[pinterbanget]

Summary

This adds research/pr4554-lowering-check/, an independent check of PHASE-TABLES.md §2 (finite-precision lowering of linear straight-line programs) and §4 (perturbed shear denominators) in Dugongue's #4554 (head 4f46c6a9). With #4556–#4562, every constructive component of #4554 now has an independent check. All checked claims are confirmed. No new κ.

Checks

• Induction steps. They hold exactly in rationals for all h ≤ 200 across a grid of C0 (1,200 cases):
  • magnitudes ≤ N^b C^h;
  • the closed form ε(V+1)(C0+3)^(h+1) dominates both the add step and the scale step (C0+1)E + εV + ε.
• Random programs. 60 random layered ADD/SUB/SCALE programs ran in exact rationals against a rounded, perturbed-scalar copy. Every node is within the error bound (worst ratio 0.0094) and the magnitude bound.
• FFT DAGs. On radix-2 FFT DAGs up to N = 512, the observed error lies below the sharper FFT-ERROR.md chain (my Independently check #4554's native FFT multiplier: exact error-chain recurrences, parameters to ell=200, separate fixed-grid multiplier (no new κ) #4557), which lies below the §2 bound. The §2 bound is valid but very loose here, 2·10^9 against an observed 3·10^−6 at N = 512. That fits its role as a generic O(log N)-bits certificate.
• Bilinear extension and §4. The bilinear product extension and the perturbed shear denominators (≥ 3/4 and ≥ 1/2) hold in 2,000 cases.

python3.12 -B scripts/research_package.py --package research/pr4554-lowering-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4554-lowering-check outcome=completed   (~1 s, stdlib only)

Limitation: the checks are finite; the universal statement rests on the written induction, whose steps are checked exactly.

Head: d1f2fa275dbd3388190e6ff30499b7ea90562575. Base: canonical main f626db5c.

Credit: Dugongue (#4554). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code