[pinterbanget]

Summary

This adds research/pr4532-retuned-majorant/. It retunes Dillon's #4532 critical-root majorant on the p16 (#4470) profile, keeping κ = 0.003020165, the native profile and the isolated root. The new witness passes #4532's own exact gate checker (critical_guards, pinned):

M = 2^24, a = 3, b = 2, s = 1/10, λ = 1/5, ℓ0 = 64, p = 3/10, c = 101, cover exponent .99725, β = .564.

The checker covers tails, forward ordering, moment ratio, mean gap, concavity, the mirror at the cover exponent, the tangent cover and the recurrence funding.

Against #4532's witness (M = 1024, ℓ0 = 650, p = 2/5, c = 133), ln A falls from 10.24 to 1.11. The certified least frozen rank for #4535 then becomes:

	d = 10^−10 (#4535's slack)	d = 10^−12 (#4564)
#4532 witness	2^77,014,944,503 (#4563)	2^29,328,002,299 (#4564)
retuned	2^31,585,308,786	2^11,825,387,808

The last entry is 84.6× smaller in exponent than #4535's 2^(10^12). The height envelope falls from 2·10^11 to 2.46·10^9, and log₂ C_N from 3.4·10^12 to 4.19·10^10. No new κ.

Checks

• Gates. The pinned checker passes both the control and the retuned witness. The retuned funding is 0.043565, against 0.042809 required, and the mirror is 0.563849 < β.
• Mutations. Three are rejected: ℓ0 = 40 (tangent cover), p = 1/5 (funding) and β = .55 (mirror window).
• Ranks. They are certified with my own logarithms in exact rationals: least, monotone beyond and above n0. The control reproduces Certify #4535 at a 13x smaller finite rank: N = 2^77,014,944,503 instead of 2^10^12 (same κ = 0.003020165) #4563 and Certify #4535 at outer slack d=1e-12: all 54 predicates pass, frozen rank N = 2^29,328,002,299 (34x below 2^10^12, same κ) #4564 exactly.

python3.12 -B scripts/research_package.py --package research/pr4532-retuned-majorant
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4532-retuned-majorant outcome=completed   (~4 s, stdlib only)

Limitations:

• Only the critical-root compiler geometry, the majorant and the frozen rank change. Improve conditional multiplication kappa to 0.003020165 via critical-root transfer #4535's physical bridge must apply to the new fixed word as before, and no physical constant is computed.
• The parameters come from a coarse float search, certified exactly; better ones may exist.

Head: d6a9a75bf48b047927bc4103def6f821909bb835. Base: canonical main f626db5c.

Credit: Dillon (#4532 theorem and checker), hexapode (#4535), zxv and Jacob Alan Sussman, Cinna Davis (#4470). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code