{
  "schema_version": 1,
  "claim_id": "c14-pair-geometry-001",
  "phenomenon_id": "c14-average-criticality",
  "chapter": "c14",
  "provenance_class": "a",
  "hypothesis": "Critical zero-bias ReLU propagation can preserve each input's second moment while normalized pair separation decays with depth.",
  "hardware_claim_boundary": "Laptop-CPU wide-limit control plus seeded finite-width Gaussian-layer simulation; not a claim about trained representations.",
  "harness_ref": "ch-14-r2",
  "harness_wheel_sha256": "6df4544a4407ed84f1d4326969a5b3e5616444cb91e5e1c7f5f434a5b6a31f7a",
  "result": {
    "seed": 3972769481,
    "initial_correlation": 0.5,
    "width": 128,
    "depth": 64,
    "trials": 2048,
    "wide_correlation": {
      "1": 0.6089977810442294,
      "4": 0.778895137394332,
      "16": 0.9402945923657069,
      "64": 0.9924912290287992
    },
    "wide_final_angle_radians": 0.12262289160547502,
    "finite_width_correlation": {
      "1": {
        "mean": 0.6100275859142419,
        "median": 0.6122567034952433,
        "quantile_10": 0.5282178781826129,
        "quantile_90": 0.6871938648030543
      },
      "4": {
        "mean": 0.7770352255232115,
        "median": 0.7855145315559309,
        "quantile_10": 0.6799837720063612,
        "quantile_90": 0.8619689896211085
      },
      "16": {
        "mean": 0.9400461287819876,
        "median": 0.950091165520989,
        "quantile_10": 0.8881899428825086,
        "quantile_90": 0.9790364971410362
      },
      "64": {
        "mean": 0.9924933782625873,
        "median": 0.9960837482457736,
        "quantile_10": 0.9820165438590835,
        "quantile_90": 0.9994240190032146
      }
    }
  },
  "payload_sha256": "82a9d291cb25f1cd232317f4bb9e0031b29f900e0627bdad5831b7ddf0d6de74"
}
