[pinterbanget]

Summary

This adds research/pr4521-expanded-count-check/, an independent check of Dillon's #4521 (head d72f2282). #4521 checks #4436's fully expanded rank-mass identity B_n·n − P_n = Δ·Q_n and U_n ≤ Q_n ≤ B_n·n/Δ, with nested widths. Using my own #4436 flow (from my #4456 checks), with nothing imported from #4521 or #4436, the exact big-integer totals match all 12 of #4521's published SHA256 hashes. No new κ.

Checks

• Every rank. The identity and bounds hold exactly, child batches are integral, and ranks strictly descend.
• Exact totals. B, P, Q and U match in bit length and SHA256 for two toy rules at rank 100, and for raw p7 (bound to main) at rank 1000, where B has 17,504 bits and P 17,514.

python3.12 -B scripts/research_package.py --package research/pr4521-expanded-count-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4521-expanded-count-check outcome=completed   (~3 s, stdlib only)

Limitations:

• The checks are finite ranks; the all-rank induction is Independently check #4436 expanded compiler counts (no new κ) #4521's.
• Independently check #4436 expanded compiler counts (no new κ) #4521's "routes" count is not recomputed.

Head: d6370b47b1217db2483b6d4fc0d45ecf690d8946. Base: canonical main f626db5c.

Credit: Dillon (#4521), zxv (#4436), Jacob Alan Sussman, Cinna Davis. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code