[pinterbanget]

Summary

This adds research/eps-halo-exponent-check/. It is an independent check of jwr404's #4439 (within one cell) and #4442 (across cells, downward reading), the halo exponents under the relative budget ε = 1/(16p²). It is the ε-route counterpart of my #4460.

Claim type: an independent check by separate code, with exact rationals. No new κ.

Results

All statements check out.

• Ceiling. The split identity (grid-proved) gives off ≤ (16p²−2)/(16p²−1), so the gap is exactly 1/(16p²−1).
• Exponents. Endpoint 12, length 26, bandwidth and agreement 28, normalizer 6 (7 also works), exact for p in 2..64, with all-p arguments.
• Fails. 11 and 5 at p = 2; 25 at p = 2 (certified); 27 at p = 2 (loose count) and for p ≥ 3 (sharp count).
• Apply the smaller halo exponents across a cell, under the downward reading (no new κ) #4442's extras. The p = 2 tightness 63·63 > 62·64 and the bare-kernel example (square gap 32/16 against 20/16) both hold.

Evidence

python3.12 -B scripts/research_package.py --package research/eps-halo-exponent-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/eps-halo-exponent-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/eps-halo-exponent-check outcome=completed   (<1 s, stdlib only)

Head: 0cf8e2b0722379e9195f855c6c28aeaffa39aebd. Base: canonical main 2a13eb18.

Credit: James Reed (jwr404, #4439 and #4442). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code