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Certify exact worst bills for adaptive typed row choices - #6472

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aliromman wants to merge 2 commits into
CrocSwap:mainfrom
aliromman:codex/ten-kappa-32

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@aliromman aliromman commented Nov 3, 2026 •

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A fixed-matrix test does not check every legal combination of supplier rows. This adds an exact producer and independent checker for finite nonnegative rational row menus. It returns either the exact worst unit-toll bill under all adaptive choices, with an attaining stationary policy and a common contraction bound, or a specific legal policy with a noncontraction witness.

The proof covers finite policy improvement and geometric tail bounds. The usable example has exact total (5,3) despite a row sum above one. A separate control catches an unsafe combination of two individually nilpotent modes. This is a scoped certificate implementation, with classical M-matrix, Bellman and independent-row-uncertainty theory credited. No general theorem priority or new kappa is claimed.

Normal and optimized CPython 3.12.13 checks agree on 2,538 families, all 12,200 policies, 1,629 prefix bounds and 18 rejection controls. An independent determinant/Cramer oracle checks the decisions and exact totals. Registered metadata, committed bytes/modes, official export integrity and read-only Git-free normal/optimized replay pass. See validation. Full-history preflight was not run in this shallow checkout. Both hosted checks, planning and the registered scientific replay, passed at this exact head in run 41551454128. CI certifies the bounded replay, not independent scientific acceptance.

python3.12 -B scripts/research_package.py --package research/adaptive-row-bill

Only research/adaptive-row-bill/ is added. Each row must already include every child, adapter and restoration charge, and row choices must be independently legal. No current physical supplier menu is bound here. Selected compiler applicability, native realization, all five selected assumptions and independent human review remain open. The default producer budget is 4,096 policy solves; exhaustion emits no certificate.

Advance claim. Canonical base 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority 8, selected PR6030; submission refresh unchanged. Related work: PR5785 is the fixed-matrix interface; PR5892 already covers observed forcing and reachability; PR6271 treats synchronized paid switching. New PRs through #6466 and live Discussion claims concern other contracts. Sparse and unpublished work remain coverage limits.

Prepared for Ali Romman with substantial OpenAI Codex assistance; no subagents. Credit Nick Petalas, David Ganz / Dugongue, Jose Manuel, the retained typed-recursion lineage and Kozyakin's classical theory. No predecessor scientific result is counted again. No merge, closure or selected-frontier change.

Verified head: 6621e59b773b179a0340627eadbe295eb5254d07.

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