{
  "K": 26,
  "atomicity": {
    "all_have_essential_gene": true,
    "n_checked": 26,
    "per_mechanism": {
      "A": {
        "essential_genes": [
          "commit_capabilities"
        ],
        "has_essential_gene": true,
        "n_genes": 3,
        "shared_foundation_genes": [
          "explicit_fallback",
          "bind_transcript"
        ]
      },
      "AA": {
        "essential_genes": [
          "pqc_owe"
        ],
        "has_essential_gene": true,
        "n_genes": 1,
        "shared_foundation_genes": []
      },
      "AB": {
        "essential_genes": [
          "length_privacy"
        ],
        "has_essential_gene": true,
        "n_genes": 1,
        "shared_foundation_genes": []
      },
      "AC": {
        "essential_genes": [
          "code_lattice_hybrid"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "AD": {
        "essential_genes": [
          "eap_pqc_downgrade_firewall"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "AE": {
        "essential_genes": [
          "group_key_binding"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "AF": {
        "essential_genes": [
          "recovery_gate"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "AG": {
        "essential_genes": [
          "agility_gate"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "AH": {
        "essential_genes": [
          "domain_separation"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "B": {
        "essential_genes": [
          "idempotent_install"
        ],
        "has_essential_gene": true,
        "n_genes": 1,
        "shared_foundation_genes": []
      },
      "H": {
        "essential_genes": [
          "mlo_link_bind"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "J": {
        "essential_genes": [
          "policy_bind"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "K": {
        "essential_genes": [
          "eaptls_capsule_bind"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "L": {
        "essential_genes": [
          "cred_cache"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "M": {
        "essential_genes": [
          "adaptive_fec"
        ],
        "has_essential_gene": true,
        "n_genes": 3,
        "shared_foundation_genes": [
          "bind_transcript",
          "fragment_root"
        ]
      },
      "N": {
        "essential_genes": [
          "tail_bound"
        ],
        "has_essential_gene": true,
        "n_genes": 1,
        "shared_foundation_genes": []
      },
      "P": {
        "essential_genes": [
          "merkle_beacon_root"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "beacon_auth"
        ]
      },
      "Q": {
        "essential_genes": [
          "zero_rtt_resumption"
        ],
        "has_essential_gene": true,
        "n_genes": 1,
        "shared_foundation_genes": []
      },
      "R": {
        "essential_genes": [
          "roam_key_binding"
        ],
        "has_essential_gene": true,
        "n_genes": 3,
        "shared_foundation_genes": [
          "bind_transcript",
          "roam_epoch"
        ]
      },
      "S": {
        "essential_genes": [
          "compression_binding"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "T": {
        "essential_genes": [
          "implicit_kem_auth"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "U": {
        "essential_genes": [
          "xwing_combiner"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "V": {
        "essential_genes": [
          "sig_role_binding"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "X": {
        "essential_genes": [
          "frame_size_binding"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      },
      "Y": {
        "essential_genes": [
          "ft_roam_fs_binding"
        ],
        "has_essential_gene": true,
        "n_genes": 3,
        "shared_foundation_genes": [
          "bind_transcript",
          "roam_epoch"
        ]
      },
      "Z": {
        "essential_genes": [
          "verifiable_decap"
        ],
        "has_essential_gene": true,
        "n_genes": 2,
        "shared_foundation_genes": [
          "bind_transcript"
        ]
      }
    },
    "shared_foundation_genes": {
      "beacon_auth": 1,
      "bind_transcript": 20,
      "explicit_fallback": 1,
      "fragment_root": 1,
      "roam_epoch": 2
    }
  },
  "drat": {
    "cadical": "cadical",
    "drat_verified": true,
    "ran": true,
    "sat_at_K": true,
    "unsat": true
  },
  "drat_ran": true,
  "n_demands": 33,
  "n_mechanisms": 32,
  "ok": true,
  "solvers": {
    "branch_and_bound": 26,
    "rc2_maxsat": 26,
    "z3_optimize": 26
  },
  "solvers_agree": true,
  "taxonomy_completeness_bound": {
    "fleet_escapes": 0,
    "fleet_total_evaluations": 5600,
    "note": "empirical bound on taxonomy-completeness (v36-O4)"
  },
  "uniquely_required": [
    "A",
    "AA",
    "AB",
    "AC",
    "AD",
    "AE",
    "AF",
    "AG",
    "AH",
    "B",
    "H",
    "J",
    "K",
    "L",
    "M",
    "N",
    "P",
    "Q",
    "R",
    "S",
    "T",
    "U",
    "V",
    "X",
    "Y",
    "Z"
  ],
  "upper_bound": {
    "all_closed": true,
    "demands_closed_by_witness": 33,
    "n_demands": 33
  },
  "what": "Triangulated with available local engines, DRAT-checkable when its optional encoder is present, minimum-cover optimum K with upper-bound re-check and bounded atomicity/taxonomy.",
  "witness": [
    "A",
    "AA",
    "AB",
    "AC",
    "AD",
    "AE",
    "AF",
    "AG",
    "AH",
    "B",
    "H",
    "J",
    "K",
    "L",
    "M",
    "N",
    "P",
    "Q",
    "R",
    "S",
    "T",
    "U",
    "V",
    "X",
    "Y",
    "Z"
  ],
  "z3_lower_bound_unsat": true
}