E-003 — Finite Gtilde verification T=1000/2000/4000, psi0+psiMT
08-17-2026 · 6 rows · script
research/numerics/scripts/E-003-finite-Gtilde.py
Metadata
Finite compression G̃ on [T,2T]=[2000,4000): trace, HS norm, PSD-ness, rank–trace bound vs paper predictions (Props 4.1–4.3, Thm 5.7)
Validation checks
| psi0@T=1000 | PASS |
| psiMT@T=1000 | PASS |
| psi0@T=2000 | PASS |
| psiMT@T=2000 | PASS |
| psi0@T=4000 | PASS |
| psiMT@T=4000 | PASS |
Parameters
| T_values | [1000, 2000, 4000] |
| windows | ['psi0', 'psiMT'] |
| zeros_source | E-002 (dps 25) |
| precision | float64 |
Chart
Data preview (6 rows total)
| T | window | L | N_I | tr_G_over_N | HS2_over_N | R_psi_expected | HS2_rel_err | expected_O(1/L) | frame_selftest_rel_err | rank_numeric | d | min_eigenvalue | rank_trace_lower_bound_over_N | two_minus_R |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1000 | psi0 | 5.0699 | 868 | 0.99931 | 1.55051 | 1.33333 | 0.16288 | 0.1972 | 8.89e-06 | 776 | 806 | -1.265e-15 | 0.44671 | 0.66667 |
| 1000 | psiMT | 5.0699 | 868 | 0.99931 | 1.55932 | 1.32750 | 0.17463 | 0.1972 | 8.34e-06 | 776 | 806 | -9.194e-16 | 0.43791 | 0.67250 |
| 2000 | psi0 | 5.7630 | 1957 | 0.99967 | 1.51259 | 1.33333 | 0.13444 | 0.1735 | 8.95e-06 | 1770 | 1834 | -1.549e-15 | 0.48608 | 0.66667 |
| 2000 | psiMT | 5.7630 | 1957 | 0.99967 | 1.51964 | 1.32750 | 0.14474 | 0.1735 | 8.37e-06 | 1770 | 1834 | -1.366e-15 | 0.47903 | 0.67250 |
| 4000 | psi0 | 6.4562 | 4356 | 1.00008 | 1.48722 | 1.33333 | 0.11542 | 0.1549 | 1.15e-05 | 3978 | 4110 | -1.523e-15 | 0.51312 | 0.66667 |
| 4000 | psiMT | 6.4562 | 4356 | 1.00008 | 1.49281 | 1.32750 | 0.12452 | 0.1549 | 1.07e-05 | 3976 | 4110 | -1.572e-15 | 0.50753 | 0.67250 |