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Prove exact numerical peaks for BIT directory and ADD phases - #2810
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#2915's ordered high-field ADD Answers the ordered-ADD component of PR #2982's single-cube handoff for the unchanged PR #2915 kernels.added and its pooled stream.add_pass. For odd Q>=3, canonical positive B,M,S and c in {-4,-2,-1,1,2,4}, with V=BQMQS: exactly 10+[S>1] additional scratch roles suffice and are attained in every call, sharpening PR #2809's conservative 32-role lexical allowance; six additional numerical words suffice and one fixture attains six (PR #2810's add_pass bound composed with the actual coefficient callback); and the complete local physical read/write/ unit-move bill, including encoded arithmetic and pool acquisitions, is at most 4096V, or 4102V with returned-output disposal. The exact non-arithmetic invoice extends PR #2877's and PR #2473's countdown and payload bills, zero case included, with pool acquisitions, the one-bit-suffix path and the marginal lifecycles. It matches the unchanged source on 109 complete packets (37,241 payload bits), and one fewer scratch role or numerical slot rejects at the real allocators. Route setup, B1 swaps, machine steps, physical backing and whole-stage stock remain open; no supplier, selected-frontier or kappa change is claimed. Adds research/high-add-scratch-invoice/ only. Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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PR2801 leaves directory production and stream arithmetic outside its coefficient-lifetime allowance. This package proves their exact successful-call numerical peaks for unchanged PR2697 source, with all entry residents retained in the baseline:
directory.produce: exactlymax(d²,6)additional residue Words, hence 4,096 at dimension 64, and no additional index Words.stream.add_pass: at most six additional residues outside callbacks, including the returned coefficient. A restored fresh-result callback allowance(R,I)composes to(max(R,6),I)for the complete ADD.(37672,34)allowance aboveConsumer.applyentry therefore extends across each entire adapter ADD interval. PrecedingLayout.extentsand other caller phases remain excluded.The written source proof covers the stated all-parameter successful-call domain. Exact finite execution checks 228 complete ADD cases, seven complete directories (including dimension 64), and literal ownership/content restoration. A separate math-storage-lifetimes AI specialist supplies an independent integer allocation-event model and 135 coefficient cases. Failure witnesses show why exception rollback and equal repeated coefficients are separate obligations.
Validation at
8abae69a53337dd3d0965db3470ab249b0216f22: registered CPython 3.12 replay, optimized CPython 3.14 replay, six external integrity/defect controls, selected-record binding check, and read-only Git-free export. Exact source files and typed receipts authenticate before execution; stale bytecode cannot replace them. Details and reproducible commands are inresearch/selected-stream-directory-numerical-audit/VALIDATION.md.Scientific base
db3edc00; submission refresh28f54620at 22:38 UTC on 2026-10-15 leaves relevant guidance, selected record and predecessor heads unchanged. Submission overlap covers 734 open PRs, 1,448 discussion records and 1,985 local records with complete pagination; metadata coverage is not a novelty certificate. Canonical investigation.Credit Jose Manuel/jmbarrancoml for PR2697 runtime and Nick Petalas for PR2759/2770/2778/2781/2801 component results and handoff; retained source notices and Apache-2.0 license. New audit by Ross Richardson with substantial OpenAI Codex assistance and a separate AI specialist. No human/formal-kernel review, full caller/physical-stock theorem, supplier admission or new kappa is claimed. No selected record or frozen predecessor is changed.