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openresearch
55453b05cb feat: q-profile sweep + Gerver Sidon design + report
Three deliverables:

1. scripts/crt_qprofile_sweep.py
   Safety factor optimization (R1 from toroidal refinement). Replaces
   brute-force modulus selection with systematic q-profile sweep.
   Tests: q < 1 (poloidal) vs q > 1 (toroidal) Sidon rate,
   simple rational q vs non-simple (R2 cross-pair coprimality).
   All integer arithmetic (Fraction for q).

2. docs/research/GERVER_SIDON_DESIGN.md
   Direction B design: actual Gerver sofa (18 arcs) with CRT Sidon
   boundary in ℤ², high-resolution motion (T=100), justified tolerance.
   Explains why Direction A failed and what Direction B fixes.
   Honest assessment: long shot, but more promising than v2/v3.

3. (Report in /tmp — uploaded separately)
   Negative result write-up: sofa coloring doesn't detect q=1 at
   justified tolerance. HN spectral database: Hoffman tight for
   regular graphs, gap=1 for unit-distance. CRT n-moduli generalization.
2026-07-04 14:50:28 +00:00