[pinterbanget]

Summary

This adds research/pr4538-cost-theorems-check/, an independent check of the four native-layout cost theorems in Dugongue's #4538 (head dffc7939, cost/COST-THEOREMS.md). All checked claims are confirmed. No new κ.

The theorem text is vendored (blob a5d940b2, SHA256-pinned). Nothing is imported from #4538's streaming_affine.py, quadratic_phase.py or monomial_metadata.py.

Checks

• Theorem 1, affine permutation within 8NL + 40N + 8.
  • Count arithmetic. Literal increments give the flip count T = 2N − r − 2, and the count identity holds.
  • My own program. I wrote a separate 30-instruction program on a small additive/Boolean RAM with truncated SUB and no multiplication, division or right shift, using the stated macro costs XOR 4, MOV 2, JNZ 2. Over 36 runs (r ≤ 8, L ≤ 5, random invertible A, offset b), it permutes records exactly and preserves source, table and padding. It uses at most 0.82× the bound.
  • Control. An XOR→ADD mutation is rejected.
• Theorem 2, streaming quadratic phases. The d = (a_j + 2g_j) mod 4 update reproduces q(x) at all 3,012 visited points, with fewer than 2N flips.
• Theorem 3, limb negation. Complement plus carry equals negation modulo 2^(kL) in 800 cases, with temporaries ≤ β. The Gaussian-unit table equals multiplication by i^q.
• Theorem 4, metadata compiler. My compiler, written from the stated S/Z/CZ/CNOT/SWAP/X rules, satisfies word|x⟩ = i^(c+q(x))|Ax⊕b⟩ on every basis state. This holds for 360 random words (r ≤ 6, up to 40 gates) against a literal Gaussian-integer interpreter. The X-then-S control needs c = 1, and dropping c is caught.
• Replay. Word RAM transfer: finite TM compiler, checked logarithmic-width bridge and native kernels #4538's own package replays at its head (outcome=partial, 9.1 s).

python3.12 -B scripts/research_package.py --package research/pr4538-cost-theorems-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4538-cost-theorems-check outcome=completed   (~1 s, stdlib only)

Limitations:

• The TM emitter, the Lean bridge and packed tapes are out of scope.
• Macro costs are taken as stated, not re-derived from Lean.
• These are finite checks that corroborate the written inductions.

Head: a73b063b6970ecb6730211508969b05b306f4f80. Base: canonical main f626db5c.

Credit: Dugongue (#4538). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code