R12 S6 Contextual Affine Law CPU Mechanics Result

Decision: pass_s6_cpu_mechanics

S6 defines a new operation law by two categorical demonstrations over an affine position action and asks a learned unit to infer and recurrently apply laws absent from training. This result establishes the exact mechanics and data split only; no neural model, board, fit, development score, or confirmation artifact exists.

Custody

• Original preregistration SHA-256: 0790584421afe6e27eb892173ca41c15c6931691434ba8f1205272c63b52b5ff.
• The first CPU falsifier failed before writing a report because the raw hash split omitted value 1 from the modulus-5 training card_y1 coordinate.
• V1.1 documents the sole split repair at SHA-256 a57d4108c0ae6e44555a30bae2dd59b13d479d2bbb3a406eee202113b572c013. It moves the lexicographically first held-out law that supplies a missing coordinate into training, without changing the theorem, architecture, controls, thresholds, or claim boundary.
• The repaired falsifier report is artifacts/r12/s6_contextual_affine_law_cpu_falsifier.json, SHA-256 a31a232c83a53d0b7aff87b4a495abd6740d98589059325951e2e4688e2bded6.

Exact Results

All frozen gates pass over moduli 5, 7, 11, and diagnostic modulus 13:

• 328/328 affine laws have unique two-witness cards;
• every one-witness class contains exactly m-1 possible laws;
• 3,748/3,748 law-position destinations reconstruct exactly;
• 3,748/3,748 categorical pop-insert cells close exactly;
• every modulus has a noncommutative order twin and separating late query;
• train, development, and reserved-confirmation law sets are disjoint;
• all admitted training splits cover every card coordinate and destination;
• treatment input contains only modulus, card_y0, card_y1, and current_location.

The repaired split counts are:

Only modulus 5 required a promotion: m5_a4_b2 moved from confirmation to training to supply missing card_y1=1. No row or score existed when this repair was frozen.

Boundary And Authorization

This is an identifiability and mechanics pass, not learned reasoning. An exact host affine decoder remains a favorable ceiling, and any fixed finite board can be tabled. The permitted next action is to commit these bytes, draw one post-commit development seed, build atomic training cells plus a disjoint recurrent development board, and fit the preregistered card-conditioned module. Confirmation generation remains forbidden until every development gate passes.