{
  "schema_version": "1.1.0",
  "id": "fibonacci-m12-p24",
  "name": "Fibonacci M12P24",
  "modulus": 12,
  "pisano_period": 24,
  "conventions": {
    "index_origin": 0,
    "clock_labels": [
      24,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20,
      21,
      22,
      23
    ],
    "orientation": "clockwise from north",
    "zero_display": 12,
    "alpha_circle_positions": 24,
    "beta_circle_positions": 12,
    "node_rule": "Native residues divisible by 3, including zero; no modulo9 projection."
  },
  "alpha": {
    "residues": [
      0,
      1,
      1,
      2,
      3,
      5,
      8,
      1,
      9,
      10,
      7,
      5,
      0,
      5,
      5,
      10,
      3,
      1,
      4,
      5,
      9,
      2,
      11,
      1
    ],
    "display_values": [
      12,
      1,
      1,
      2,
      3,
      5,
      8,
      1,
      9,
      10,
      7,
      5,
      12,
      5,
      5,
      10,
      3,
      1,
      4,
      5,
      9,
      2,
      11,
      1
    ]
  },
  "beta": {
    "interval_sums": [
      4,
      14,
      22,
      20,
      10,
      14
    ],
    "interval_residues": [
      4,
      2,
      10,
      8,
      10,
      2
    ],
    "display_cycle": [
      4,
      2,
      10,
      8,
      10,
      2
    ],
    "recognised_doubling_cycle": null,
    "rotation_to_recognised": null,
    "start_value": 4,
    "start_interval_clock_positions": [
      24,
      4
    ],
    "start_interval_values": [
      1,
      1,
      2
    ],
    "endpoint_rule": "Exclude Gamma nodes; include wraparound interval.",
    "circle_positions": 12,
    "cycle_length": 6,
    "m9_doubling_cycle_present": false
  },
  "gamma": {
    "alpha_indices": [
      0,
      4,
      8,
      12,
      16,
      20
    ],
    "clock_positions": [
      24,
      4,
      8,
      12,
      16,
      20
    ],
    "clockwise_values": [
      12,
      3,
      9,
      12,
      3,
      9
    ],
    "triangle_paths": [
      [
        0,
        8,
        16,
        0
      ],
      [
        4,
        12,
        20,
        4
      ]
    ]
  },
  "epsilon": null,
  "epsilon_status": "Null: requires sequential mapping of all three values 3, 6 and 9. M12/P24 contains no 6.",
  "views": [
    {
      "id": "alpha",
      "name": "Alpha",
      "description": "Clock position 24 is north; zero is displayed as 12.",
      "svg": "views/m12/alpha.svg?v=2",
      "png": "views/m12/alpha.png?v=2"
    },
    {
      "id": "beta",
      "name": "Beta",
      "description": "Interval-derived sequence; not a doubling cycle modulo 12.",
      "svg": "views/m12/beta.svg?v=2",
      "png": "views/m12/beta.png?v=2"
    },
    {
      "id": "gamma",
      "name": "Gamma",
      "description": "Same nodal positions as M9; different native values.",
      "svg": "views/m12/gamma.svg?v=2",
      "png": "views/m12/gamma.png?v=2"
    },
    {
      "id": "fibonacci-m12p24",
      "name": "Fibonacci M12P24",
      "description": "Alpha uses 24 positions; Beta uses twelve positions.",
      "svg": "views/m12/fibonacci-m12p24.svg?v=2",
      "png": "views/m12/fibonacci-m12p24.png?v=2"
    }
  ],
  "research": {
    "focus": "OXTR gene expression",
    "biological_significance_status": "Not yet assessed",
    "statistical_significance_status": "Not yet assessed",
    "quantum_annealing_status": "Not yet performed"
  },
  "verification": {
    "python": "Exact state recurrence, node positions, triangle spacing and native doubling checked.",
    "wolfram": "Pending independent verification."
  },
  "geometry_summary": {
    "rule_version": "selected-nodes-v2",
    "scope": "Selected Gamma nodes, derived Beta and Epsilon traversal only. Other node selections and rotated shapes are not yet assessed.",
    "circle_role": "Pisano-period plotting framework",
    "angle_convention": "Clockwise from north; 0 degrees means the reference north-south alignment.",
    "shapes": [
      {
        "name": "Equilateral triangle",
        "status": "Present",
        "count": 2,
        "orientation": "North / south",
        "rotation_degrees": 0,
        "alpha_paths": [
          [
            0,
            8,
            16,
            0
          ],
          [
            4,
            12,
            20,
            4
          ]
        ]
      },
      {
        "name": "Hexagon",
        "status": "Present",
        "count": 1,
        "orientation": "North\u2013south",
        "rotation_degrees": 0,
        "alpha_paths": [
          [
            0,
            4,
            8,
            12,
            16,
            20,
            0
          ]
        ]
      },
      {
        "name": "2D stellated octahedron",
        "status": "Present",
        "count": 1,
        "orientation": "North\u2013south",
        "rotation_degrees": 0,
        "alpha_paths": [
          [
            0,
            8,
            16,
            0
          ],
          [
            4,
            12,
            20,
            4
          ]
        ],
        "definition": "Two intersecting equilateral triangles in this 2D construction."
      },
      {
        "name": "Chevron",
        "status": "Absent",
        "count": 0,
        "orientation": null,
        "rotation_degrees": null,
        "beta_values": []
      },
      {
        "name": "Unicursal hexagram",
        "status": "Absent",
        "count": 0,
        "orientation": null,
        "rotation_degrees": null,
        "alpha_paths": [],
        "traversal_values": [],
        "rule": "The continuous Epsilon traversal must contain all three node values 3, 6 and 9."
      }
    ],
    "other_orientations_status": "Not yet assessed"
  }
}