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Prove exact total tape traffic for PR2753 linear sign - #2877
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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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PR2753's linear sign already has an endpoint proof, exact source-movement checks and a 3B residue-counter setup control. This adds an independently derived, all-parameter invoice for every logical Tape/Word read, write and unit movement during the successful sign interval, including numerical setup/disposal and all countdown setup, normalization, decrement and cleanup. The written proof gives a conservative T < 2048V bound on canonical Ring inputs.
A complete countdown costs
15n + 14d - 5 popcount(n) + 36for n>0, with a separate zero case. Composing the literal loops yields the exact total formula. An endpoint-preserving padded-two mutation raises one fixture from 24,454 to 35,353 operations while keeping its 386 source movements unchanged; the total-cost gate detects it. Padded residue width demonstrates the necessity of the canonical-width premise and is rejected by the production Ring constructor.All changes are confined to
research/linear-sign-total-traffic/: proof, separate arithmetic formulas, authenticated predecessor exports, portable checker, fixed receipt and task/replay metadata. David Arias / PR2753 head7dba5452a4071a856a0b11cebdcd2d3b6bcd7659and Jose Manuel / PR2697 retain algorithm and predecessor-check credit. Original notices are preserved. Substantial OpenAI Codex assistance is disclosed; no human or formal-kernel review is claimed.Validation on CPython 3.12.14: registered normal and optimized replay pass, covering 387 countdowns, 150 signs / 24,624 addresses, provenance and restoration, malformed inputs, width/counter/endpoint/source/typed-receipt controls. Git-free optimized CPython 3.14.7 replay, read-only inventory of all 20 package files, publication-byte preflight and diff checks pass. No full selected cold replay, physical compiler, complete caller/H2, supplier admission or new kappa is claimed.
Task
supplier-boundary-audit, refined to this local time obligation; picker noncedbd1c5cd78cdfc2470dc907fd989ab72, priority revision 5. Started at main4b82082f901945f8d0314f143576c7ad31e021fc, rebased onto refreshed canonical mainc7df0bb890cae0cc393cdd32dad19c3facc80992; guidance, selected record and predecessor head were unchanged. Final overlap covered 491 open PRs and 1,522 Discussion records with complete pagination and no warnings. Exact timestamps, source pins, limitations and open next questions are in the package. Canonical investigation/claim.Reproduce: