[ywz65]

PR2449 proves a linear local charge for its encoded ADD using amortized counters. This independent audit derives exact all-length countdown bills from that source, includes separately metered input-word reads, and accounts for the complete split/merge traversal, scratch erasure and head returns. It confirms the local implication under the stated callback tariff; no defect or new exponent is claimed.

The reviewed source is ef4640fbf9c360ef66dbc5d29916e741d515bf39. The new package retains only the three runtime modules and their proof/README/NOTICE, byte-for-byte, with Git blobs and SHA256 pins. It imports none of PR2449's checker, oracle, coefficient generator or receipt.

The proof separates three costs:

• Exact counter lifecycle formulas, including N=0, powers of two and the final 1-to-0 decrement. Canonical spectator widths are necessary; an arbitrarily padded singleton breaks a volume-only bound and is rejected by the source.
• Exact payload movement (10V+13, 3V, 10V+16) for reads/writes/moves. Combined with counters and extent checks, a conservative bound is 947V symbol operations.
• Conditional arithmetic/preparation O(B + UM L^2). The retained root-coupled B <= A_q w^1800 yields the source's local C_q V result by explicit factorial absorption.

The executable calls its coefficient callback twice total, once per traversal, at one fixed current prefix. The review states that boundary explicitly. It does not supply a varying-header driver, complete residual, recursive child, full selected callback proof, finite-machine compiler or global family/owner caller. Jose Manuel's active residual implementation remains separate work.

Validation: CPython 3.12.7 registered normal/optimized replay and CPython 3.14.5 optimized primary pass. There are 1,026 complete counter cases, 386 full Boolean-basis forward/inverse cases, exact operation invoices, five semantic controls and five test groups. Tests catch extra source reads, omitted erasure, changed split/merge coefficients, wrong inverse sign, source/receipt corruption and missing receipts; a read-only Git-free export passes. An independent agent reviewer checked the all-length derivation and added 36 counter boundary cases through 8193 and 18 simultaneous-spectator mixed-payload inverse cases; no material issue found. No independent human or formal-kernel review is claimed.

Reproduce with Python 3.12:

python3.12 scripts/research_package.py --package research/binary-add-cost-audit

Base: canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4, freshly fetched. The selected frontier and frozen inputs are unchanged. TASK.json records scope, overlap coverage and limits. Open next questions focus on reviewing the separately developed residual composition and formalizing the counter transition model.

Credit Jose Manuel (jmbarrancoml) for PR2449/2405 and its retained source527, supplier, descriptor, stream and relative-origin lineage. Prepared for ywz65 with substantial OpenAI Codex assistance in derivation, implementation, checking and writing.