1{
  2  "seed": 2742,
  3  "dimension": 8,
  4  "beta": 2.0,
  5  "kappa": 1.5,
  6  "algebra_check": {
  7    "max_projector_tangent_or_idempotence_residual": 4.996003610813204e-16
  8  },
  9  "prediction_checks": {
 10    "P1_intrinsic_constraint": {
 11      "prediction": "post-retraction intermediate |norm-1| stays at floating-point precision, independent of h",
 12      "h_values": [
 13        0.04,
 14        0.02,
 15        0.01,
 16        0.005
 17      ],
 18      "observed_max_each": [
 19        3.3306690738754696e-16,
 20        3.3306690738754696e-16,
 21        3.3306690738754696e-16,
 22        3.3306690738754696e-16
 23      ],
 24      "observed_max_over_sweep": 3.3306690738754696e-16
 25    },
 26    "P2_ambient_local_scaling": {
 27      "prediction": "one-step unconstrained radial norm violation scales as h^0.5",
 28      "h_values": [
 29        0.04,
 30        0.02,
 31        0.01,
 32        0.005
 33      ],
 34      "median_violation": [
 35        0.15964280557484123,
 36        0.10434855319828107,
 37        0.07064219815090811,
 38        0.04870436004161971
 39      ],
 40      "q95_violation": [
 41        0.44884177971481565,
 42        0.29967856228582523,
 43        0.203877847211808,
 44        0.14159686175450092
 45      ],
 46      "observed_loglog_exponent": 0.5700982569303314
 47    },
 48    "P3_fixed_state_control_cost": {
 49      "prediction": "beta/4 E||u||^2 scales exactly as amplitude^2",
 50      "amplitudes": [
 51        0.25,
 52        0.5,
 53        1.0,
 54        2.0,
 55        4.0
 56      ],
 57      "costs": [
 58        0.027382698972403738,
 59        0.10953079588961495,
 60        0.4381231835584598,
 61        1.7524927342338392,
 62        7.009970936935357
 63      ],
 64      "observed_loglog_exponent": 2.0,
 65      "intrinsic_endpoint_alignment_by_amplitude": [
 66        0.5379656535225372,
 67        0.5762669444184964,
 68        0.6068380879001029,
 69        0.6569455105838411,
 70        0.7410485078624091
 71      ]
 72    }
 73  },
 74  "endpoint_comparison_equal_steps": {
 75    "intrinsic": {
 76      "max_violation": 3.3306690738754696e-16,
 77      "median_violation": 2.220446049250313e-16,
 78      "mean_final_norm_error": 5.0515147620444624e-17,
 79      "mean_alignment": 0.6095356317860299,
 80      "mean_control_energy": 0.09991351576752919,
 81      "q95_violation": 2.220446049250313e-16
 82    },
 83    "projected_each": {
 84      "max_violation": 3.3306690738754696e-16,
 85      "median_violation": 2.220446049250313e-16,
 86      "mean_final_norm_error": 5.0515147620444624e-17,
 87      "mean_alignment": 0.6095356317860299,
 88      "mean_control_energy": 0.09991351576752919,
 89      "q95_violation": 2.220446049250313e-16
 90    },
 91    "projected_final": {
 92      "max_violation": 1.2964174194605937,
 93      "median_violation": 0.6071647854997377,
 94      "mean_final_norm_error": 3.874678355941796e-17,
 95      "mean_alignment": 0.6873637767586465,
 96      "mean_control_energy": 0.21509418408407457,
 97      "q95_violation": 0.9736673453575195
 98    },
 99    "ambient": {
100      "max_violation": 1.2964174194605937,
101      "median_violation": 0.6071647854997377,
102      "mean_final_norm_error": 0.42196461170884325,
103      "mean_alignment": 0.9739198921624161,
104      "mean_control_energy": 0.21509418408407457,
105      "q95_violation": 0.9736673453575195
106    }
107  }
108}