Checks · Maximal Coherence for Prescribed Intrinsic Populations and Youla Values: Two Questions of Gil

Printed output of the verification program

The text the program printed when it ran. It is the same text the program writes to verification-gil.json, so the two files are identical, byte for byte, with the same SHA-256. What each block and key means is set out on the page of verification-gil.json.

Output of: The verification program (checks/verify_gil.py), shown beside it on that page

Written by: verify_gil.py, a program by Claude Fable 5.1 (Anthropic)
Size: 1,626 bytes
SHA-256: 66d2230b31078f6d2adc3f357029cf1639b1bfa07a35f42f97cc9a31b4153e2d

The note's page Every file published with it This file on GitHub

{
  "seed": 20260929,
  "versions": {
    "python": "3.12.10",
    "numpy": "2.2.6",
    "scipy": "1.16.3"
  },
  "A_free_youla": {
    "instances": 30,
    "random_samples_per_instance": 300,
    "max_random_excess": -4.711275597385489e-05,
    "method": "projected gradient ascent, 20 starts x 4000 steps, singular values clipped at 1, final snap to a partial isometry",
    "max_optimized_excess": 5.551115123125783e-16,
    "min_optimized_excess": -7.178675857100192e-05,
    "worst_shortfall": 7.178675857100192e-05,
    "instances_within_1e-6": 19,
    "instances_within_1e-4": 30
  },
  "B_prescribed_youla": {
    "instances": 30,
    "max_random_excess": 8.004708007547379e-14,
    "method": "Nelder-Mead over SO(n) via expm of a skew parameter, 20 starts",
    "max_optimized_excess": 1.500466417780899e-13,
    "min_optimized_excess": 1.0842021724855044e-18,
    "worst_shortfall": 0.0,
    "instances_within_1e-6": 30
  },
  "C_inequality_family": {
    "units": "squared cohesion ||N||_F^2 = 2 x (LP value); halve for the LP's own units",
    "max_abs_diff_full_family_LP_vs_theorem": 5.551115123125783e-17,
    "max_abs_diff_prefix_family_LP_vs_theorem": 5.551115123125783e-17,
    "max_excess_coarse_family_LP_over_theorem": 0.019409162878746528,
    "max_excess_CB_plus_degree_LP_over_theorem": 0.0004419584168336016,
    "instances_CB_plus_degree_LP_exceeds_theorem": 4,
    "instances": 30
  },
  "D_odd_sets": {
    "checks": 8760,
    "max_excess": -0.032159502235817206
  },
  "source_sha256": "2f476e76a830e3da491820cb4cd37e12c9ab3831ea0393797289cf9257561b57"
}