[ToikY]

This supplies the kernel-internal clean-bit implementation released in PR #6523, for Ali Romman's exact PR #6509 conservative Gaussian pair. It computes one pair in place with literal CNOT/Toffoli gates and returns every supplied owned bit to zero.

The contract is 6≤W≤256, two separately compiled public signs σ=±1, four signed W-bit components with |v|≤2^(W-6), and 14W+6 supplied clean bits besides the 4W data bits. Operands may be borrowed and temporarily written exclusively. The complete logical bill is T=96W-80, C=276W-104, NOT=0, total 18W+6 wires. For b=bit_length(18W+5) and G=C+T, the declared fixed selector encoding costs 9+2G+b(2C+3T) bits. This prices logical syntax, not physical routing or zero-stock preparation.

The source #3152 adder/HALF templates retain their guards and legal local wire IDs, then undergo injective renaming. The proof covers center parity/sign, exact reversible halves, compute-copy-uncompute/swap and reachable inverse inputs bounded by 2M, with intermediates bounded by 8M+1 < 2^(W-1). No reset, discarded bit or nonzero CLEAR is an emitted operation.

Evidence:

• 502 primary compilations/counts/hashes cover every width/sign. 16 retained words are independently interpreted on all 14,814 complete states, checking public outputs, every owned bit and literal reverse; each actual run covers 100,549,104 gate visits. The other word hashes are primary evidence, not independent truth execution.
• Four primary strict modes, two independent actual-artifact normal/optimized modes, 17 oracle controls and 21 intended external rejections pass. Four equal-count, valid-wire mutants reach center/rotation/cleanup/HALF state failures. The oracle blind first was arithmetic/bill forecast only; actual-word evidence came later.
• Common profile SHA256: 29cc4d8dd40c336f574a89b462fe71e6fe2f7afae21ee81796a26db4530f08be. Code and scientific artifacts remain unchanged from first seals; regenerated gate equality uses decompressed values, not gzip bytes.
• Scientific commit 2c5ed12d519c15cc6a8dd5b0fe3b132298c853b0 passes all four registered commands, 29-file byte/mode/history checks and initial official export with both declared inputs. Final documentation commit5207dd74d3667bb6e27884488d31bc8c24d597ad passes exact29file byte/mode/history checks, official export integrity with2inputs, and all four direct read-only Git-free empty-PATH cold commands. Exported bytes/modes remain unchanged.

The original external expectation that primary reject SCHEMA whitespace exceeded its contract: primary authenticates sources/cases; oracle additionally authenticates SCHEMA bytes. The unsupported expectation and clean exit are preserved, with only the harness corrected. Working schema/code/artifacts never changed. VALIDATION/RUN-RECORDS document this scope correction and exact first stages.

Credit Ali Romman #6509/#6511, ToikY #6523, Nick Petalas #3152/#3081, Clear1nsight #4017, Cuccaro-Draper-Kutin-Moulton, Bennett, Tekalign/Barenco and retained #3159/#3241/scalar lineage. Numerical rounding/inverse and generic arithmetic/uncomputation methods are prior.

Clean-stock funding, actual caller placement, full native layer, tape/precision/compiler/outer admission remain open. No optimality, speedup, physical tariff, κ or frontier change is claimed. Maintainer edits/auto-merge disabled; no merge. Hosted CI succeeded on original run 41732103736: 711 helper tests (24 skipped), all four registered package commands including both actual 16-word/14,814-state comparisons, and both staged/unstaged drift checks passed. Synthetic test commit d0ca896737b34a082b44d300fb4c634c110a36eb has the exact verified tree and expected main/PR parents; no actual merge occurred. Mode, source-history and export preflights above were local. Public head: bcc263f3d9843ac82cc191e7e60da6380254405a.

Substantial OpenAI Codex assistance with separate AI primary/oracle implementations and static review; independent human and formal proof-kernel acceptance are unclaimed.