{
  "bell5": 52,
  "case": "Stirling rows, Bell/Fubini triangular transfers and reciprocal parity packets",
  "checks_by_group": {
    "composition": 88,
    "generating": 110,
    "moments": 300,
    "packet_transfer": 158,
    "packets": 44,
    "partitions": 45,
    "reconstruction": 26,
    "reference": 25,
    "surjections": 36,
    "touchard": 94,
    "triangular": 165
  },
  "degree": 10,
  "fubini5": 541,
  "moment_bridge_n5": {
    "0": {
      "exponential_moment": "0",
      "touchard": "0"
    },
    "1": {
      "exponential_moment": "541",
      "touchard": "52"
    },
    "1/2": {
      "exponential_moment": "91/2",
      "touchard": "257/32"
    },
    "2": {
      "exponential_moment": "9002",
      "touchard": "454"
    }
  },
  "packet_split_n5": {
    "even_degree_tap_contribution": 135,
    "odd_degree_tap_contribution": 406
  },
  "packet_split_n5_mod3": {
    "residue_0": 30,
    "residue_1": 380,
    "residue_2": 131
  },
  "reconstruction_n4": {
    "candidate_ordered_samples": [
      "0",
      "75",
      "746",
      "3129",
      "8916"
    ],
    "candidate_touchard_at_2": 90,
    "recovered_stirling_row": [
      0,
      1,
      7,
      6,
      1
    ],
    "true_ordered_samples": [
      "0",
      "75",
      "730",
      "3045",
      "8676"
    ],
    "true_touchard_at_2": 94
  },
  "row5": [
    0,
    1,
    15,
    25,
    10,
    1
  ],
  "scope": "Exact classical finite combinatorics and formal-series identities; no new Lean replay or universal recovery theorem.",
  "total_assertions": 1091,
  "weighted_row5": [
    0,
    1,
    30,
    150,
    240,
    120
  ],
  "witness_n4": {
    "alternative_row": [
      0,
      5,
      2,
      7,
      1
    ],
    "bell": 15,
    "difference": [
      0,
      4,
      -5,
      1,
      0
    ],
    "fubini": 75,
    "true_row": [
      0,
      1,
      7,
      6,
      1
    ]
  }
}