[pinterbanget]

Summary

This adds research/pr4554-native-tables-check/, an independent check of the paid native tables in Dugongue's #4554 (head 4f46c6a9): the root powers z^e (PHASE-TABLES.md §1) and exp(−x) (NATIVE-EXP-TABLE.md). It follows my #4556, #4557 and #4558 on the same PR. All checked claims are confirmed. No new κ.

The texts are vendored (blobs 2dab8f3e and ee6e734c, SHA256-pinned). Nothing is imported from #4554's table code.

Checks

• Root-power tables. My own implementation of the squarings, digit tables and queries, with nearest rounding to 1/Q at the smallest Q ≥ 64(E+d).
  • Query error. Six (D, t) pairs up to D = 2^20, each with all four worst-direction grid seeds (error < 1/Q). All 20,852 queries are within 16(E+d)/Q of a decimal reference (AGM π); the worst is 0.076 of the bound.
  • Magnitudes. Coordinates, products and sums stay within 2Q, 4Q² and 8Q².
  • Factor count. A literal tree unfolding confirms the 2E+d error-factor count.
• Exp table. Constants (c, C, η, d, c0) = (1, 2, 1/4, 13, 6) satisfy η(d+1) > c+η+2, at n = 2^16, 2^20 and 2^24.
  • Taylor base. It satisfies 0 ≤ q̂ ≤ e^(−h) with C_d ≤ 0.96.
  • Table entries. Every entry satisfies 0 ≤ e^(−jh) − Ê_j ≤ j(C_d+1)2^(−S); the worst is 0.70 of the bound.
  • Queries. 612 queries all have error < 2^−p.
  • Cutoff. The tail condition holds for every 2 ≤ log₂(n+2) ≤ 4096, so no cutoff is needed for these constants.
  • Signed corollary. The reciprocal exp(+x) meets < 2^−p.
• Binding. 10 statements are bound verbatim to the vendored texts.

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

Limitations:

• PHASE-TABLES.md §2 (linear-program lowering) is out of scope.
• The exp table is checked for one constant set and three sizes.
• References are high-precision decimal, not interval-certified.

Head: 4ed34481357b2331be54da8b2661e38638658438. Base: canonical main f626db5c.

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

🤖 Generated with Claude Code