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      "enum_exhaustive": true,
      "n_uncovered_total": 2301,
      "n_tested": 6,
      "n_solver_errors": 0,
      "sample_note": "capped sample 6/2301",
      "best": {
        "attach": [
          [
            "n2",
            "n4"
          ],
          [
            "n2",
            "n6"
          ],
          [
            "n3",
            "n5"
          ],
          [
            "n3",
            "n6"
          ]
        ],
        "ratio": 0.7500002000000001,
        "demands": [
          1.0,
          0.4999996000000005,
          1.0,
          1.0
        ],
        "w": [
          0.5000004000000001,
          0.4999983999987205,
          0.5000003999999999,
          1.0
        ]
      }
    },
    {
      "tree": "n7-chain6",
      "k": 5,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 53130,
      "enum_exhaustive": false,
      "n_uncovered_total": 1618,
      "n_tested": 1,
      "n_solver_errors": 1,
      "sample_note": "capped sample 1/1618",
      "best": null
    },
    {
      "tree": "n7-chain-fork",
      "k": 3,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 1771,
      "enum_exhaustive": true,
      "n_uncovered_total": 134,
      "n_tested": 25,
      "n_solver_errors": 0,
      "sample_note": "capped sample 25/134",
      "best": {
        "attach": [
          [
            "n1",
            "n3"
          ],
          [
            "n4",
            "n6"
          ],
          [
            "n6",
            "s"
          ]
        ],
        "ratio": 0.7500000000000027,
        "demands": [
          1.000000000000006,
          1.0,
          1.0
        ],
        "w": [
          0.49999999999999933,
          0.7499999999999998,
          0.249999999999999
        ]
      }
    },
    {
      "tree": "n7-chain-fork",
      "k": 4,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 10626,
      "enum_exhaustive": true,
      "n_uncovered_total": 2145,
      "n_tested": 6,
      "n_solver_errors": 1,
      "sample_note": "capped sample 6/2145",
      "best": {
        "attach": [
          [
            "n3",
            "n6"
          ],
          [
            "n4",
            "s"
          ],
          [
            "n4",
            "s"
          ],
          [
            "n5",
            "n6"
          ]
        ],
        "ratio": 0.7500000000000024,
        "demands": [
          1.0,
          0.0,
          1.0,
          0.5000000000000129
        ],
        "w": [
          0.5000000000000049,
          0.0,
          0.5000000000000049,
          0.4999999999999982
        ]
      }
    },
    {
      "tree": "n7-chain-fork",
      "k": 5,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 53130,
      "enum_exhaustive": false,
      "n_uncovered_total": 1633,
      "n_tested": 1,
      "n_solver_errors": 1,
      "sample_note": "capped sample 1/1633",
      "best": null
    },
    {
      "tree": "n7-star6",
      "k": 3,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 1771,
      "enum_exhaustive": true,
      "n_uncovered_total": 1,
      "n_tested": 1,
      "n_solver_errors": 0,
      "sample_note": "full uncovered set tested",
      "best": {
        "attach": [
          [
            "n1",
            "n2"
          ],
          [
            "n1",
            "n3"
          ],
          [
            "n2",
            "n3"
          ]
        ],
        "ratio": 0.6666666666666675,
        "demands": [
          1.0,
          1.0000000000000013,
          1.0
        ],
        "w": [
          -0.0,
          0.33333333333333265,
          0.3333333333333341
        ]
      }
    },
    {
      "tree": "n7-star6",
      "k": 4,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 10626,
      "enum_exhaustive": true,
      "n_uncovered_total": 6,
      "n_tested": 6,
      "n_solver_errors": 1,
      "sample_note": "full uncovered set tested",
      "best": {
        "attach": [
          [
            "n1",
            "n2"
          ],
          [
            "n1",
            "n3"
          ],
          [
            "n1",
            "n4"
          ],
          [
            "n2",
            "n3"
          ]
        ],
        "ratio": 0.7500000000000031,
        "demands": [
          0.9999999999999984,
          0.9999999999999993,
          1.000000000000006,
          1.0
        ],
        "w": [
          0.24999999999999623,
          0.24999999999999645,
          0.25000000000000117,
          -0.0
        ]
      }
    },
    {
      "tree": "n7-star6",
      "k": 5,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 53130,
      "enum_exhaustive": false,
      "n_uncovered_total": 33,
      "n_tested": 1,
      "n_solver_errors": 1,
      "sample_note": "capped sample 1/33",
      "best": null
    },
    {
      "tree": "n7-twochains",
      "k": 3,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 1771,
      "enum_exhaustive": true,
      "n_uncovered_total": 147,
      "n_tested": 25,
      "n_solver_errors": 0,
      "sample_note": "capped sample 25/147",
      "best": {
        "attach": [
          [
            "n1",
            "n6"
          ],
          [
            "n2",
            "n5"
          ],
          [
            "n4",
            "n6"
          ]
        ],
        "ratio": 0.7500000000000061,
        "demands": [
          1.000000000000001,
          1.0000000000000038,
          0.9999999999999983
        ],
        "w": [
          0.500000000000005,
          0.4999999999999895,
          0.750000000000007
        ]
      }
    },
    {
      "tree": "n7-twochains",
      "k": 4,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 10626,
      "enum_exhaustive": true,
      "n_uncovered_total": 2301,
      "n_tested": 6,
      "n_solver_errors": 1,
      "sample_note": "capped sample 6/2301",
      "best": {
        "attach": [
          [
            "n1",
            "n4"
          ],
          [
            "n2",
            "n6"
          ],
          [
            "n3",
            "n4"
          ],
          [
            "n3",
            "n5"
          ]
        ],
        "ratio": 0.7500000000000024,
        "demands": [
          1.0,
          1.0,
          1.0,
          0.5000000000000031
        ],
        "w": [
          0.5000000000000053,
          0.49999999999999645,
          0.2499999999999971,
          0.5000000000000089
        ]
      }
    },
    {
      "tree": "n7-twochains",
      "k": 5,
      "category": "n7",
      "n_nodes": 7,
      "raw_combo_count": 53130,
      "enum_exhaustive": false,
      "n_uncovered_total": 1723,
      "n_tested": 1,
      "n_solver_errors": 1,
      "sample_note": "capped sample 1/1723",
      "best": null
    }
  ],
  "k6_spot_check": {
    "tree": "n4-fork-at-n1(spot,3-arc)",
    "attach": [
      [
        "n1",
        "n2"
      ],
      [
        "n1",
        "n3"
      ],
      [
        "n1",
        "s"
      ],
      [
        "n2",
        "n3"
      ],
      [
        "n2",
        "s"
      ],
      [
        "n3",
        "s"
      ]
    ],
    "elapsed_s": 24.635954504999972,
    "ok": true,
    "ratio": 0.6666676666666667,
    "p": [
      0.0,
      0.0,
      0.0,
      1.9999999999834963e-06,
      0.6666646666666667,
      0.6666686666666666
    ],
    "q": [
      1.0,
      1.0,
      1.0,
      0.999998,
      0.3333353333333333,
      0.3333313333333333
    ],
    "demands": [
      1.0,
      1.0,
      1.0,
      1.0,
      1.0,
      0.9999999999999999
    ],
    "w": [
      0.0,
      0.0,
      0.0,
      1.9999999999834963e-06,
      0.6666646666666667,
      0.6666686666666667
    ]
  },
  "k7_note": "k=7 not attempted at all -- not a silent cap. Measured growth k=5->k=6 was a ~5-9x jump (4-8s -> 36s+) even at the smallest 3-arc tree, faster than the ~2x the raw 2^k binary count alone would predict (branch-and-bound cost, not just problem size, blows up). Extrapolating the same factor projects k=7 at several hundred seconds PER CALL on the cheapest structure available -- a single call would risk consuming most of whatever budget remained for one uncertain data point. Left untouched.",
  "global_best": {
    "tree": "n7-chain6",
    "k": 4,
    "category": "n7",
    "attach": [
      [
        "n2",
        "n4"
      ],
      [
        "n2",
        "n6"
      ],
      [
        "n3",
        "n5"
      ],
      [
        "n3",
        "n6"
      ]
    ],
    "ratio": 0.7500002000000001,
    "demands": [
      1.0,
      0.4999996000000005,
      1.0,
      1.0
    ],
    "w": [
      0.5000004000000001,
      0.4999983999987205,
      0.5000003999999999,
      1.0
    ]
  },
  "count_ge_075": 503,
  "count_ge_090": 0,
  "count_ge_099": 0,
  "n_ratios_computed": 702,
  "total_solver_errors": 17,
  "positive_hits": [],
  "bugs": [],
  "truncated": false,
  "truncated_note": null,
  "total_elapsed_s": 202.34037017099945,
  "stage1_wall_time_s_note": "stage 1 (pre-resume) ran ~640s of real wall time before being killed on a single pathological MILP call; that time is not included in this process's elapsed()/total_elapsed_s, which only covers the continuation. See the final report for the combined wall-clock total."
}