Coordinate-aware indexed compilation: conditional κ = 5.2275423755251e-5

[rohanarun]

Under the inherited all-size compiler and analytic hypotheses, κ = 52275423755251/10^18 = 5.2275423755251×10⁻⁵, approximately 0.00618% above #85 (fb1f2c57681cd7c0b86a192de9367a7af87c9cca). Bit saving: 52278156618199/10^18.

Ready for review. Full make -j1 verify, independent regeneration and seven focused controls passed on research commit d1b2a3a7caec9a101363e5c534a4680a1d2086ba in 3627.67 seconds. Coverage includes 84 isolated test modules and 20 historical patch checks. No tracked source drift occurred. All 45 GitHub checks passed on that research commit. The later commit adds only the validation receipt, README status and its source hash. See research/indexed-geometric-pricing/validation.json for the full log hash and setup history.

This composes two checked changes with Chafik Boukhalfa's PR84 construction:

1. Price candidate transitions in their final coordinate order during compilation. Transform only the discovery oracle's frame masks, then compile in original labels and relabel the final physical word once. All legality and dirty-workspace checks remain unchanged.
2. At h23, try bounded two/three-carrier exchanges after the inherited single/two-exchange passes. Each accepted move lowers an integer proposal score and preserves each affected basis, the set of occupied future uses, and cardinality. A restricted search frontier means no weighted-optimality claim.

Quantity	This witness
h23 / h25 roles	26834 / 35345
Physical width W	132460795
Total recursive rank	76163110225
Rank deficit	1846900

Eight cloud proposals passed complete physical/dirty-basis replay and fresh CRT profiles. The selected pair was independently regenerated locally, byte-for-byte. Exact rational composition of complete paid profiles verifies 47 strict constraints, seven margins, independent moment bounds, both next-grid exclusions, and exclusion of PR85's entire child list at the new saving. Seven control tests include four adversarial carrier-exchange cases and a byte-level binding of portable derived engines to the independently run sources.

python3 research/indexed-geometric-pricing/verify.py --regenerate
python3 research/indexed-geometric-pricing/test_controls.py
make verify

The general finite argument, source closure, literal words and certificate are in research/indexed-geometric-pricing/. No inherited check, copy, endpoint correction or recovery is omitted. All-size residual compilation, tape/routing, prime selection, recovery and analytic transfer remain inherited hypotheses; finite tests do not prove them. This is not a global-optimality or practical-speed claim.

Credit: Chafik Boukhalfa (#84 and predecessors), Thomas DiFiore (#74), Rohan Arun (#78/#82/#85), Alejandro Zarzuelo Urdiales (#70), eumemic, Rohan Garg, Avi Eisenberg, Dominik Scholz, OpenAI and all previous contributors. Original source archives, licenses and assistance disclosures remain unchanged. Prepared by Rohan Arun with OpenAI Codex assistance.

[Mister-Meeseeks]

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

Contribution: Coordinate oracle and short carry cycles.

Review and limits: Exact-head CI evidence; independence and partition conditions retained.

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: f0fe4453a088c62af3ee795691fa92c502ed8b57. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.