E-007b — Extended-precision positivity floor (T=400 full-rank points)
08-17-2026 · 3 rows · script
research/numerics/scripts/E-007-extended-precision-floor.py
Metadata
Smallest positive eigenvalue of Gabor-truncated Weil form at dps 40, Hann window (exact FT), T=200, bandwidths 0.5-2.0
Parameters
| T | 400.0 |
| lambdas | [0.5, 0.75, 1.0] |
| dps | 40 |
| window | Hann (exact closed-form FT) |
Caveats
- small T=200: finite-L effects larger than E-006
- d > N' for lambda >= 1.5: dimensional deficiency
Chart
Data preview (3 rows total)
| lambda | T | support_a | d | N_prime | full_rank | rank_above_noise | lambda_max | lambda_min_pos | minpos_over_mean | log10_ratio |
|---|---|---|---|---|---|---|---|---|---|---|
| 0.5 | 400.0 | 2.07679 | 132 | 317 | True | 132 | 6.132843 | 5.1055857e-7 | 2.338e-7 | -6.6312 |
| 0.75 | 400.0 | 3.11519 | 198 | 317 | True | 198 | 4.1498788 | 5.4758736e-8 | 3.761e-8 | -7.4247 |
| 1.0 | 400.0 | 4.15359 | 264 | 317 | True | 264 | 3.2023404 | 8.3456297e-9 | 7.641e-9 | -8.1169 |