[pinterbanget]

Summary

This adds research/pr4554-gaussian-chirp-check/, an independent check of GAUSSIAN-CHIRP.md in Dugongue's #4554 (head 4f46c6a9): the centred Gaussian block maps that give the PR its title. It follows my #4556–#4559. All checked claims are confirmed. No new κ.

The spec is vendored (blob 4e31f302, SHA256-pinned). Nothing is imported from #4554's chirp or block code.

Checks

• Theorem 1. D[x]E[y]H[x+y] = W[x,y] holds as a polynomial identity in the exponents. Σ_y W Z = D·(H ∗ rev(E·Z))[x+l−1] holds with an explicit linear convolution at 60 digits on 40 rectangles.
• Conditioning (A). Every D, E and H exponent is at most Cp, checked exactly in rationals on 300 parameter sets.
• Geometry. 3,522 retained blocks over 120 random geometries satisfy the K bound and |c0| ≤ R+(u+v)(q−1), and (D) implies (A). The tail rule passes 116 cases.
• Precision rule. (C) implies (B) ≤ 2^(−p0−4) in all 576 cases.
• End-to-end. My own fixed-point block evaluator runs at the P that (C) prescribes, with grid chirps and twiddles, nearest rounding, a radix-2 FFT linear convolution with N0 = 4q, and selection at x+l−1. In all 6 runs the error is far below 2^−p0 and within (B).

Observation. (C) is valid but conservative. At conditioning scale p = 52, the observed precision loss is about 180 bits, against about 484 bits that (C) reserves above p0. The open question proposes a sharper rule.

python3.12 -B scripts/research_package.py --package research/pr4554-gaussian-chirp-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4554-gaussian-chirp-check outcome=completed   (seconds, stdlib only)

Limitations:

• The exp-table generation of the chirps is checked separately, in Independently check #4554's paid phase and exp tables: own tables vs 16(E+d)/Q and 2^-p, worst-direction seeds (no new κ) #4559.
• Theorem 3's operation count is not re-counted.

Head: 4ee0d1ed4ffd202adb745c65835c89b5f6317bcf. Base: canonical main f626db5c.

Credit: Dugongue (#4554); the Harvey–van der Hoeven sources; classical chirp convolution. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code