-quarter-ternary-catalyst

Next question

TASK.json records a concrete handoff toward a denominator-uniform ternary dyadic obstruction; no further alphabet extension is included.

[Mister-Meeseeks]

Batch review at 95574417a16c4ebe0aa19ccc1ce28effcbec9982.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Quarter-integral ternary frame alphabet nine-call floor with arbitrary restored dirty workspace: full decomposition census, positional coefficient-rank screen and six lattice-character obstructions. Narrower than the unrestricted PR1628 theorem but retains independent finite-alphabet evidence.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.