[pinterbanget]

Summary

This adds research/batch-width-recount/. It is an independent recomputation of mihir-s-05's #4507, the least chronological batch widths for #4436's direct mixed flow. It uses my independent #4436 flow and a separately written per-cut enumerator.

Claim type: an independent recomputation. No new κ.

Results

All of #4507's numbers reproduce.

• Exits. Aggregate per-cut exits equal the flow's exits at every rank.
• Toy widths for {2:4,3:1} ← {1:6,2:2} through rank 12: …, 4375, 110600. The counterexample also reproduces: pooled multiplier 175 against chronological 700, because eight rank-8 leaf cuts each hold one job.
• Fixtures at rank 100. 433 → 42 bits (95 of 96 ranks strictly reduced) and 1,002 → 88 bits (97 of 98).
• Raw p7 at rank 1,000. 17,504 → 2,524 bits, with the factor in [2^14980, 2^14981) and strict reduction at 879 of 880 ranks. Every new width divides the nested width.

Evidence

python3.12 -B scripts/research_package.py --package research/batch-width-recount --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/batch-width-recount
  PASS_REGISTERED_RESEARCH_PACKAGE research/batch-width-recount outcome=completed   (~1 s, stdlib only)

Head: 915b94b890cde927fba98e02db32ae2864f6bf05. Base: canonical main f9f85c1e.

Credit: mihir-s-05 (#4507) and zxv (#4436). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code