{
  "definition_note": {
    "name": "ON-RDSS BHHP_k",
    "k0": "plain HP greatest fixed point",
    "k_plus_1": "adds one mapped backward obligation into BHHP_k, while forward matching remains at the current level",
    "status": "runtime approximation inspired by bounded-backtracking literature; not yet claimed identical to Fröschle-Hildebrandt indexing"
  },
  "classical_fixture_levels": [
    {
      "k": 0,
      "initial_related": true,
      "relation_size": 17
    },
    {
      "k": 1,
      "initial_related": false,
      "relation_size": 10
    },
    {
      "k": 2,
      "initial_related": false,
      "relation_size": 4
    },
    {
      "k": 3,
      "initial_related": false,
      "relation_size": 0
    },
    {
      "k": 4,
      "initial_related": false,
      "relation_size": 0
    },
    {
      "k": 5,
      "initial_related": false,
      "relation_size": 0
    },
    {
      "k": 6,
      "initial_related": false,
      "relation_size": 0
    }
  ],
  "first_level_that_separates_fixture": 1,
  "monotone_relation_sizes": true,
  "finding": "For this classical HP-not-HHP fixture, the ON-RDSS bounded checker already separates at the first added backtracking level.",
  "runtime_interpretation": {
    "BHHP_0": "forward history-preserving verification",
    "BHHP_k": "finite rollback-sensitive certificate grade",
    "Full_HHP": "unbounded hereditary/backward obligation"
  }
}