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      "unrestricted_exact_source_sampler_implemented": false
    },
    "limits": {
      "vertices": 6,
      "states": 512,
      "steps": 64,
      "work_units": 2000000
    },
    "arithmetic": "exact integers and fractions",
    "formal_program_verification": "not_run",
    "work_unit_definition": "Candidate graph tests, selected-edge degree updates, kernel proposals and nonzero distribution transitions; not bit operations or wall time.",
    "status": "complete",
    "feasible": true,
    "state_count": 2,
    "work_units": 316,
    "transition_denominator": 180,
    "rows_symmetric": true,
    "rows_stochastic_and_lazy": true,
    "switch_component_sizes": [
      1,
      1
    ],
    "switch_connected": false,
    "starting_state_index": 0,
    "starting_state_edges": [
      [
        0,
        5
      ],
      [
        1,
        2
      ],
      [
        3,
        4
      ]
    ],
    "total_variation_by_step": [
      {
        "step": 0,
        "total_variation": "1/2"
      },
      {
        "step": 1,
        "total_variation": "1/2"
      },
      {
        "step": 2,
        "total_variation": "1/2"
      },
      {
        "step": 3,
        "total_variation": "1/2"
      },
      {
        "step": 4,
        "total_variation": "1/2"
      },
      {
        "step": 5,
        "total_variation": "1/2"
      },
      {
        "step": 6,
        "total_variation": "1/2"
      },
      {
        "step": 7,
        "total_variation": "1/2"
      },
      {
        "step": 8,
        "total_variation": "1/2"
      },
      {
        "step": 9,
        "total_variation": "1/2"
      },
      {
        "step": 10,
        "total_variation": "1/2"
      },
      {
        "step": 11,
        "total_variation": "1/2"
      },
      {
        "step": 12,
        "total_variation": "1/2"
      }
    ],
    "first_quarter_tv_from_selected_start": null,
    "source_quarter_tv_bound": null,
    "valid_neighbor_count_histogram": {
      "0": 2
    },
    "generic_accepted_switch_jump_chain": {
      "stationary_law": "proportional to valid-switch neighbor count in a connected nontrivial fiber",
      "exact_stationary_tv_from_uniform": null,
      "scope": "Generic chain selecting uniformly among distinct valid switch neighbors. This is not a complete audit of any external library implementation."
    },
    "finite_states": [
      {
        "index": 0,
        "edges": [
          [
            0,
            5
          ],
          [
            1,
            2
          ],
          [
            3,
            4
          ]
        ]
      },
      {
        "index": 1,
        "edges": [
          [
            0,
            1
          ],
          [
            2,
            3
          ],
          [
            4,
            5
          ]
        ]
      }
    ],
    "interpretation": "Finite exhaustive kernel and one-start law calculation. Extra host constraints can disconnect the chain. Empirical/fixed-start convergence does not verify the source theorem or worst-case large-graph mixing; exact unrestricted residual sampling is not implemented."
  },
  "declared_source_parameters": [
    {
      "vertices": 4,
      "quarter_tv_steps_bound": 131072,
      "exact_sampler_ordinary_branch_steps": 29184,
      "correction_probability": "2^(-34)",
      "correction_dense_tabulation_scale": "2^(12) times a polynomial in n",
      "interpretation": "Declared upper schedules, not observed runtime or lower bounds. Exact sampler has expected cost and unbounded rejection tails."
    },
    {
      "vertices": 6,
      "quarter_tv_steps_bound": 3359232,
      "exact_sampler_ordinary_branch_steps": 2034720,
      "correction_probability": "2^(-70)",
      "correction_dense_tabulation_scale": "2^(30) times a polynomial in n",
      "interpretation": "Declared upper schedules, not observed runtime or lower bounds. Exact sampler has expected cost and unbounded rejection tails."
    },
    {
      "vertices": 34,
      "quarter_tv_steps_bound": 3571587809792,
      "exact_sampler_ordinary_branch_steps": 6524631277824,
      "correction_probability": "2^(-2254)",
      "correction_dense_tabulation_scale": "2^(1122) times a polynomial in n",
      "interpretation": "Declared upper schedules, not observed runtime or lower bounds. Exact sampler has expected cost and unbounded rejection tails."
    },
    {
      "vertices": 100,
      "quarter_tv_steps_bound": 20000000000000000,
      "exact_sampler_ordinary_branch_steps": 41946441768000000,
      "correction_probability": "2^(-19810)",
      "correction_dense_tabulation_scale": "2^(9900) times a polynomial in n",
      "interpretation": "Declared upper schedules, not observed runtime or lower bounds. Exact sampler has expected cost and unbounded rejection tails."
    },
    {
      "vertices": 1000,
      "quarter_tv_steps_bound": 2000000000000000000000000,
      "exact_sampler_ordinary_branch_steps": 4468598291768868000000000,
      "correction_probability": "2^(-1998010)",
      "correction_dense_tabulation_scale": "2^(999000) times a polynomial in n",
      "interpretation": "Declared upper schedules, not observed runtime or lower bounds. Exact sampler has expected cost and unbounded rejection tails."
    }
  ],
  "triangle_event": {
    "uniform_probability": "1/7",
    "generic_accepted_switch_stationary_probability": "1/5",
    "reason": "Ten two-triangle graphs have 18 valid neighbors; sixty six-cycles have 12. Stationary jump-chain mass is proportional to valid neighbor count."
  },
  "formal_program_verification": "not_run",
  "source_proof_verification": "not_run"
}