{
  "question": "Which of the five normalized SP Shem pairs retain a500-year birth binding to the17K Noah endpoint selected by the same cumulative LXX_OFF Flood index?",
  "finite_domain": {
    "C312_admitted_SP_indices": [
      3,
      4,
      5,
      6,
      7
    ],
    "regular_Gears": [
      1,
      2,
      3
    ],
    "rails": [
      "primary",
      "companion"
    ],
    "variant_normalization": {
      "from": {
        "Cainan": 0,
        "Terah60": 1,
        "full430": 0
      },
      "to": {
        "Cainan": 0,
        "Terah60": 0,
        "full430": 1
      },
      "BC_shift": 155
    }
  },
  "held_parameters": {
    "K": 529,
    "17K": 8993,
    "comparison_offset": 2832,
    "quarter_phases": [
      "-1/4",
      "1/4"
    ]
  },
  "distinct_tests": [
    "Same-index center difference500",
    "Same tradition, Gear and rail, with source600-year Shem life retained",
    "Equality of translated unordered seasonal pair sets",
    "Pointwise relation inherited from the same cumulative phase component",
    "Direct17K Noah support versus stronger C287 four-node support"
  ],
  "procedure": [
    "Select only target-admitted rows from C312.",
    "Add155 to both Shem endpoints and bind their complete records to C286 and File18.",
    "Select SP Noah at8993−C from the existing register; preserve its Gear/rail.",
    "Check source birth/lifespan relations and compare the same-index candidates.",
    "Use C271 actual Noah phase records and C307 orientation to distinguish pair sets from same-ancestry components.",
    "Retain every failure; do not change index pairing, endpoints, anchors or phases."
  ],
  "next_step_boundary": "A reversed cross-index pairing may be proposed after this test, but its finite mapping is not executed in C313."
}