E-014 — Cor 1.6 diagnostics: theta-count interlacing, v+/- localization, zero-flow to a=10, imag-axis read-off (theta=pi)
08-18-2026 · 80 rows · script
research/numerics/scripts/E-014-cor16-diagnostics.py
Metadata
theta-independence of zero count; v± localization; zero-flow map vs a; imaginary-axis least-squares read-off of theta(a), phi(a,z)
Validation checks
| V1_theta_count_interlacing | PASS |
| V2_lattice_persists | PASS |
| V3_xi_crosscheck_and_readoff | PASS |
| V4_vmirror_symmetry | PASS |
Key values
| P1_counts | [-76, -76, -76, -76, -76, -75, -75, -75, -75, -76, -76, -76, -76, -76, -76, -76] |
| P1_spread | 1 |
| P2_localization | {'4.0': [0.8113352211750133, 0.8042463400966671], '6.0': [0.815502234769262, 0.8096659632054103], '8.0': [0.8230467697557222, 0.8186214210851552], '10.0': [0.8289899043479302, 0.8251449076417641]} |
| P3_first_zeros | {'4.0': [0.78678146, 1.57356499, 2.36035269, 3.14714677, 3.93394961], '6.0': [0.52407766, 1.04815542, 1.57223347, 2.09631224, 2.62039153], '8.0': [0.3929738, 0.78594774, 1.17892187, 1.57189604, 1.96487117], '10.0': [0.31431482, 0.62862966, 0.94294449, 1.2572596, 1.57157429]} |
| P4_readoff | {'4.0': {'best_theta': 3.141592653589793, 'best_resid': 0.017714374721797224, 'best_phase_agree': 1.0, 'median_resid': 0.022342865357109994}, '6.0': {'best_theta': 3.141592653589793, 'best_resid': 0.021508567165581402, 'best_phase_agree': 1.0, 'median_resid': 0.0244687465471507}, '8.0': {'best_theta': 3.141592653589793, 'best_resid': 0.023225193635352376, 'best_phase_agree': 1.0, 'median_resid': 0.025389981806922614}, '10.0': {'best_theta': 3.141592653589793, 'best_resid': 0.024192319237001752, 'best_phase_agree': 1.0, 'median_resid': 0.025897228710069387}} |
| xi_flint_crosscheck_rel | 0.00000000000000004721803879534242 |
Parameters
| a_sweep | [4.0, 6.0, 8.0, 10.0] |
| h | 0.01 |
| lambda | -1.0 |
| y_grid | [1.0, 20.0, 96] |
| phi_deg | 4 |
Caveats
- Galerkin discretization h=0.01 (E-010 h-convergence: z1 rel drift 4e-4 between h=0.01 and 0.005 at a=4)
- read-off on the imaginary axis tests only the modulus shape + phase of e^phi W vs F away from zeros; zero-density gap (F4 of D-020) means a good fit is NOT expected at large a — the residual trend is the observable
Chart
Data preview (80 rows total)
| part | a | theta_or_j | value |
|---|---|---|---|
| P1_count | 6.0 | 0.000000 | -76 |
| P1_count | 6.0 | 0.392699 | -76 |
| P1_count | 6.0 | 0.785398 | -76 |
| P1_count | 6.0 | 1.178097 | -76 |
| P1_count | 6.0 | 1.570796 | -76 |
| P1_count | 6.0 | 1.963495 | -75 |
| P1_count | 6.0 | 2.356194 | -75 |
| P1_count | 6.0 | 2.748894 | -75 |
| P1_count | 6.0 | 3.141593 | -75 |
| P1_count | 6.0 | 3.534292 | -76 |
| P1_count | 6.0 | 3.926991 | -76 |
| P1_count | 6.0 | 4.319690 | -76 |
| P1_count | 6.0 | 4.712389 | -76 |
| P1_count | 6.0 | 5.105088 | -76 |
| P1_count | 6.0 | 5.497787 | -76 |
| P1_count | 6.0 | 5.890486 | -76 |
| P2_loc_T | 4.0 | - | 0.81133522 |
| P2_loc_L2 | 4.0 | - | 0.80424634 |
| P3_zero | 4.0 | 1 | 0.7867814646 |
| P3_zero | 4.0 | 2 | 1.5735649911 |
| P3_zero | 4.0 | 3 | 2.3603526899 |
| P3_zero | 4.0 | 4 | 3.1471467731 |
| P3_zero | 4.0 | 5 | 3.9339496133 |
| P3_zero | 4.0 | 6 | 4.7207638123 |
| P3_zero | 4.0 | 7 | 5.5075922862 |