{
  "title": "Finite-domain successor-search certificate",
  "scope": "Exact finite facts about rationals that reproduce the 15-bit floor map. Does not rewrite OMEGA_NAUGHT/1.0 or accept a successor contract.",
  "lambda_enclosure": {
    "source": "OMEGA_NAUGHT_PROOF/1.0",
    "decimal_scale": "1000000000000000000000000000000000000000000000000000000000000",
    "lambda_lower_60": "339949771344778929576702809321279193551009905014259416689444",
    "lambda_upper_60": "339949771344778929576702809321279193551009905014259416689445"
  },
  "frozen_1.0": {
    "Q": "339949771344778",
    "S": "1000000000000000",
    "gcd": 2,
    "reduced_Q": "169974885672389",
    "reduced_S": "500000000000000",
    "first_mismatch": 42189065
  },
  "I_15": {
    "left_inclusive": "4196/12343",
    "right_exclusive": "7039/20706",
    "endpoint_det": 1,
    "width": "1/255574158",
    "active_lower_n": [12343, 24686],
    "active_upper_n": 20706,
    "farey_min_denominator": 33049
  },
  "profiles": [
    {
      "id": "frozen_1.0",
      "Q": "339949771344778",
      "S": "1000000000000000",
      "reduced": false,
      "bits_Q": 49,
      "bits_S": 50,
      "Q_times_32767": "11139134157654340726",
      "signed32": false,
      "A": 42189065,
      "path": "globally_map_equivalent_unreduced_bytes"
    },
    {
      "id": "globally_normalized",
      "Q": "169974885672389",
      "S": "500000000000000",
      "reduced": true,
      "bits_Q": 48,
      "bits_S": 49,
      "Q_times_32767": "5569567078827170363",
      "signed32": false,
      "A": 42189065,
      "path": "globally_map_equivalent_normalization"
    },
    {
      "id": "minimum_modulus",
      "Q": "4196",
      "S": "12343",
      "reduced": true,
      "bits_Q": 13,
      "bits_S": 14,
      "Q_times_32767": "137490332",
      "signed32": true,
      "A": 45392,
      "path": "minimum_modulus_finite_bridge"
    },
    {
      "id": "signed32_horizon",
      "Q": "49136",
      "S": "144539",
      "reduced": true,
      "bits_Q": 16,
      "bits_S": 18,
      "Q_times_32767": "1610039312",
      "signed32": true,
      "A": 2490212,
      "path": "maximum_horizon_signed32_kernel"
    },
    {
      "id": "baseline_horizon_min",
      "Q": "846547",
      "S": "2490212",
      "reduced": true,
      "bits_Q": 20,
      "bits_S": 22,
      "Q_times_32767": "27738805549",
      "signed32": false,
      "A": 42189065,
      "path": "baseline_horizon_finite_replacement"
    },
    {
      "id": "first_admissible_dyadic",
      "Q": "22813643",
      "S": "67108864",
      "reduced": true,
      "bits_Q": 25,
      "bits_S": 27,
      "Q_times_32767": "747534640181",
      "signed32": false,
      "A": 33049,
      "path": "dyadic_implementation_candidate"
    }
  ],
  "signed32_bound": {
    "Q_cap": 65538,
    "next_interval": "[846547/2490212, 797411/2345673)",
    "next_det": 1,
    "min_numerator_beyond": 846547,
    "no_signed32_A_greater_than": 2490212
  },
  "extinction": {
    "depth": 10,
    "rows": [
      { "k": 0, "states": 32768, "largest_fiber": 1, "branch_bits": 0 },
      { "k": 1, "states": 11140, "largest_fiber": 3, "branch_bits": 2 },
      { "k": 2, "states": 3787, "largest_fiber": 9, "branch_bits": 4 },
      { "k": 3, "states": 1288, "largest_fiber": 27, "branch_bits": 5 },
      { "k": 4, "states": 438, "largest_fiber": 80, "branch_bits": 7 },
      { "k": 5, "states": 149, "largest_fiber": 236, "branch_bits": 8 },
      { "k": 6, "states": 51, "largest_fiber": 695, "branch_bits": 10 },
      { "k": 7, "states": 17, "largest_fiber": 2045, "branch_bits": 11 },
      { "k": 8, "states": 6, "largest_fiber": 6016, "branch_bits": 13 },
      { "k": 9, "states": 2, "largest_fiber": 17697, "branch_bits": 15 },
      { "k": 10, "states": 1, "largest_fiber": 32768, "branch_bits": 15 }
    ]
  },
  "predecessor": {
    "max_set": 3,
    "branch_bits": 2,
    "histogram": { "1": 1, "2": 650, "3": 10489 }
  },
  "certificate_sha256": "26d230fba560a5e08f2380207afc5f8b43cdea25ac67de3de1761ab56fc21e5e",
  "accepted_successor": false
}