[ToikY]

Change and mathematical scope

With the other 523 terminal payloads fixed, the literal #7001/#6726 BIT word permits at most 6 independent marked return directions at literal birth and 12 under the quiet-window union. The raw quotient permits 22 independent choices. Preserving the 545-dimensional terminal endpoint requires invertibility of I + D.

The verifier exhausts 220 literal and 1,316 quiet choices across all 22 marked banks. Quiet scope grants compatible old virtual prefixes, coframed mixing, holding, favorable clocks, free setup and ordinary work, and no contention. The fixed κ target 10018846261809/2500000000000000 needs 21 independent returns. Literal and quiet directed net upper margins are −3.2800219379862585 and −1.8832084665200306. NO VERIFIED GAIN. κ change is exactly 0%.

Task and overlap

Canonical base e545235, revision 8. The bit-helper-contract card is changed to an aggregate obstruction on the selected BIT endpoint. #7209 at 77feabf supplies the bank classes and zero stock under individually restored same-chart delivery. This package grants mixed old payloads and favorable timing, then enforces the joint endpoint condition. #7244 at scientific head 4156504 supplies the complete comparator and retained BIT binding.

Validation

From the checkout root with CPython 3.12 and assertions enabled:

python3.12 -B scripts/research_package.py --package research/bit-fixed-payload-quotient-bound
python3.12 -B scripts/check_research_commit.py --package research/bit-fixed-payload-quotient-bound --check-modes --check-source-history

The offline replay authenticates six exact public source paths, regenerates the full receipt with SHA-256 6f4c3afc1185668de6e98ea1608170ae9db8ee5c2c5318b5d5a6577d609252e3, and independently reconstructs endpoint stock. Clean CPython 3.12.14 replay, predecessor and synthetic controls, a forged endpoint stock, a changed input and a duplicate manifest key gave expected results. All 25 committed paths and six navigation checks passed. Source pins and directed fractions are in the package. A changed supplier, selected cold replay, and all-size multiplier were outside scope.

The branch reuses navigation prerequisite f2206e6 as a separate commit for hosted planning. The research commit is isolated to its package. Hosted status is pending at opening.

Credit

Credit Jerry Chen / CubeJerry #7001 and #6726 for the native BIT word, ToikY #7209 for bank classes and interval price, and Clear1nsight #7244 for the complete comparison and BIT binding. OpenAI Codex materially assisted. Exact source history and notices accompany the package.

Open next questions

Both fixed-payload scopes exhausted all cases. Altered unmarked payloads, changed paid prefixes, new source routing and other splitting rules remain open. Start with the aggregate projections of all 523 unmarked arrivals into the old quotient as specified in the package's NEXT.md. The fixed-library calculation requires at least five altered arrivals for 21 independent returns. Any candidate still needs simultaneous terminal rank and exact paid native scheduling, ownership and restoration.