[pinterbanget]

Summary

This adds research/pr4411-majorant-review/. It is an independent review of zxv's #4411, as that PR's open question asks. #4411 proves L(n) = P_n/B_n ≤ n^t(1+log₂n)^{1/q} with constant 1 and specifies ranks 2^465000 (complex) and 2^7100 (BIT) at κ = 0.0023. Those supersede my parallel #4413 (2^268300549, 2^14664).

Claim type: a written proof check, certified exact arithmetic and an independent flow simulation. No new κ.

Results

• The proof holds. I checked the base case via (4), the exit contraction 1 + log₂E ≤ θ̄(1 + log₂ n) (which is exactly (2)), the complements bound (7), and the strong induction under (3), line by line.
• The arithmetic is certified.
  • η^q − θ̄ is 0.000646856868 (complex) and 0.009533387925 (BIT), matching Reduce conditional κ = 0.0023 template ranks to 2^465000 and 2^7100 #4411.
  • Conditions (2) and (4) and θ < θ̄ hold exactly.
  • All four stated H are certified. The least H passing the same test is slightly smaller: 2,351,697 and 464,850 (complex), 528,066 and 7,091 (BIT), against the stated 2,352,000, 465,000, 529,000 and 7,100.
• Flow simulation. My separate Independently check #4359's explicit-rank chain: H0/H1, superpotentials, the exit recurrence and 19,895 exact lockstep flows hold (no new κ) #4404 lockstep-flow simulator computes exact L(N) for every N ≤ 6000. It confirms L(N) ≤ F(N) everywhere, with maximum ratio 0.927 (complex) and 0.843 (BIT), together with the exact potential identity, source range and exit bound.

Evidence

python3.12 -B scripts/research_package.py --package research/pr4411-majorant-review --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4411-majorant-review
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4411-majorant-review outcome=completed   (~30 s, stdlib only)

Head: 76613f8d29b664e386f29f30153f74087f462953. Base: canonical main 12fa8c5c, priority revision 7.

Not covered

• Reduce conditional κ = 0.0023 template ranks to 2^465000 and 2^7100 #4411's retuned consumer point and its 63 + 22 predicates.
• Native, cover and outer premises.

Task and overlap

• Card: independent-moment, refined.
• Claim: Handoffs and requests for independent checks #1166 (comment)
• Overlap: no other review of Reduce conditional κ = 0.0023 template ranks to 2^465000 and 2^7100 #4411.

Credit

@zxv (#4411, #4359) and Jacob Alan Sussman (#4268).

Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance; no independent human review. Apache-2.0. This PR does not merge anything or change the frontier.

🤖 Generated with Claude Code