Globally replayed source-assisted bit word: conditional kappa = 0.000661755179959122

[rohanarun]

Change and mathematical scope

Combine the source-assisted low-frame construction of icekylinx's PR184 with the newer PR168 bit graph and PR182's unchanged complex supplier. Emit and independently replay the complete globally allocated bit word, then use PR185's finite ordinary-leaf composition and the paid balanced assembly.

Conditional bound:

kappa = 330877589979561 / (5 * 10^17) = 0.000661755179959122,

0.170723% above PR185's 0.000660627334074291. The complex supplier now binds. Concurrent PR186 reports 0.000661885549259598, which exceeds this combined bound; this is not a current-record claim. This independently emitted source-assisted bit supplier has a stronger paid bit saving and is a separate construction for future checked composition.

The new bit word has 17,588 physical auxiliary roles and 21,108 persistent roles, with deficit 1,936 unchanged. It retains the high-frame boundary, 3,960 gauges and 1,760 compensated aliases, removes 440 low retirees, and explicitly executes 5,280 original-X controls at already paid source-pair frames. The complete transcript has 64,824 forward operations and 890,560 unit payload XORs including old-value responses, inverse cleanup and partner deliveries. Its paid coarse saving is 167724995262213/250000000000000000.

PR184's original result used an older graph and disclosed the absence of an exported global bit transcript. This package supplies the newer complete word, re-derives its actual dirty response, checks its arbitrary dirty restoration, and recounts actual frame chains. It does not assume that matching fresh boundary masks alone proves a physical word.

Payload correctness is over F2 under the retained bit interface. Signed integer inverse checks and coefficient majorants are separate; no integer decoder identity is claimed. All-size compiler, uniform weighted supplier, restored-row, routing, precision and analytic/fixed-tape assumptions remain conditional. No global optimum or practical speedup is claimed.

Validation

• Fresh complete producer and exact rational frame/source-control chronology, role/target nesting, donor chronology and full paid histogram.
• Independent forward and full-reverse replay of every one of the 21,108 source, target and dirty columns; three mutation controls rejected. Signed integer inverse argument and two dirty-data runs also restore X/Z.
• Complete scalar gate inventory and noncancelling defining-integer coefficient majorants; all payload coefficients are units over F2.
• Exact paid supplier moments, rare-class fallback, finite leaf composition, all 47 strict inequalities, seven margins and adjacent-grid exclusions.
• Every one of 24,161 used frames is covered by exact prime witnesses: 23,869 retained and 292 newly computed. Four corruption controls pass; the inherited prime threshold and toll are unchanged.
• Source-bound packaged focused gate passes before submission. Full native/formal CI passed all 47 jobs on research commit 246035b5e67e9ad1bf8c3d2ac756e6e1aca176ee: 14 native groups on three Python versions, three formal targets, the parent physical replay and the new full-word gate. All native and own reproduction checks passed. Only receipt/README/status pin metadata changes follow that tested commit.

Run python3 -B research/source-assisted-bit-bootstrap/verify.py --full.

Prepared by Rohan Arun with OpenAI Codex assistance. Credit icekylinx and the disclosed GPT-6 Astra/Codex assistance for PR184's source-assisted lift; eumemic's PR168 and its module/frame/word lineage; Chafik Boukhalfa's PR181/182 complex supplier; James Chang, DaysSky, Zhihao Chen, Swapnil Jain, RaD and all predecessor authors retained in NOTICE.md. The contribution here is the newer globally emitted and independently replayed bit composition, its paid recount and exact joint certificate.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Source-assisted injection before original sources mix.

Review and limits: Fresh --full replay; conservative Gram ancestry, donor complements and full global word paid.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: 201737a1ec4f936e166e2481fb9e88104cb2ccc7. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.