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{
  "certified_leaves_total": 237490,
  "certified_volume_fraction": 1.0000000000000002,
  "enclosure_mode": "centered",
  "failure_regions": 0,
  "family": "two_tight_pairs (nfill=0 core)",
  "family_box": {
    "d0_um": {
      "hi": 60.0,
      "lo": 25.0
    },
    "jog_mult": {
      "hi": 0.4,
      "lo": -0.4
    },
    "pt_mult": {
      "hi": 1.2,
      "lo": 1.0
    },
    "sep_mult": {
      "hi": 4.5,
      "lo": 2.5
    }
  },
  "forced_pairwise_overprediction_basis": "sup_certified_k_hi",
  "forced_pairwise_overprediction_pct": 10.000002061387825,
  "geometry": {
    "description": "Four parallel circular conductors forming two tight pairs. pitch = 1.6 * d0 * pt_mult; separation = pitch * sep_mult; jog = jog_mult * separation. Conductor centres at (0,0), (pitch,0), (separation,jog), (separation+pitch,jog); every conductor has diameter d0.",
    "self_term_radius_scale": 1.0,
    "units": "d0_um in micrometres; the multipliers are dimensionless"
  },
  "honest_scope": "A complete interval theorem about the frozen MONOPOLE-CLOSURE model only. The closure-vs-BEM/PDE model gap remains additive and unresolved. This witness does not establish Maxwell, BEM, driven-S, fabrication, or measured-silicon truth.",
  "k_bar": 0.9090909090909091,
  "open_boxes": 0,
  "parameters": [
    "d0_um",
    "pt_mult",
    "sep_mult",
    "jog_mult"
  ],
  "processed_leaves_total": 474724,
  "provenance": {
    "partition_regions": 256,
    "prover_wall_seconds": 243.5342594169997,
    "schema": "genesis.family_impossibility.parallel.v1",
    "source_sha256": "51c6f38f9d3d09b654886b2278ba86712596978b4ad1366ec96bcfcec2ff272c",
    "source_witness": "family_two_tight_pairs_k10pct_parallel_2026_07.json",
    "witness_content_sha256": "5b10e5a58013fa0e9bf9fb7900d885e4bd70e808bbad59e374d15a03be9ab2a3"
  },
  "statement": "For every layout in the family box, the monopole-closure many-body screening factor satisfies k <= 0.909090909091. A pairwise-superposition extractor assumes k == 1, so it over-predicts the worst coupling by at least 10.0000% on every member of the family.",
  "status": "THEOREM_CERTIFIED",
  "sup_certified_k_hi": 0.9090908920546464
}