[pinterbanget]

Summary

This adds research/pr4541-packed-transfer-check/, an independent check of Dugongue's #4541 (head 46ca24a8), the packed Word RAM transfer O((T+n+m)/log(n+2) + (n+2)^(1/16) log(n+2)). It covers the §1 parameter arithmetic and the macro-step invariant and halting of §§2–3. All checked claims are confirmed. No new κ.

The verifier was written from #4541's PROOF.md text alone, vendored with its blob 43a6afbe and SHA256 pinned. Nothing is imported from #4541's code.

Checks

• §1, exact integers, 720,240 cases (k ≤ 8, c ∈ {2,4,8}, s ≤ 10, λ ≤ 3000):
  • 16b ≤ λ above the stated cutoff, so the table has at most (n+2)^(1/16) rows;
  • 128Kc·r ≥ λ;
  • L ≤ B;
  • codec exponent cr < b;
  • the origin margin H > 2·2^(a−4)(n+2)^d (12,288 cases).
• §§2–3, independent packed simulator. It implements B-field words with dirty high bits, interleaved tapes, signed coordinates at H, two-word windows with all reads before writes, an r-step local table and the head update old + local − r. Against direct execution on 486 random multi-tape machines:
  • 263 halting runs match exactly on state, count, heads and every cell;
  • 223 nonhalting runs match at every macro boundary;
  • the runs include 46 halts found at an epoch boundary with elapsed zero, and 11,090 block-crossing windows;
  • dirty high bits are preserved;
  • the shifted-writeback rejection control is caught in 19 of 20 runs.
• Binding. 9 statements are bound verbatim to the vendored proof.
• Replay. Packed Word RAM transfer: conditional O(n / log^κ n) multiplication (no new TM κ) #4541's own package replays at its head (outcome=partial, 4.3 s).

python3.12 -B scripts/research_package.py --package research/pr4541-packed-transfer-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4541-packed-transfer-check outcome=completed   (~2 s, stdlib only)

Limitations:

• The packed IO codec (§4), the corollary's TM antecedent and the RamStd lowering are out of scope.
• The simulator runs are a finite random family. They corroborate the written universal argument but do not replace it.

Head: a821e926e3d7eaeae8b12be974dc5083360f6494. Base: canonical main f626db5c.

Credit: Dugongue (#4541); Hopcroft, Paul and Valiant (1975). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code