[jwr404]

Summary

This adds research/gaussian-twonorm-guard/. It answers open question 2 of #4402: do any #4100 precision guards change when the inverse 2-norm drops from the bandwidth form to 1/sqrt(delta delta_col)?

Claim type: a caller inventory plus an exact comparison under the floors already written in GAUSSIAN.md. No new κ. This does not prove a column gap for the rounded reference H.

• The callers in research/unconditional-batched-crt write exponents 10, 20, 40, 42, 45, 48, 100, 128 and 400. AUDIT.md names the notes and writes no p^10. The broad < p^6 sentence does not use the bandwidth formula.
• For every integer p >= 2, with bandwidth b <= p - 1 and delta >= 1/(16p^2), the bandwidth 2-norm ceiling is strictly below p^10. At p = 2 it is not below p^9, so 10 is the smallest uniform exponent for that corner.
• If delta_col meets the same floor, the column-gap ceiling is at most 16p^2, also strictly below p^10.
• Both ceilings satisfy the hypothesis those later exponents assume, so none of them has to increase. At p = 19 the bandwidth ceiling is already below p^6 and the column-gap ceiling is below p^3.

Test plan

python3.12 -B scripts/research_package.py --package research/gaussian-twonorm-guard
  PASS_REGISTERED_RESEARCH_PACKAGE research/gaussian-twonorm-guard outcome=completed

Maintainer replay has not been run. Head: 25cf6de154c641faaf6c85fe6e9bf5f51bdeb57e. Base: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244, priority revision 7, selected record unchanged. Checked 2026-10-21T16:40:11Z.

Not covered

• Cross-cut entries, truncation and rounding, so delta_col >= 1/(16p^2) is not claimed for H.
• A smaller halo or normalizer. That arithmetic is the open next question; it is not required for correctness.

Claim: #1166 (reply in thread)

Prepared by James Reed with substantial Cursor Grok 4.7 assistance. Apache-2.0. Maintainer edits are allowed; this PR does not merge anything or change the frontier.

Made with Cursor