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    {
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    },
    {
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      "note": "Resource limit: this is not a failure"
    },
    {
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  ],
  "MOV_positive_control": {
    "status": "pass",
    "control": "supersingular_MOV_pairing",
    "field_prime": 131203,
    "subgroup_prime": 32801,
    "subgroup_bits": 16,
    "embedding_degree": 2,
    "hidden_k": 5271,
    "recovered_k": 5271,
    "pairing_operations_EC": 66,
    "finite_field_multiplications_BSGS": 210,
    "elapsed_seconds": 0.00978478800971061,
    "note": "Genuine reduced Tate pairing followed by Fp² discrete log."
  },
  "Smart_positive_control": {
    "status": "pass",
    "control": "anomalous_Smart_padic_log",
    "runs": [
      {
        "bits": 16,
        "field_prime": 33391,
        "group_order": 33391,
        "curve": "y^2=x^3+6",
        "hidden_k": 430,
        "recovered_k": 430,
        "status": "pass",
        "lift_attempts": 1,
        "padic_group_operations": 44,
        "elapsed_seconds": 0.000455
      },
      {
        "bits": 32,
        "field_prime": 2149979011,
        "group_order": 2149979011,
        "curve": "y^2=x^3+2",
        "hidden_k": 1186431551,
        "recovered_k": 1186431551,
        "status": "pass",
        "lift_attempts": 1,
        "padic_group_operations": 80,
        "elapsed_seconds": 0.000752
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      {
        "bits": 48,
        "field_prime": 140738012294419,
        "group_order": 140738012294419,
        "curve": "y^2=x^3+7",
        "hidden_k": 92279105668979,
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        "status": "pass",
        "lift_attempts": 1,
        "padic_group_operations": 128,
        "elapsed_seconds": 0.002253
      }
    ],
    "note": "Hensel lift to Z/p², multiply by p into E1, ratio of p-adic elliptic logs. Linear in log p, not √n."
  },
  "not_implemented": [],
  "caps": {
    "group_ops_cap_le_32_bit": 600000,
    "group_ops_cap_36_bit": 160000
  },
  "limitations": [
    "36-bit rho cap is 160 000 group operations, below the expected ~1.25*sqrt(n) ≈ 290 000; heavy censoring there is by design, not a method failure.",
    "24-bit exhaustive: independent random secrets but correlated shared-prefix timing, not independent CPU timings.",
    "Brute force time estimates are not comparable with separately timed rho / BSGS.",
    "rho20 counts preprocessing group operations; walk_steps are separate.",
    "Floyd rho3 baseline counts total group operations including 3 walk updates per comparison; old code does not expose exact walk steps.",
    "Failed/capped trials are right censored and MUST NOT be treated as exact completion.",
    "KM median is undefined where survival never falls to 50%.",
    "ML classifier uses both normalized public X and Y and 5-NN bitwise majority, plus majority bit and random exact key baselines.",
    "No support for a cryptographic breakthrough."
  ]
}