{
  "status": "passed",
  "scope": "Small exact diagnostics of endpoint-interleaving volume, effective intervals, raw-bound refinement sections and their effective endpoints. Not a proof of these properties for all states, a formal verification of locality or the asymptotic adversary, or a simulation of all adversary trajectories.",
  "arithmetic": "Python integers and fractions.Fraction only",
  "seed": 1108,
  "volume_systems": 54,
  "seeded_systems": 40,
  "explicit_systems": 14,
  "volume_methods": [
    "coordinate permutations and ordered endpoint-gap assignments",
    "independent previous integer subset-polynomial recurrence"
  ],
  "positive_systems_by_size": {
    "0": 1,
    "1": 10,
    "2": 11,
    "3": 8,
    "4": 10,
    "5": 9
  },
  "zero_volume_systems_by_size": {
    "2": 2,
    "4": 2,
    "5": 1
  },
  "effective_intervals_and_sections": {
    "effective_region_volume_checks": 48,
    "independent_section_volume_checks": 423,
    "raw_effective_section_volume_checks": 423,
    "remaining_effective_interval_checks": 1110
  },
  "section_anchor_fractions_of_effective_width": [
    "1/4",
    "1/2",
    "3/4"
  ],
  "additional_explicit_cases": [
    "touching_incomparable_intervals",
    "remote_lower_endpoint",
    "remote_upper_endpoint"
  ],
  "all_passed": true,
  "systems": [
    {
      "name": "empty_region_coordinates",
      "kind": "explicit",
      "vertices": 0,
      "edges": 0,
      "volume": "1",
      "passed": true
    },
    {
      "name": "unit_interval",
      "kind": "explicit",
      "vertices": 1,
      "edges": 0,
      "volume": "1",
      "passed": true
    },
    {
      "name": "unit_square",
      "kind": "explicit",
      "vertices": 2,
      "edges": 0,
      "volume": "1",
      "passed": true
    },
    {
      "name": "root_triangle",
      "kind": "explicit",
      "vertices": 2,
      "edges": 1,
      "volume": "1/2",
      "passed": true
    },
    {
      "name": "five_element_chain",
      "kind": "explicit",
      "vertices": 5,
      "edges": 4,
      "volume": "1/120",
      "passed": true
    },
    {
      "name": "clipped_fork",
      "kind": "explicit",
      "vertices": 4,
      "edges": 3,
      "volume": "2849/49152",
      "passed": true
    },
    {
      "name": "incomparable_attachments",
      "kind": "explicit",
      "vertices": 5,
      "edges": 4,
      "volume": "10127/245760",
      "passed": true
    },
    {
      "name": "isolated_narrow",
      "kind": "explicit",
      "vertices": 1,
      "edges": 0,
      "volume": "1/1048576",
      "passed": true
    },
    {
      "name": "disconnected_narrow",
      "kind": "explicit",
      "vertices": 4,
      "edges": 1,
      "volume": "3/4096",
      "passed": true
    },
    {
      "name": "touching_incomparable_intervals",
      "kind": "explicit",
      "vertices": 2,
      "edges": 0,
      "volume": "1/4",
      "passed": true
    },
    {
      "name": "remote_lower_endpoint",
      "kind": "explicit",
      "vertices": 4,
      "edges": 2,
      "volume": "1/768",
      "passed": true
    },
    {
      "name": "remote_upper_endpoint",
      "kind": "explicit",
      "vertices": 4,
      "edges": 2,
      "volume": "1/768",
      "passed": true
    },
    {
      "name": "directed_cycle",
      "kind": "explicit",
      "vertices": 2,
      "edges": 2,
      "volume": "0",
      "passed": true
    },
    {
      "name": "infeasible_intervals",
      "kind": "explicit",
      "vertices": 2,
      "edges": 1,
      "volume": "0",
      "passed": true
    },
    {
      "name": "seeded_n1_case0",
      "kind": "seeded",
      "vertices": 1,
      "edges": 0,
      "volume": "3/4",
      "passed": true
    },
    {
      "name": "seeded_n1_case1",
      "kind": "seeded",
      "vertices": 1,
      "edges": 0,
      "volume": "3/8",
      "passed": true
    },
    {
      "name": "seeded_n1_case2",
      "kind": "seeded",
      "vertices": 1,
      "edges": 0,
      "volume": "3/8",
      "passed": true
    },
    {
      "name": "seeded_n1_case3",
      "kind": "seeded",
      "vertices": 1,
      "edges": 0,
      "volume": "1/2",
      "passed": true
    },
    {
      "name": "seeded_n1_case4",
      "kind": "seeded",
      "vertices": 1,
      "edges": 0,
      "volume": "1/8",
      "passed": true
    },
    {
      "name": "seeded_n1_case5",
      "kind": "seeded",
      "vertices": 1,
      "edges": 0,
      "volume": "3/4",
      "passed": true
    },
    {
      "name": "seeded_n1_case6",
      "kind": "seeded",
      "vertices": 1,
      "edges": 0,
      "volume": "1/4",
      "passed": true
    },
    {
      "name": "seeded_n1_case7",
      "kind": "seeded",
      "vertices": 1,
      "edges": 0,
      "volume": "1/4",
      "passed": true
    },
    {
      "name": "seeded_n2_case0",
      "kind": "seeded",
      "vertices": 2,
      "edges": 0,
      "volume": "15/32",
      "passed": true
    },
    {
      "name": "seeded_n2_case1",
      "kind": "seeded",
      "vertices": 2,
      "edges": 0,
      "volume": "35/64",
      "passed": true
    },
    {
      "name": "seeded_n2_case2",
      "kind": "seeded",
      "vertices": 2,
      "edges": 0,
      "volume": "25/64",
      "passed": true
    },
    {
      "name": "seeded_n2_case3",
      "kind": "seeded",
      "vertices": 2,
      "edges": 0,
      "volume": "15/64",
      "passed": true
    },
    {
      "name": "seeded_n2_case4",
      "kind": "seeded",
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      "edges": 0,
      "volume": "3/64",
      "passed": true
    },
    {
      "name": "seeded_n2_case5",
      "kind": "seeded",
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      "edges": 0,
      "volume": "3/16",
      "passed": true
    },
    {
      "name": "seeded_n2_case6",
      "kind": "seeded",
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      "edges": 0,
      "volume": "5/64",
      "passed": true
    },
    {
      "name": "seeded_n2_case7",
      "kind": "seeded",
      "vertices": 2,
      "edges": 1,
      "volume": "1/128",
      "passed": true
    },
    {
      "name": "seeded_n3_case0",
      "kind": "seeded",
      "vertices": 3,
      "edges": 0,
      "volume": "105/512",
      "passed": true
    },
    {
      "name": "seeded_n3_case1",
      "kind": "seeded",
      "vertices": 3,
      "edges": 0,
      "volume": "15/64",
      "passed": true
    },
    {
      "name": "seeded_n3_case2",
      "kind": "seeded",
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      "edges": 0,
      "volume": "25/128",
      "passed": true
    },
    {
      "name": "seeded_n3_case3",
      "kind": "seeded",
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      "edges": 0,
      "volume": "175/512",
      "passed": true
    },
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      "name": "seeded_n3_case4",
      "kind": "seeded",
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      "edges": 1,
      "volume": "1/128",
      "passed": true
    },
    {
      "name": "seeded_n3_case5",
      "kind": "seeded",
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      "edges": 1,
      "volume": "7/64",
      "passed": true
    },
    {
      "name": "seeded_n3_case6",
      "kind": "seeded",
      "vertices": 3,
      "edges": 0,
      "volume": "21/128",
      "passed": true
    },
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      "name": "seeded_n3_case7",
      "kind": "seeded",
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      "edges": 1,
      "volume": "1/512",
      "passed": true
    },
    {
      "name": "seeded_n4_case0",
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      "volume": "13/192",
      "passed": true
    },
    {
      "name": "seeded_n4_case1",
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      "edges": 2,
      "volume": "625/16384",
      "passed": true
    },
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      "volume": "11/512",
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      "volume": "27/8192",
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      "volume": "12609/1310720",
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  ]
}