{
  "scope": "Local reversible binary lifts of a prescribed closure cycle; not all possible seed evolutions",
  "current_wording": "Space expands and time splits as the particle/antiparticle poles of one seed, sharing the clock dimension.",
  "no_growth_law_assumed": true,
  "triangle_lifts": [
    {
      "edge_flip_bits": [
        0,
        0,
        0
      ],
      "loop_flip": 0,
      "clock_orbit_lengths": [
        3,
        3
      ],
      "pairing_graph_connected": true,
      "switching_normal_form": [
        0,
        0,
        0
      ]
    },
    {
      "edge_flip_bits": [
        0,
        0,
        1
      ],
      "loop_flip": 1,
      "clock_orbit_lengths": [
        6
      ],
      "pairing_graph_connected": true,
      "switching_normal_form": [
        0,
        0,
        1
      ]
    },
    {
      "edge_flip_bits": [
        0,
        1,
        0
      ],
      "loop_flip": 1,
      "clock_orbit_lengths": [
        6
      ],
      "pairing_graph_connected": true,
      "switching_normal_form": [
        0,
        0,
        1
      ]
    },
    {
      "edge_flip_bits": [
        0,
        1,
        1
      ],
      "loop_flip": 0,
      "clock_orbit_lengths": [
        3,
        3
      ],
      "pairing_graph_connected": true,
      "switching_normal_form": [
        0,
        0,
        0
      ]
    },
    {
      "edge_flip_bits": [
        1,
        0,
        0
      ],
      "loop_flip": 1,
      "clock_orbit_lengths": [
        6
      ],
      "pairing_graph_connected": true,
      "switching_normal_form": [
        0,
        0,
        1
      ]
    },
    {
      "edge_flip_bits": [
        1,
        0,
        1
      ],
      "loop_flip": 0,
      "clock_orbit_lengths": [
        3,
        3
      ],
      "pairing_graph_connected": true,
      "switching_normal_form": [
        0,
        0,
        0
      ]
    },
    {
      "edge_flip_bits": [
        1,
        1,
        0
      ],
      "loop_flip": 0,
      "clock_orbit_lengths": [
        3,
        3
      ],
      "pairing_graph_connected": true,
      "switching_normal_form": [
        0,
        0,
        0
      ]
    },
    {
      "edge_flip_bits": [
        1,
        1,
        1
      ],
      "loop_flip": 1,
      "clock_orbit_lengths": [
        6
      ],
      "pairing_graph_connected": true,
      "switching_normal_form": [
        0,
        0,
        1
      ]
    }
  ],
  "general_census": [
    {
      "length": 1,
      "lifts": 2,
      "pairing_preserved": 2,
      "pairing_graph_connected": 2,
      "single_clock_orbit": 1,
      "two_clock_orbits": 1
    },
    {
      "length": 2,
      "lifts": 4,
      "pairing_preserved": 4,
      "pairing_graph_connected": 4,
      "single_clock_orbit": 2,
      "two_clock_orbits": 2
    },
    {
      "length": 3,
      "lifts": 8,
      "pairing_preserved": 8,
      "pairing_graph_connected": 8,
      "single_clock_orbit": 4,
      "two_clock_orbits": 4
    },
    {
      "length": 4,
      "lifts": 16,
      "pairing_preserved": 16,
      "pairing_graph_connected": 16,
      "single_clock_orbit": 8,
      "two_clock_orbits": 8
    },
    {
      "length": 5,
      "lifts": 32,
      "pairing_preserved": 32,
      "pairing_graph_connected": 32,
      "single_clock_orbit": 16,
      "two_clock_orbits": 16
    },
    {
      "length": 6,
      "lifts": 64,
      "pairing_preserved": 64,
      "pairing_graph_connected": 64,
      "single_clock_orbit": 32,
      "two_clock_orbits": 32
    },
    {
      "length": 7,
      "lifts": 128,
      "pairing_preserved": 128,
      "pairing_graph_connected": 128,
      "single_clock_orbit": 64,
      "two_clock_orbits": 64
    },
    {
      "length": 8,
      "lifts": 256,
      "pairing_preserved": 256,
      "pairing_graph_connected": 256,
      "single_clock_orbit": 128,
      "two_clock_orbits": 128
    },
    {
      "length": 9,
      "lifts": 512,
      "pairing_preserved": 512,
      "pairing_graph_connected": 512,
      "single_clock_orbit": 256,
      "two_clock_orbits": 256
    },
    {
      "length": 10,
      "lifts": 1024,
      "pairing_preserved": 1024,
      "pairing_graph_connected": 1024,
      "single_clock_orbit": 512,
      "two_clock_orbits": 512
    },
    {
      "length": 11,
      "lifts": 2048,
      "pairing_preserved": 2048,
      "pairing_graph_connected": 2048,
      "single_clock_orbit": 1024,
      "two_clock_orbits": 1024
    },
    {
      "length": 12,
      "lifts": 4096,
      "pairing_preserved": 4096,
      "pairing_graph_connected": 4096,
      "single_clock_orbit": 2048,
      "two_clock_orbits": 2048
    }
  ],
  "invert_every_tick": [
    {
      "closure_length": 1,
      "orbit_lengths": [
        2
      ],
      "loop_inverts_seed": true
    },
    {
      "closure_length": 2,
      "orbit_lengths": [
        2,
        2
      ],
      "loop_inverts_seed": false
    },
    {
      "closure_length": 3,
      "orbit_lengths": [
        6
      ],
      "loop_inverts_seed": true
    },
    {
      "closure_length": 4,
      "orbit_lengths": [
        4,
        4
      ],
      "loop_inverts_seed": false
    },
    {
      "closure_length": 5,
      "orbit_lengths": [
        10
      ],
      "loop_inverts_seed": true
    },
    {
      "closure_length": 6,
      "orbit_lengths": [
        6,
        6
      ],
      "loop_inverts_seed": false
    },
    {
      "closure_length": 7,
      "orbit_lengths": [
        14
      ],
      "loop_inverts_seed": true
    },
    {
      "closure_length": 8,
      "orbit_lengths": [
        8,
        8
      ],
      "loop_inverts_seed": false
    },
    {
      "closure_length": 9,
      "orbit_lengths": [
        18
      ],
      "loop_inverts_seed": true
    },
    {
      "closure_length": 10,
      "orbit_lengths": [
        10,
        10
      ],
      "loop_inverts_seed": false
    },
    {
      "closure_length": 11,
      "orbit_lengths": [
        22
      ],
      "loop_inverts_seed": true
    },
    {
      "closure_length": 12,
      "orbit_lengths": [
        12,
        12
      ],
      "loop_inverts_seed": false
    }
  ],
  "exact_findings": [
    "Pairing preservation alone permits both loop signs.",
    "Including the particle/antiparticle pairing as a connection edge makes both classes connected.",
    "A single clock orbit through the full lift is equivalent to odd loop inversion.",
    "For closure length three that orbit is a six-cycle, with T^3=C and T^6=I.",
    "The original invert-every-tick primitive on the minimal three-step loop selects that class without a sign fit.",
    "Local fiber relabeling leaves two mathematical classes, classified by loop inversion."
  ],
  "remaining_questions": [
    "Why the developing structure has this binary-cover local transport description.",
    "How persistent connection in the physical theory constrains clock orbits, rather than only pairing edges.",
    "The physical evolution laws distinguishing temporal splitting from spatial expansion.",
    "How contracting/binding observables arise, rather than merely closure of an internal clock orbit."
  ]
}