{
  "step": "C313",
  "review_type": "Independent finite arithmetic check; input-state membership inherited from frozen registers",
  "status": "passed",
  "input_sha256": {
    "C312_DATA.json": "b73bd2d6c54b74901d41c8aa199dc1fe963bdd1981cabafe9f7c3b498f9a7d17",
    "C286_DATA.json": "71867add8e2b0000e7d11270e2ee28969ef41d788b5a1ec74add0b6237cc9905",
    "C287_DATA.json": "1f3fe8798fb89b1559247a1b209aabfa854d0ae5399b45623f4c398a36fa8ce0",
    "C307_DATA.json": "ff036a22598d2cb784ab39fefc3f0207d8f653237e7530afe602c6c4baf087a0"
  },
  "normalization_BC": 155,
  "center_model": {
    "q": "-5290+j",
    "n": "q+8993",
    "s": "-q-2077",
    "d": "s-600",
    "n_minus_s": "490+2j",
    "same_cumulative_component_gap": "490+2j+2epsilon"
  },
  "cases": [
    {
      "j": 3,
      "cumulative_Flood_q": -5287,
      "C312_Shem_gear": 3,
      "C312_Shem_rail": "primary",
      "normalized_Shem_pair": [
        3210,
        2610
      ],
      "same_Gear_rail_biographical_Noah": 3710,
      "Noah17K": 3706,
      "Noah17K_gear": 1,
      "Noah17K_rail": "primary",
      "center_gap": 496,
      "source_binding_and_center_match": false,
      "complete_Shem_life_admitted": true,
      "Noah17K_admitted": true,
      "complete_C287_four_node_form_admitted": true,
      "cumulative_ON_Shem_index_needed_for_four_node_form": 5,
      "whole_pair_set_matches_after500": false,
      "same_cumulative_ancestry_components_both500": false,
      "phases": [
        {
          "cumulative_component_offset": "-1/4",
          "Noah17K": "14823/4",
          "Shem_birth_cross_bridge": "12841/4",
          "Shem_death_cross_bridge": "10441/4",
          "common_ancestor_Noah_minus_Shem": "991/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        },
        {
          "cumulative_component_offset": "1/4",
          "Noah17K": "14825/4",
          "Shem_birth_cross_bridge": "12839/4",
          "Shem_death_cross_bridge": "10439/4",
          "common_ancestor_Noah_minus_Shem": "993/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        }
      ]
    },
    {
      "j": 4,
      "cumulative_Flood_q": -5286,
      "C312_Shem_gear": 3,
      "C312_Shem_rail": "companion",
      "normalized_Shem_pair": [
        3209,
        2609
      ],
      "same_Gear_rail_biographical_Noah": 3709,
      "Noah17K": 3707,
      "Noah17K_gear": 2,
      "Noah17K_rail": "companion",
      "center_gap": 498,
      "source_binding_and_center_match": false,
      "complete_Shem_life_admitted": true,
      "Noah17K_admitted": true,
      "complete_C287_four_node_form_admitted": true,
      "cumulative_ON_Shem_index_needed_for_four_node_form": 6,
      "whole_pair_set_matches_after500": false,
      "same_cumulative_ancestry_components_both500": false,
      "phases": [
        {
          "cumulative_component_offset": "-1/4",
          "Noah17K": "14827/4",
          "Shem_birth_cross_bridge": "12837/4",
          "Shem_death_cross_bridge": "10437/4",
          "common_ancestor_Noah_minus_Shem": "995/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        },
        {
          "cumulative_component_offset": "1/4",
          "Noah17K": "14829/4",
          "Shem_birth_cross_bridge": "12835/4",
          "Shem_death_cross_bridge": "10435/4",
          "common_ancestor_Noah_minus_Shem": "997/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        }
      ]
    },
    {
      "j": 5,
      "cumulative_Flood_q": -5285,
      "C312_Shem_gear": 2,
      "C312_Shem_rail": "primary",
      "normalized_Shem_pair": [
        3208,
        2608
      ],
      "same_Gear_rail_biographical_Noah": 3708,
      "Noah17K": 3708,
      "Noah17K_gear": 2,
      "Noah17K_rail": "primary",
      "center_gap": 500,
      "source_binding_and_center_match": true,
      "complete_Shem_life_admitted": true,
      "Noah17K_admitted": true,
      "complete_C287_four_node_form_admitted": true,
      "cumulative_ON_Shem_index_needed_for_four_node_form": 7,
      "whole_pair_set_matches_after500": true,
      "same_cumulative_ancestry_components_both500": false,
      "phases": [
        {
          "cumulative_component_offset": "-1/4",
          "Noah17K": "14831/4",
          "Shem_birth_cross_bridge": "12833/4",
          "Shem_death_cross_bridge": "10433/4",
          "common_ancestor_Noah_minus_Shem": "999/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        },
        {
          "cumulative_component_offset": "1/4",
          "Noah17K": "14833/4",
          "Shem_birth_cross_bridge": "12831/4",
          "Shem_death_cross_bridge": "10431/4",
          "common_ancestor_Noah_minus_Shem": "1001/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        }
      ]
    },
    {
      "j": 6,
      "cumulative_Flood_q": -5284,
      "C312_Shem_gear": 2,
      "C312_Shem_rail": "companion",
      "normalized_Shem_pair": [
        3207,
        2607
      ],
      "same_Gear_rail_biographical_Noah": 3707,
      "Noah17K": 3709,
      "Noah17K_gear": 3,
      "Noah17K_rail": "companion",
      "center_gap": 502,
      "source_binding_and_center_match": false,
      "complete_Shem_life_admitted": true,
      "Noah17K_admitted": true,
      "complete_C287_four_node_form_admitted": false,
      "cumulative_ON_Shem_index_needed_for_four_node_form": 8,
      "whole_pair_set_matches_after500": false,
      "same_cumulative_ancestry_components_both500": false,
      "phases": [
        {
          "cumulative_component_offset": "-1/4",
          "Noah17K": "14835/4",
          "Shem_birth_cross_bridge": "12829/4",
          "Shem_death_cross_bridge": "10429/4",
          "common_ancestor_Noah_minus_Shem": "1003/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        },
        {
          "cumulative_component_offset": "1/4",
          "Noah17K": "14837/4",
          "Shem_birth_cross_bridge": "12827/4",
          "Shem_death_cross_bridge": "10427/4",
          "common_ancestor_Noah_minus_Shem": "1005/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        }
      ]
    },
    {
      "j": 7,
      "cumulative_Flood_q": -5283,
      "C312_Shem_gear": 1,
      "C312_Shem_rail": "primary",
      "normalized_Shem_pair": [
        3206,
        2606
      ],
      "same_Gear_rail_biographical_Noah": 3706,
      "Noah17K": 3710,
      "Noah17K_gear": 3,
      "Noah17K_rail": "primary",
      "center_gap": 504,
      "source_binding_and_center_match": false,
      "complete_Shem_life_admitted": true,
      "Noah17K_admitted": true,
      "complete_C287_four_node_form_admitted": false,
      "cumulative_ON_Shem_index_needed_for_four_node_form": 9,
      "whole_pair_set_matches_after500": false,
      "same_cumulative_ancestry_components_both500": false,
      "phases": [
        {
          "cumulative_component_offset": "-1/4",
          "Noah17K": "14839/4",
          "Shem_birth_cross_bridge": "12825/4",
          "Shem_death_cross_bridge": "10425/4",
          "common_ancestor_Noah_minus_Shem": "1007/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        },
        {
          "cumulative_component_offset": "1/4",
          "Noah17K": "14841/4",
          "Shem_birth_cross_bridge": "12823/4",
          "Shem_death_cross_bridge": "10423/4",
          "common_ancestor_Noah_minus_Shem": "1009/2",
          "complete_Shem_life": "600",
          "source_biography_same_output_phase_gap": "500"
        }
      ]
    }
  ],
  "counts": {
    "fixed_domain": 5,
    "normalization_and_complete_Shem_life": 5,
    "admitted_Noah17K": 5,
    "center_and_typed_binding_success": 1,
    "center_and_typed_binding_failure": 4,
    "same_cumulative_ancestry_phase_success": 0,
    "whole_pair_set_translation500_success": 1
  },
  "caveats": [
    "The five17K edges exist independently of C287 four-node completeness.",
    "The j5 source biography and phase-pair set translate by500, but same-cumulative-ancestor transport gives499.5/500.5.",
    "No new endpoint, interpolated phase, source rule, Gear scope, or C314 computation is introduced."
  ]
}