{
  "algorithm": {
    "triple": "(C1, f, C2), where f is a profile- and causal-order-preserving bijection",
    "hp": "greatest fixed point under forward/backward event extension",
    "hhp": "hp-style fixed point plus hereditary closure under matched subconfigurations",
    "profile_fields": [
      "label",
      "type",
      "authority",
      "residual"
    ],
    "warning": "finite prime-event-structure checker; not a general CEES/GES hhp solver"
  },
  "experiment_A_symmetric_branches": {
    "hp_related": true,
    "hhp_related": true,
    "hp_maps": [
      [
        [
          "a",
          "b"
        ],
        [
          "ra",
          "rb"
        ]
      ]
    ],
    "hhp_maps": [
      [
        [
          "a",
          "b"
        ],
        [
          "ra",
          "rb"
        ]
      ]
    ],
    "hp_relation_size": 13,
    "hhp_relation_size": 13,
    "finding": "Symmetric histories with matching future behaviour pass both finite hp and hhp checks."
  },
  "experiment_B_same_current_history_shape_but_different_future_profile": {
    "hp_related": false,
    "hhp_related": false,
    "finding": "The branch quotient is rejected once the unmatched future has a different profile/authority."
  },
  "experiment_C_meta_adds_branch_specific_future": {
    "hp_related_after_meta": false,
    "hhp_related_after_meta": false,
    "finding": "A Meta-added future on one branch invalidates the prior hp/hhp-like branch equivalence."
  },
  "experiment_D_structure_renaming": {
    "hp_empty_related": true,
    "hhp_empty_related": true,
    "hp_relation_size": 3,
    "hhp_relation_size": 3,
    "finding": "Two isomorphic two-event causal structures are related from the empty configurations."
  },
  "candidate_BQCert_upgrade": {
    "old": "bounded history/future signature proxy",
    "new": "configuration triple relation with causal-history isomorphism + forward/back matching + hereditary closure",
    "on_rdss_extensions": [
      "authority profile",
      "residual profile",
      "version pin",
      "certificate scope"
    ]
  }
}