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Tighten completed P104 feedback with per-operand ideal norms - #2726
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PR2166 bounds state-relative errors in the completed P104 word by multiplying its largest ideal state P by its largest weighted defect coefficient K. This retains each instruction's ideal operand norm before accumulating defects instead. The exact new coefficient is J=66,657,328, with K=2,134,050; the resulting bound E <= BuJ/(1-u*K) gives 27 uniform guard bits, improving the source's sufficient 39-bit estimate. For requested accuracy b>=3, 26 guard bits suffice.
The exact 34,333-instruction word, 844-role boundary, 32,722 defect sites and native rank mass6,782 are unchanged. Both ideal operands and absolute scalar magnitudes are included before each operation. The proof retains the source's unitary-chart, exact-reset and completed-output relative-error contract, with E covering every boundary. These are sufficient guards from this inequality, not minimal physical precision. No actual rounded child, selected precision-bill reduction, favorable supplier budget or new kappa is claimed.
The replay regenerates the complete original PR2166 receipt, then checks all changed boundaries with the new weights and all844 ideal endpoints. The authenticated source integer-row machinery is credited. A separately written Fraction reverse pass checks the full peak covector and six endpoint rows; a literal synthetic weighted-defect injection attains J. This does not claim sharpness for actual correlated rounding. Six semantic controls and five real CLI export/failure groups cover operands, signs, escaped errors, feedback, sources, typed receipts, optimized execution and overwrite refusal.
Validation: registered CPython3.12.14 replay and allfive artifact groups PASS; CPython3.14.5 optimized primary PASS; separate AI proof/code review clear; exact committed-byte preflight PASS. Git-free/read-only export passes. No human, Lean, full native-producer or selected cold replay is claimed.
Source PR2166 a655734 is retained byte-exactly with SHA-256/Git-blob pins. Credit Nick Petalas, Jose Manuel/PR2139, Adam Gall/PR2096, Arham Tahir's distinct QQ16 guard auditPR2670 and retained P104/compiler lineage. Prepared for ywz65 with substantial OpenAI Codex assistance; Apache-2.0.
Started from canonical mainc3c94c2e, priority5. Final mainc22e42de has unchanged guidance/selected/family state, and source2166 is unchanged. Current overlap snapshot has765openPRs; Discussion coverage remains timestamped and rate-limited. The earlier duplicate output-slice candidate was retired unpublished and is not counted here.