[JoyboyBrian]

The sharp parameter-entry work leaves the actual binary row quotient and stock guard unexecuted. This package supplies an opt-in fresh_rows.quotient refinement, executes it through the literal caller guard, and records the setup/state tradeoff rather than claiming a uniform speedup.

• For valid fixed contexts with modulus q^w, the adapter replaces m² encoded radix traversals and m²(w−1) q-divisions with one traversal and w−1 divisions by C=q^(m²). The scoped argument proves identical quotient and accepted divisibility domain; the actual Machine.node quotient/save/stock guard and save helpers run on binary Count tapes.
• Matched actual replays cover m2,w1/2/3; m4,w2; and m64,w1. A candidate-only m64,w2 run uses the real 9475/28416/GL64 factors. The original m64,w2 replay and full caller payload remain unrun.
• The invoice includes separate record/residue actions, every Count-division input/divisor width, remainder-state cardinality, and explicit square-and-multiply construction. At m64,w1, residue actions drop 4,808,704→1,174 while record actions stay 755,782; constructing the 6,493-bit divisor costs 13 multiplies / 14,066,186 schoolbook bit products, exceeding the scan saving under that unamortized charge. The reported linear-bit proxy is diagnostic, not a proved binary-TM bound. No unconditional physical improvement follows.
• Valid-context rejection controls preserve borrowed input and erase temporaries. The deliberately malformed modulus control exposes the inherited two-slot radix_power rejection leak in both versions; the receipt explicitly marks failed restoration and harness-only rollback, outside the theorem. No frozen caller repair is smuggled into this adapter.

Credit: David Arias's PR2753 quotient/Count code; ToikY's directory setup/radix-cost work; #4757 5dba1acc2ef67e65e6a40e963f727b01edc5e132 sharp entry; NickPetalas #3246, Tekalign #3264, Mihir #4685, and codyw912 #4734 stock/adapters. No reproof of the 9475 factor, selected-frontier change, supplier admission or complete multiplication theorem is claimed. New work: Brian (JoyboyBrian), substantial OpenAI Codex assistance, Apache-2.0.

Validation at 4cc9b9719fdab59f0f33243b9c323fe4d69346f5: ordinary and optimized exact replay; package metadata; committed-byte/source-history preflight (30 files, only canonical base 624de9dc66858af0945e5f8a0942488d62280d43); official export/integrity check; Git-free cold ordinary/optimized replays (1.053s/1.120s) with empty bytecode caches; live-source corruption and boolean→integer receipt corruption rejection; all 31 export files unchanged. Affected-package planner selects only this package. Root source review found no blocker after the cost-model clarification. Hosted CI has not been verified.

Canonical investigation: #4682 (comment) . README includes concrete open questions for physically priced division, amortization, malformed-context cleanup, and admitted-root payload integration.

Submission checkpoint: canonical main refreshed at 19:57 UTC remains 624de9dc66858af0945e5f8a0942488d62280d43, priority revision7 unchanged. Final cache completed 19:59:26 UTC with 316 open PRs, 3,732 Discussion records and 6,319 local notes (complete reported inventory/pagination, no warnings). Scoped offline searches found the credited predecessors and this investigation/coordination pointer, with no additional same-obligation lead requiring a pivot. This is not an exhaustive novelty certificate. Relevant #4176/#4757/#4759/#4685 heads were live-rechecked unchanged and merged.