[pinterbanget]

Summary

This adds research/pr4583-header-check/, an independent check of mihir-s-05's #4583 (head 8d259a89). #4583 gives a serialized PR4100 sparse-union header of H = 2gh + g + 2⌈log₂(g+1)⌉ + 2 bits, shows H ≤ 810 p^β log₂ p = o(p) at #4100's core side, and gives the explicit cutoff p ≥ 2^(40·10^30). All checked claims are confirmed. No new κ.

Checks

• Separate codec from Bind PR4100 union headers to the actual core size (no new kappa) #4583's field table.
  • 2,888 round trips, including every boundary subset of a small domain, with every width equal to H.
  • 2,094 active-header checks: active axis, keep decision and active ordinal.
  • 3,600 rejected corruptions.
• Exact width chain, 6,448 cases. h = ⌈400 log₂ p⌉ is computed as (p^400 − 1).bit_length(). Then H ≤ 2gh + 5g, and H ≤ 810·g·t_lo with t_lo < log₂ p.
• Cutoff and binding.
  • δ = 3/10^30 is bound to the pinned Propose unconditional κ = 0.00173097911567079247276057 via batched CRT #4100 ledger's β and its group_headers slack, and L = 2^⌈400 log₂ p⌉ to GAUSSIAN.md.
  • δ·t0 = 120, with 810·t0 < 2^115 and 1620·t0 < 2^116.
  • The tail is monotone.

python3.12 -B scripts/research_package.py --package research/pr4583-header-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4583-header-check outcome=completed   (<1 s, stdlib only)

Limitation: the tape-simulator adaptation and the reader-cost accounting in #4583 are out of scope.

Head: e7538ae03738d903d1fb6bfde970573c31bda71b. Base: canonical main f626db5c.

Credit: mihir-s-05 (#4583); the #4100, #4327 and #4376 lineage. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code