{
  "step": "C314",
  "status": "passed",
  "input_sha256": {
    "PREVIOUS_DATA.json": "4b3186077604518aaf979b7237b358eee7f9453c79bf41ed74f64dea39059635",
    "C286_DATA.json": "71867add8e2b0000e7d11270e2ee28969ef41d788b5a1ec74add0b6237cc9905",
    "C287_DATA.json": "1f3fe8798fb89b1559247a1b209aabfa854d0ae5399b45623f4c398a36fa8ce0",
    "C271_REGISTER.json": "54c510fb3c5860340276f64f9b1b40fef4a24e323ac52b0830193895ee91ae6a"
  },
  "scope": "Independent finite arithmetic and frozen-register membership check; no source-rule audit or global-axis claim.",
  "formulas": {
    "Noah": "N(i,en)=3703+i+en",
    "Shem_birth": "S(j,es)=3213-j-es",
    "Shem_death": "D(j,es)=2613-j-es",
    "binding_equation": "N-S=490+i+j+en+es",
    "necessary_and_sufficient_for500_on_integer_indices_and_quarter_phases": "i+j=10 and en=-es",
    "finite_label_map": "J(j,es)=(10-j,-es)",
    "local_coordinate_sum": "q_Noah+q_Shem=-10570 (equation consequence, no new global axis)"
  },
  "rows": [
    {
      "Shem_index_j": 3,
      "Noah_index_i": 7,
      "gear": 3,
      "rail": "primary",
      "source_biography_BC": [
        3710,
        3210,
        2610
      ],
      "typed_binding_preserved": true,
      "phase_cases": [
        {
          "Shem_ancestry_offset": "-1/4",
          "Noah_ancestry_offset": "1/4",
          "Shem_cumulative_coordinate": "-21149/4",
          "Noah_cumulative_coordinate": "-21131/4",
          "Noah_component": "14841/4",
          "Shem_birth_component": "12841/4",
          "Shem_death_component": "10441/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3711n",
          "unique_matching_index_and_phase": [
            7,
            "1/4"
          ]
        },
        {
          "Shem_ancestry_offset": "1/4",
          "Noah_ancestry_offset": "-1/4",
          "Shem_cumulative_coordinate": "-21147/4",
          "Noah_cumulative_coordinate": "-21133/4",
          "Noah_component": "14839/4",
          "Shem_birth_component": "12839/4",
          "Shem_death_component": "10439/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3710t",
          "unique_matching_index_and_phase": [
            7,
            "-1/4"
          ]
        }
      ],
      "direct_17K_Noah_admitted": true,
      "C287_complete_at_Noah_i": false,
      "C287_complete_at_Shem_j": true,
      "C287_complete_at_both_indices": false,
      "Noah_i_C287_ON_Shem_required_index": 9,
      "index_reflection_is_involution": true
    },
    {
      "Shem_index_j": 4,
      "Noah_index_i": 6,
      "gear": 3,
      "rail": "companion",
      "source_biography_BC": [
        3709,
        3209,
        2609
      ],
      "typed_binding_preserved": true,
      "phase_cases": [
        {
          "Shem_ancestry_offset": "-1/4",
          "Noah_ancestry_offset": "1/4",
          "Shem_cumulative_coordinate": "-21145/4",
          "Noah_cumulative_coordinate": "-21135/4",
          "Noah_component": "14837/4",
          "Shem_birth_component": "12837/4",
          "Shem_death_component": "10437/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3710n",
          "unique_matching_index_and_phase": [
            6,
            "1/4"
          ]
        },
        {
          "Shem_ancestry_offset": "1/4",
          "Noah_ancestry_offset": "-1/4",
          "Shem_cumulative_coordinate": "-21143/4",
          "Noah_cumulative_coordinate": "-21137/4",
          "Noah_component": "14835/4",
          "Shem_birth_component": "12835/4",
          "Shem_death_component": "10435/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3709t",
          "unique_matching_index_and_phase": [
            6,
            "-1/4"
          ]
        }
      ],
      "direct_17K_Noah_admitted": true,
      "C287_complete_at_Noah_i": false,
      "C287_complete_at_Shem_j": true,
      "C287_complete_at_both_indices": false,
      "Noah_i_C287_ON_Shem_required_index": 8,
      "index_reflection_is_involution": true
    },
    {
      "Shem_index_j": 5,
      "Noah_index_i": 5,
      "gear": 2,
      "rail": "primary",
      "source_biography_BC": [
        3708,
        3208,
        2608
      ],
      "typed_binding_preserved": true,
      "phase_cases": [
        {
          "Shem_ancestry_offset": "-1/4",
          "Noah_ancestry_offset": "1/4",
          "Shem_cumulative_coordinate": "-21141/4",
          "Noah_cumulative_coordinate": "-21139/4",
          "Noah_component": "14833/4",
          "Shem_birth_component": "12833/4",
          "Shem_death_component": "10433/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3709n",
          "unique_matching_index_and_phase": [
            5,
            "1/4"
          ]
        },
        {
          "Shem_ancestry_offset": "1/4",
          "Noah_ancestry_offset": "-1/4",
          "Shem_cumulative_coordinate": "-21139/4",
          "Noah_cumulative_coordinate": "-21141/4",
          "Noah_component": "14831/4",
          "Shem_birth_component": "12831/4",
          "Shem_death_component": "10431/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3708t",
          "unique_matching_index_and_phase": [
            5,
            "-1/4"
          ]
        }
      ],
      "direct_17K_Noah_admitted": true,
      "C287_complete_at_Noah_i": true,
      "C287_complete_at_Shem_j": true,
      "C287_complete_at_both_indices": true,
      "Noah_i_C287_ON_Shem_required_index": 7,
      "index_reflection_is_involution": true
    },
    {
      "Shem_index_j": 6,
      "Noah_index_i": 4,
      "gear": 2,
      "rail": "companion",
      "source_biography_BC": [
        3707,
        3207,
        2607
      ],
      "typed_binding_preserved": true,
      "phase_cases": [
        {
          "Shem_ancestry_offset": "-1/4",
          "Noah_ancestry_offset": "1/4",
          "Shem_cumulative_coordinate": "-21137/4",
          "Noah_cumulative_coordinate": "-21143/4",
          "Noah_component": "14829/4",
          "Shem_birth_component": "12829/4",
          "Shem_death_component": "10429/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3708n",
          "unique_matching_index_and_phase": [
            4,
            "1/4"
          ]
        },
        {
          "Shem_ancestry_offset": "1/4",
          "Noah_ancestry_offset": "-1/4",
          "Shem_cumulative_coordinate": "-21135/4",
          "Noah_cumulative_coordinate": "-21145/4",
          "Noah_component": "14827/4",
          "Shem_birth_component": "12827/4",
          "Shem_death_component": "10427/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3707t",
          "unique_matching_index_and_phase": [
            4,
            "-1/4"
          ]
        }
      ],
      "direct_17K_Noah_admitted": true,
      "C287_complete_at_Noah_i": true,
      "C287_complete_at_Shem_j": false,
      "C287_complete_at_both_indices": false,
      "Noah_i_C287_ON_Shem_required_index": 6,
      "index_reflection_is_involution": true
    },
    {
      "Shem_index_j": 7,
      "Noah_index_i": 3,
      "gear": 1,
      "rail": "primary",
      "source_biography_BC": [
        3706,
        3206,
        2606
      ],
      "typed_binding_preserved": true,
      "phase_cases": [
        {
          "Shem_ancestry_offset": "-1/4",
          "Noah_ancestry_offset": "1/4",
          "Shem_cumulative_coordinate": "-21133/4",
          "Noah_cumulative_coordinate": "-21147/4",
          "Noah_component": "14825/4",
          "Shem_birth_component": "12825/4",
          "Shem_death_component": "10425/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3707n",
          "unique_matching_index_and_phase": [
            3,
            "1/4"
          ]
        },
        {
          "Shem_ancestry_offset": "1/4",
          "Noah_ancestry_offset": "-1/4",
          "Shem_cumulative_coordinate": "-21131/4",
          "Noah_cumulative_coordinate": "-21149/4",
          "Noah_component": "14823/4",
          "Shem_birth_component": "12823/4",
          "Shem_death_component": "10423/4",
          "Noah_minus_Shem": "500",
          "Shem_life": "600",
          "Noah_minus_Shem_death": "1100",
          "Noah_C271_reflected_phase": "AD 3706t",
          "unique_matching_index_and_phase": [
            3,
            "-1/4"
          ]
        }
      ],
      "direct_17K_Noah_admitted": true,
      "C287_complete_at_Noah_i": true,
      "C287_complete_at_Shem_j": false,
      "C287_complete_at_both_indices": false,
      "Noah_i_C287_ON_Shem_required_index": 5,
      "index_reflection_is_involution": true
    }
  ],
  "involution": {
    "domain_indices": [
      3,
      4,
      5,
      6,
      7
    ],
    "index_orbits": [
      [
        3,
        7
      ],
      [
        4,
        6
      ],
      [
        5
      ]
    ],
    "index_fixed_point": 5,
    "phase_label_orbits": [
      [
        [
          3,
          "-1/4"
        ],
        [
          7,
          "1/4"
        ]
      ],
      [
        [
          3,
          "1/4"
        ],
        [
          7,
          "-1/4"
        ]
      ],
      [
        [
          4,
          "-1/4"
        ],
        [
          6,
          "1/4"
        ]
      ],
      [
        [
          4,
          "1/4"
        ],
        [
          6,
          "-1/4"
        ]
      ],
      [
        [
          5,
          "-1/4"
        ],
        [
          5,
          "1/4"
        ]
      ]
    ],
    "phase_label_fixed_points": 0,
    "closed_on_this_five_case_domain": true
  },
  "counts": {
    "source_labelled_biographies": 5,
    "exact_phase_biographies": 10,
    "full_finite_component_comparisons_for_uniqueness": 100,
    "unique_matching_components": 10,
    "C287_complete_at_Noah_i": 3,
    "C287_complete_at_Shem_j": 3,
    "C287_complete_at_both_indices": 1
  },
  "boundary_findings": [
    "The direct17K Noah records exist for all five pairings.",
    "For j3 and j4, paired i7 and i6 require C287 ON-Shem indices9 and8, outside the retained0..7 field.",
    "The reverse C287 boundary affects j6 and j7 when checking completeness at the original Shem-index side.",
    "Only j=i5 has C287 complete rows at both paired indices.",
    "No absent component is repaired and no field is extended."
  ],
  "interpretation": "The reversal is forced once these endpoint formulas, normalization and500-year target are fixed. It is a derived correspondence between differently indexed, oppositely phased cumulative ancestries, not a recovered source-prescribed selector, an event-identity replacement, or a new global Mirror axis.",
  "suggested_next_bounded_question": "Test whether the finite500-year correspondence commutes with the admitted regular SP Noah-to-Flood relation while preserving the complete Shem-life endpoint and both SP rails; keep source-event and seasonal labels explicit.",
  "later_step_executed": false
}