[pinterbanget]

Summary

This adds research/pr4554-native-stability-check/, an independent check of NATIVE-STABILITY.md in Dugongue's #4554 (head 4f46c6a9). It covers the fixed-point lowering of a closed rational Gaussian provider, its instantiation to #956, and the shear-division bounds. With #4556–#4561, every constructive component of #4554 now has an independent check, except PHASE-TABLES.md §2. All checked claims are confirmed. No new κ.

The spec is vendored, along with #956's PROFILE.json from #956 head fa4df77c, both SHA256-pinned. Nothing is imported from either PR's code.

Checks

• Gate norms, exact rational tests. x += a·y has norm ≤ 1+ā, scaling ≤ max(1,ā), and COPY √2, over 3,000 values of a.
• Roundoff.
  • Programs. 40 random rational ADD/SCALE programs lowered with truncation toward zero all stay within the transported local-error bound; the worst ratio is 0.035.
  • Formulas. The precision formula gives ≤ 2^(−B−2), and the integral width has three spare bits (3,321 cases). The (1−i)^e Walsh rescaling is exact.
• Research: close the PR390 heterogeneous physical provider in exact RAM #956 instantiation.
  • m = 73, W = 58,899 and largest child rank 48 are bound to Research: close the PR390 heterogeneous physical provider in exact RAM #956's PROFILE.json.
  • The integer-root certificate holds at all 12 ranks, and the moment μ < 1 (gap 5.7·10⁻⁵) funds θ = 1023/1024. Both are recomputed here.
  • The depth bound 1 + ⌈log(e+1)/log(73/48)⌉ holds.
• Shear divisions. t1 ≥ 1 and Re t2 = −[(a−1/2)²+b²+3/4] ≤ −3/4 hold exactly. The perturbation bounds (2U+1)δ and 32/9 hold in 9,003 cases, including the extremal μ = 1/2.

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

Limitations:

• The template constant K is not computed from Research: close the PR390 heterogeneous physical provider in exact RAM #956's bytes; Native Word RAM Gaussian adapters: chirp blocks and reusable banded inverse #4554 prints no value, so formulas are checked for K ∈ {2, 3, 17}.
• Research: close the PR390 heterogeneous physical provider in exact RAM #956's full theorem is not re-proved.
• The Newton/Toeplitz preparation is not covered, as Native Word RAM Gaussian adapters: chirp blocks and reusable banded inverse #4554 states.

Head: 754e8c6849a152b4a7531ee7f2e8d8cee2d69b5a. Base: canonical main f626db5c.

Credit: Dugongue (#4554); the #956 provider lineage; ram_cost (shear argument, as credited in #4554). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code