E-006 — Positivity horizon: eigenvalue floor vs bandwidth
08-17-2026 · 4 rows · script
research/numerics/scripts/E-006-positivity-horizon.py
Metadata
Eigenvalue floor of Gabor-truncated Weil form vs bandwidth lambda; conditioning of positivity certification (cf. Groskin B_T budget, Kim et al. superexponential decay)
Parameters
| T | 2000.0 |
| lambdas | [0.5, 1.0, 1.5, 2.0] |
| window | psi0 |
| zeros_source | E-002 |
| precision | float64 |
Caveats
- all zeros on-line => PSD by construction; the floor measures conditioning, not failure
- d > N' => dimensional rank deficiency (overcomplete basis), not form degeneracy
Chart
Data preview (4 rows total)
| lambda | d | N_primes_zeros | dim_deficit | rank_numeric | lambda_max | lambda_min_pos | minpos_over_max | minpos_over_mean | log10_minpos_over_mean | pct01_eig | pct10_eig | pct50_eig |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.5 | 917 | 2044 | 0 | 869 | 4.3362e+00 | 6.6200e-10 | 1.527e-10 | 2.940e-10 | -9.53 | -1.502e-15 | 4.457e-05 | 2.645e+00 |
| 1.0 | 1834 | 2044 | 0 | 1784 | 2.5228e+00 | 2.6328e-10 | 1.044e-10 | 2.401e-10 | -9.62 | -2.628e-16 | 8.498e-03 | 1.142e+00 |
| 1.5 | 2751 | 2044 | 707 | 1974 | 2.0999e+00 | 8.9654e-10 | 4.269e-10 | 9.046e-10 | -9.04 | -1.331e-15 | -3.962e-16 | 7.972e-01 |
| 2.0 | 3668 | 2044 | 1624 | 1976 | 1.9877e+00 | 3.7066e-10 | 1.865e-10 | 3.744e-10 | -9.43 | -1.287e-15 | -4.734e-16 | 5.597e-01 |