{
  "schema": "marici.strominger.photon-shared-edge-seed.v1",
  "status": "passed",
  "label": "photon candidate",
  "source_path": "research/strominger/inputs/photon-shared-edge-seed.json",
  "effective_source": {
    "label": "photon candidate",
    "vertex_labels": [
      "A",
      "B",
      "C",
      "D"
    ],
    "arrows": [
      [
        "A",
        "B"
      ],
      [
        "B",
        "C"
      ],
      [
        "C",
        "A"
      ],
      [
        "B",
        "A"
      ],
      [
        "A",
        "D"
      ],
      [
        "D",
        "B"
      ]
    ],
    "retained_face_cycles": [
      [
        "A",
        "B",
        "C",
        "A"
      ],
      [
        "B",
        "A",
        "D",
        "B"
      ]
    ],
    "geometry_source": "research/nima/inputs/proton-six-arrows.json",
    "assembly_stage": "retained two-face seed, before tetrahedral completion",
    "mode_source": "research/nima/results/photon-two-packet-candidate.json"
  },
  "seed_cycles": [
    [
      "A",
      "B",
      "C",
      "A"
    ],
    [
      "B",
      "A",
      "D",
      "B"
    ]
  ],
  "arrows": [
    [
      "A",
      "B"
    ],
    [
      "B",
      "C"
    ],
    [
      "C",
      "A"
    ],
    [
      "B",
      "A"
    ],
    [
      "A",
      "D"
    ],
    [
      "D",
      "B"
    ]
  ],
  "assembly_stage": "retained two-face seed, before tetrahedral completion",
  "geometry": {
    "intrinsic_affine_dimension_in_existing_source": 3,
    "retained_complex_dimension": 2,
    "vertices": {
      "A": [
        "1",
        "1",
        "1"
      ],
      "B": [
        "1",
        "-1",
        "-1"
      ],
      "C": [
        "-1",
        "1",
        "-1"
      ],
      "D": [
        "-1",
        "-1",
        "1"
      ]
    },
    "oriented_faces": [
      [
        "A",
        "B",
        "C"
      ],
      [
        "B",
        "A",
        "D"
      ]
    ],
    "edge_supports": [
      [
        "A",
        "B"
      ],
      [
        "A",
        "C"
      ],
      [
        "A",
        "D"
      ],
      [
        "B",
        "C"
      ],
      [
        "B",
        "D"
      ]
    ],
    "f_vector": [
      4,
      5,
      2
    ],
    "nonempty_cells": 11,
    "betti": [
      1,
      0,
      0
    ],
    "outer_boundary": {
      "BC": 1,
      "AC": -1,
      "AD": 1,
      "BD": -1
    },
    "missing_edge": "CD",
    "full_completion_counts": {
      "vertices": 4,
      "supporting_facets": 4,
      "external_interfaces": 0,
      "carrier_facets": 4,
      "cone_cells": 4
    },
    "shape_description": "two triangular faces hinged along AB, using the existing tetrahedral metric; a topological disk, not a newly flattened diamond"
  },
  "continuation": {
    "matrix": [
      [
        0,
        0,
        1,
        1,
        0,
        0
      ],
      [
        1,
        0,
        0,
        0,
        0,
        1
      ],
      [
        0,
        1,
        0,
        0,
        0,
        0
      ],
      [
        1,
        0,
        0,
        0,
        0,
        1
      ],
      [
        0,
        0,
        1,
        1,
        0,
        0
      ],
      [
        0,
        0,
        0,
        0,
        1,
        0
      ]
    ],
    "composable_pair_rows": [
      [
        0,
        1
      ],
      [
        0,
        3
      ],
      [
        1,
        2
      ],
      [
        2,
        0
      ],
      [
        2,
        4
      ],
      [
        3,
        0
      ],
      [
        3,
        4
      ],
      [
        4,
        5
      ],
      [
        5,
        1
      ],
      [
        5,
        3
      ]
    ],
    "prefix_rank": 6,
    "aggregation_rank": 6,
    "continuation_rank": 4,
    "kernel_dimension": 2
  },
  "modes": {
    "source": "research/nima/results/photon-two-packet-candidate.json",
    "plus": {
      "formula": "(1,-1,-omega^2,-1,1,omega^2)",
      "coefficients": [
        {
          "real": "1",
          "imaginary_sqrt3_coefficient": "0"
        },
        {
          "real": "-1",
          "imaginary_sqrt3_coefficient": "0"
        },
        {
          "real": "1/2",
          "imaginary_sqrt3_coefficient": "1/2"
        },
        {
          "real": "-1",
          "imaginary_sqrt3_coefficient": "0"
        },
        {
          "real": "1",
          "imaginary_sqrt3_coefficient": "0"
        },
        {
          "real": "-1/2",
          "imaginary_sqrt3_coefficient": "-1/2"
        }
      ],
      "eigenvalue": {
        "real": "-1/2",
        "imaginary_sqrt3_coefficient": "1/2"
      }
    },
    "minus": {
      "formula": "complex conjugate of candidate_plus",
      "coefficients": [
        {
          "real": "1",
          "imaginary_sqrt3_coefficient": "0"
        },
        {
          "real": "-1",
          "imaginary_sqrt3_coefficient": "0"
        },
        {
          "real": "1/2",
          "imaginary_sqrt3_coefficient": "-1/2"
        },
        {
          "real": "-1",
          "imaginary_sqrt3_coefficient": "0"
        },
        {
          "real": "1",
          "imaginary_sqrt3_coefficient": "0"
        },
        {
          "real": "-1/2",
          "imaginary_sqrt3_coefficient": "1/2"
        }
      ]
    },
    "plane_dimension": 2,
    "existing_invariant_metric": [
      [
        3,
        0
      ],
      [
        0,
        1
      ]
    ],
    "return_steps": 3
  },
  "checks": {
    "same_six_primitive_arrows_as_proton": true,
    "mode_order_matches_registered_occurrences": true,
    "each_face_cycle_uses_existing_arrows": true,
    "shared_AB_cancels": true,
    "outer_boundary_has_four_edges": true,
    "filled_seed_has_disk_homology": true,
    "no_CD_seed_arrow": true,
    "retained_span_has_ten_rows": true,
    "prefix_lift_injective": true,
    "aggregate_factors_as_AL": true,
    "continuation_rank_four": true,
    "plus_is_existing_cyclic_eigenvector": true,
    "minus_is_conjugate_eigenvector": true,
    "selected_real_plane_rank_two": true,
    "existing_averaged_metric_invariant": true,
    "source_tetrahedron_all_squared_edges_eight": true,
    "common_processor_completion_has_four_faces": true
  },
  "distinction_from_proton": "Same primitive arrow set and source metric. This entry retains two supplied face cycles and the existing conjugate continuation plane; proton assembly includes the completed tetrahedral structure. Stopping at the seed stage is recorded, not a new particle-dependent assembler rule.",
  "physical_identification_derived": false,
  "arrow_reversal_of": null,
  "source_hashes": {
    "research/strominger/checkers/check_photon_shared_edge_seed.py": "a591e788e8cb297c5b1e4fd1ffc480bba86cceca95f4dbbb86b85236d50517ea",
    "research/strominger/inputs/photon-shared-edge-seed.json": "16fd50604f6207242f8041f86f84de35f394f14f7e9ac4b139cbb57f7cf3f131",
    "research/nima/inputs/proton-six-arrows.json": "dbc3fb179092ac6b27d60482bbb30844c9a4fb9030bc065a5b1ed85a9ebebc60",
    "research/nima/results/photon-two-packet-candidate.json": "9847f001c6c5236b7da6db889b35095cc64f16b07eaa8b496919206d89caf290",
    "research/voevodsky/inputs/relative-proton.json": "8a568f797a4832f3e7ddb19efbbca6d1c642711c0dfb816649ba6d35d5ca556b",
    "research/voevodsky/checkers/assemble_relative_geometry.py": "5e088a6d19f61f9cc449328c072ac34c3a4c62a3fb1deac88859ec10d8482d2c",
    "research/strominger/checkers/check_neutrino_arrow_seed_science.py": "cd4023dc32a2ef95e346cc946d5aae415d6c0d8f48d7dd447d26591d93e49751"
  },
  "source_sha256": "16fd50604f6207242f8041f86f84de35f394f14f7e9ac4b139cbb57f7cf3f131"
}