[pinterbanget]

Summary

This adds research/pr4585-geometry-soundness-check/, an independent soundness check of mihir-s-05's #4585 (head 025f37fe) against exact geometry. #4585 floors the 128 #4470 receiver windows using coarsened relaxed_partitions, built from mandatory contacts and bridges. Its argument needs every actually realisable word profile to be listed or to refine a listed partition. #4585's lists differ in 33 windows from the identical sets of #4567, #4581, #4582 and #4587, so that property is checked directly. It holds in all 128 windows. No new κ.

Checks

• Exact profiles. Every unit-shear word of length ≤ 5 with the window endpoint is enumerated. An exact search over actual nested subspaces of F₂⁹, with joint incidence enforced, yields every realisable profile. This is Close local improvements on #4470: shear rewrites (128 windows, 88 nonadjacent, len 6, |c|<=3) and 1- and 2-contact retiming - all 0 (no new κ) #4567's machinery, re-run here.
• Coverage. There are 235 realisable profiles: 151 listed and 84 refining a listed partition, with 0 violations (exact multiset bin-packing).
• Incumbent. It is realisable, listed and capped-rank dominant (Σ min(r,k), k ≤ 9) in every window.

python3.12 -B scripts/research_package.py --package research/pr4585-geometry-soundness-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4585-geometry-soundness-check outcome=completed   (~75 s, stdlib only)

Length 6, recorded run. 239 realisable profiles: 151 listed, 88 refining, 0 violations. The 239 equals the 239 window/profile pairs of the relaxed sets of #4567/#4581/#4582/#4587, and realisable sets sit inside relaxed sets window by window. So every relaxed profile is realised exactly by some actual word of length ≤ 6: the relaxation is tight on these windows.

Limitations:

• Lengths above 5 are covered by Prove receiver-window floors with mandatory contacts and bridges (no new kappa) #4585's written proof.
• Unit coefficients only.

Head: 81b302ecda3e24893debf3cf8013867c3a0cbf30. Base: canonical main f626db5c.

Credit: mihir-s-05 (#4585), Cinna Davis (#4470). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code