[pinterbanget]

Partial independent check of Matarener's #4603 (head caab2b42), the p16 query-shear floor. The three checked statements hold. No new κ.

research/pr4603-shear-floor-check/verify.py uses the standard library only and takes about 1 s. Nothing is imported from #4603.

Results

1. Exact identity. S_x(−Q)·S_y(Q⁻¹) = signed_swap·diag(Q⁻¹,Q)·S_x(Q) holds, checked with exact Laurent-polynomial arithmetic. The product is [[0,−Q],[Q⁻¹,1]], and a wrong-sign control is rejected.

2. Window premise, on main's pinned complex controller:

   • between each of the 15 shears and the last full call on its own pair there are only ADD and IDLE events;
   • the 15 windows are pairwise disjoint.

   So any scheme paying at least 1 per window pays at least 15, which the controller attains. An inserted SIGNED_SWAP is detected.

3. Merge bound. Merging 112 rank-one jobs into 14 rank-eight jobs saves 0.701 < 1 unit of moment at the current root.

Not covered

• the fusion Q-coefficient ranks;
• the distinct-line census;
• the BIT controller's windows;
• the parity model's rules.

Credit: Matarener (Mark) for #4603; 1337isnot1337 / Cinna Davis and zxv for the controllers. Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance.

Head: fe0419b

🤖 Generated with Claude Code