1{
  2  "compound_identity": {
  3    "h": [
  4      0.02,
  5      0.01,
  6      0.005,
  7      0.0025
  8    ],
  9    "errors": [
 10      0.006243278576986646,
 11      0.0015769036915523503,
 12      0.00039623812080580946,
 13      9.93015408996616e-05
 14    ],
 15    "loglog_slope_expected_2": 1.9915686739147795
 16  },
 17  "predictions": {
 18    "P1_compound_identity_error_is_O_h2": {
 19      "observed_slope": 1.9915686739147795,
 20      "expected": 2.0
 21    },
 22    "P2_shortest_path_min_entry_scales_alpha3": {
 23      "observed_log_slope": 3.000328903279753,
 24      "expected": 3.0,
 25      "note": "For the bidirectional 6-cycle, the worst off-diagonal entries require three edges; the leading path term is (alpha*t)^3/3!."
 26    },
 27    "P3_stronger_uniform_coupling_improves_projective_contraction": {
 28      "alphas": [
 29        0.05,
 30        0.1,
 31        0.2,
 32        0.4,
 33        0.8
 34      ],
 35      "q_bounds": [
 36        0.9999573853840754,
 37        0.9996603554483036,
 38        0.9973244232616174,
 39        0.9799237269249854,
 40        0.8752531714166867
 41      ],
 42      "q_at_alpha_0.05": 0.9999573853840754,
 43      "q_at_alpha_0.8": 0.8752531714166867
 44    }
 45  },
 46  "rows": [
 47    {
 48      "alpha": 0.05,
 49      "min_P": 9.58951945520055e-06,
 50      "q_birkhoff_bound": 0.9999573853840754,
 51      "max_sampled_ratio": 0.9904368818740336,
 52      "path_minentry_at_t0.08": 1.9693227495635823e-08,
 53      "path_prediction_alpha3_t3_over_6": 1.0666666666666668e-08,
 54      "repeated_window_ratios": [
 55        0.8944291654498862,
 56        0.8975874342752008,
 57        0.9006513184643506,
 58        0.9035844819373794,
 59        0.9063929759773381
 60      ]
 61    },
 62    {
 63      "alpha": 0.1,
 64      "min_P": 7.680825185932804e-05,
 65      "q_birkhoff_bound": 0.9996603554483036,
 66      "max_sampled_ratio": 0.944372279716586,
 67      "path_minentry_at_t0.08": 1.5754771052248844e-07,
 68      "path_prediction_alpha3_t3_over_6": 8.533333333333334e-08,
 69      "repeated_window_ratios": [
 70        0.6886449585037385,
 71        0.797978357156317,
 72        0.8769247795188834,
 73        0.8890655437792796,
 74        0.8965605690316094
 75      ]
 76    },
 77    {
 78      "alpha": 0.2,
 79      "min_P": 0.0006174201745380509,
 80      "q_birkhoff_bound": 0.9973244232616174,
 81      "max_sampled_ratio": 0.8915108767982187,
 82      "path_minentry_at_t0.08": 1.260442183468729e-06,
 83      "path_prediction_alpha3_t3_over_6": 6.826666666666667e-07,
 84      "repeated_window_ratios": [
 85        0.6805728376856377,
 86        0.8257056192834158,
 87        0.8964865403937533,
 88        0.8791229156627779,
 89        0.8671507262264395
 90      ]
 91    },
 92    {
 93      "alpha": 0.4,
 94      "min_P": 0.0050348059863144735,
 95      "q_birkhoff_bound": 0.9799237269249854,
 96      "max_sampled_ratio": 0.8004953597589071,
 97      "path_minentry_at_t0.08": 1.0085473630854028e-05,
 98      "path_prediction_alpha3_t3_over_6": 5.461333333333334e-06,
 99      "repeated_window_ratios": [
100        0.7738700322543988,
101        0.6876036475171393,
102        0.6977015394129747,
103        0.7319873434335363,
104        0.7234811407745301
105      ]
106    },
107    {
108      "alpha": 0.8,
109      "min_P": 0.043452021571022015,
110      "q_birkhoff_bound": 0.8752531714166867,
111      "max_sampled_ratio": 0.6798605371956746,
112      "path_minentry_at_t0.08": 8.074577006188443e-05,
113      "path_prediction_alpha3_t3_over_6": 4.369066666666667e-05,
114      "repeated_window_ratios": [
115        0.19163812173118022,
116        0.4905163641804326,
117        0.5379220870005692,
118        0.5286077901331985,
119        0.5274295384889923
120      ]
121    }
122  ],
123  "baseline_signed_generator": {
124    "min_transition_entry": -0.1462517985915507,
125    "valid_positive_output_sample_ratio_max": 2.491604424899665,
126    "metzler_violation": 0.8
127  },
128  "interpretation": "Positive irreducible compound dynamics produced strictly positive finite-window transitions and geometric Hilbert contraction. The signed baseline has a negative transition entry, so the positive-cone theorem is unavailable."
129}