[pinterbanget]

Summary

This adds research/pr4417-centre-review/. It is an independent review of Matarener's #4417, the nonlinear and adaptive centre-sharing floor, and its +0.67% packing screen.

Claim type: a written proof review plus a separately implemented recomputation of the screen. No new κ.

Results

• Theorem 1 holds under the inherited premises.
  • On V ⊂ ker H the decoder forces E to be injective on a real 16d-dimensional set.
  • Adaptivity on earlier fresh reads still yields one function E : V → ℝⁿ.
  • Invariance of domain covers the continuous case, and semialgebraic dimension preservation covers finite branching.
• Theorem 2 holds. It is a bit count, and Kronecker sharpness is re-checked on six small grids.
• Screen. I reimplemented the relaxation separately: coverage mass (m−1)w + centre, idle mass at rank R = 51 under m² > 2R², certified intervals, and no import of ceiling.py. All six rows match Close nonlinear and adaptive centre sharing at the fresh-information floor (no new κ) #4417 to 10⁻¹¹: ratios 1, 1.002113, 1.004233, 1.006359 and 1.006721, plus the halved-information control at 1.901107.
• Rank 72 is the extremal regroup. The per-unit-mass cost r^{−a}m^{a−1} is nonincreasing in r, so +0.67% bounds every packing of the 64 centre units into children of rank at most 72.

Evidence

python3.12 -B scripts/research_package.py --package research/pr4417-centre-review --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4417-centre-review
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4417-centre-review outcome=completed   (~20 s, stdlib only)

Head: da76aa4d3aec87a2fc51439f3f16a789d2a2b517. Base: canonical main 12fa8c5c, priority revision 7.

Not covered

• The premises of centre-history-innovation.
• Add selected centre decoder demand floor audit #3918's carrier premise.
• Terminal-only consumers.

Task and overlap

• Card: centre-path-sharing, refined.
• Claim: Handoffs and requests for independent checks #1166 (comment)
• Overlap: no other review of Close nonlinear and adaptive centre sharing at the fresh-information floor (no new κ) #4417.

Credit

@Matarener (#4417), Douglas Colkitt (the ceiling model), and Jose Manuel and #3873 (the premises).

Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance; no independent human review. Apache-2.0. This PR does not merge anything or change the frontier.

🤖 Generated with Claude Code