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Certify the native/thin path-family ceiling C < 0.003022 and price H repair headroom - #4658
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Mister-Meeseeks merged 3 commits intoOct 22, 2026
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The earlier floating native/thin stage search is now an exact complete-invoice rejection certificate. For the pinned PR4470, PR4610 and PR4626 profiles, every minimal-cut path controller with 1..64 pairs, every split and every native stage subset fails for all C >= 0.003022, C < 1. A rank-eight normalization proves monotonicity, excluding an interval rather than one test point.
The integer max-plus DP covers 57,772,384,072,799,330,241,337,377,795,082,425,233,864 split/support pairs per invoice. It retains all native helpers, copied queries, main targets and initial/middle/terminal idles. Controls exhaust small arms and all full supports through p=3, bind the literal p16 bill, and expose false gains from missing idles or duplicate helper credit.
The optimistic H112 calculation bounds repair budgets at .004/.006/.01, explicitly without a source-compatible H word. No higher kappa, supplier admission or global controller ceiling is claimed. Different words, typed interfaces, idle masks and p>64 are outside scope; #4654's new typed supplier is outside this family. Selected conditional kappa remains .00302015.
Validation: direct CPython 3.14 and registered CPython 3.12.15 replay; metadata/source pins; committed bytes and source-history preflight. No selected cold replay or formal proof-kernel acceptance. Proof and exact receipts: research/controller-stage-ceiling/.
Credit the historical kappa-hybrid-controller floating DP, Cinna Davis's PR4440/PR4470, Cao Yifan's PR4610, hexapode's PR4626, zxv, Jacob Alan Sussman and the native/compiler lineage. Prepared by Cinna Davis with substantial OpenAI Codex assistance; Apache-2.0.