{
  "all_continuous_linear_closed": true,
  "all_deterministic_learned_closed": true,
  "all_multi_bit_memory_closed": true,
  "all_ok": true,
  "all_randomized_policy_closed": true,
  "closed_routes": [
    "multi_bit_memory (arbitrary finite width, via refinement_sound + Q2')",
    "randomized_policy (Q2'-support: support subset g_min)",
    "deterministic_learned_policy (v14 uninterpreted-pi)",
    "continuous_soft_controller_on_reliability_axis (FBL converse bounds all schemes)",
    "continuous_LINEAR_policy_over_the_state_box (Q1_real+Q2'_real QF-LRA + nlsat corollary)"
  ],
  "continuous_linear_policy": {
    "argument": "Q1_real + Q2'_real (both QF_LRA UNSAT) prove g_min permits EXACTLY the non-hazard set over the CONTINUOUS box -> any policy of any class (linear/continuous/soft) permitting a g_min-blocked real state permits a hazard (unsafe); so no safe policy is strictly more permissive than g_min over the continuum. The symbolic-coefficient nlsat check corroborates for the explicit linear class.",
    "continuous_linear_closed": true,
    "flagship": "weighted_budget (linear hazard 2*pkts+lat>6 over the continuous real box [0,5]^2)",
    "non_vacuity_witness": true,
    "q1_gmin_safe_over_reals": true,
    "q2prime_exact_boundary_over_reals": true,
    "still_open": "optimality over a genuinely continuous state with an ARBITRARY NONLINEAR soft/learned controller (needs a Lipschitz/interval measure bridge + full NRA/dReal) stays DISCLOSED-OPEN \u2014 this closes the LINEAR class over the continuum, not the nonlinear one",
    "symbolic_linear_policy_no_beat": true,
    "symbolic_solver_result": "unsat"
  },
  "continuous_physics_ceiling": {
    "argument": "the finite-blocklength converse (common/finite_blocklength.py::converse_rate_sphere_packing / meta_converse_rate_exact; welded to the guard in v82) lower-bounds error for ANY scheme at (n, eps, rate, SNR); a continuous/soft controller is still a scheme, so it cannot beat the converse operating boundary \u2014 the quantitative-mechanism ceiling on the reliability axis",
    "available": true,
    "v82_executed": true
  },
  "cross_domain_foundry": {
    "deadline_coupling::ai_fabric_checkpoint__x__emlsr_switch": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 5,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    },
    "event_invalidation::beam_ntn_handover__x__csi_lcm_fallback": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 3,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    },
    "event_invalidation::beam_ntn_handover__x__harq_early_term": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 3,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    },
    "event_invalidation::beam_ntn_handover__x__pqc_wifi_handshake": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 3,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    },
    "freshness_invalidation::beam_ntn_handover__x__smd_bss_transition": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 3,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    },
    "shared_resource_hold::ai_fabric_checkpoint__x__cxl_forward_progress": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 3,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    },
    "stall_freshness_invalidation::ai_fabric_checkpoint__x__smd_bss_transition": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 3,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    },
    "stall_invalidation::ai_fabric_checkpoint__x__csi_lcm_fallback": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 3,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    },
    "stall_invalidation::ai_fabric_checkpoint__x__harq_early_term": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 3,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    },
    "stall_invalidation::ai_fabric_checkpoint__x__pqc_wifi_handshake": {
      "boolean_full_state_exact": true,
      "multi_bit_argument": "the joint invariant is memoryless, so WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) reduces any finite-memory cross-domain guard to its base; the v89 full-state exact boundary then forbids any weaker-and-safe one",
      "multi_bit_memory_closed": true,
      "n_state_bits": 3,
      "randomized_argument": "g_min == fix_needed over the full joint state, so a randomized cross-guard off fix_needed either over-fires (strictly more fallback) or re-admits the emergent escape -> support subset fix_needed",
      "randomized_policy_closed": true,
      "witness": true
    }
  },
  "disclosed_open": "optimality over a genuinely CONTINUOUS state space with an arbitrary NONLINEAR soft/learned real-valued controller \u2014 needs a measure argument + nlsat/dReal (z3 returns `unknown`; dReal is not wired). This corner stays OPEN-DISCLOSED, not faked.",
  "executed": true,
  "explicit_non_claim": "Modeling entailments within the explicit-state / z3 abstractions plus one kernel-checked Lean reduction citation. NOT a declared SEP, NOT an FTO opinion, NOT OTA. Base $668,960,344 unmoved; essentiality_bridge_v43 n_machine_checked=8 byte-identical. Booked EVIDENCE-ONLY.",
  "honesty": "Multi-bit closure LEADS with the reduction theorem (arbitrary finite memory) \u2014 exhaustive enumeration is only feasible at 1 memory bit (v83) and is cited as corroboration, not the load-bearing proof. The randomized argument reuses the existing Q2' certificate; it is a logical consequence, not a separate solver run.",
  "n_guards": 18,
  "operational_and_single_domain": {
    "csi_lcm_fallback::UseModel": {
      "deterministic_learned_closed": true,
      "deterministic_learned_proof": "proven",
      "k_bits_required": 2,
      "multi_bit_argument": "no finite-memory guard of any width beats g_min: the memoryless invariant makes pi a simulation, so by WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) a memory-augmented guard is safe iff its base guard is; a behaviorally-weaker one projects to a base escape forbidden by the Q2' UNSAT certificate (exhaustive 1-bit corroboration in artifacts/automata_max_v83.json)",
      "multi_bit_memory_closed": true,
      "q1_gmin_safe": true,
      "q2_every_blocked_state_escapes": true,
      "randomized_argument": "Q2' -> every g_min-blocked state escapes deterministically, so a randomized policy firing with p>0 there has a p>0 escape from I; any a.s.-safe policy puts zero mass on g_min-blocked states -> support subset g_min",
      "randomized_policy_closed": true,
      "randomized_skolem_witness": {
        "active": "True",
        "aged": "False",
        "drift": "True",
        "produced": "False",
        "unsafe": "False"
      }
    },
    "cxl_forward_progress::A_get_r2": {
      "deterministic_learned_closed": true,
      "deterministic_learned_proof": "proven",
      "k_bits_required": 1,
      "multi_bit_argument": "no finite-memory guard of any width beats g_min: the memoryless invariant makes pi a simulation, so by WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) a memory-augmented guard is safe iff its base guard is; a behaviorally-weaker one projects to a base escape forbidden by the Q2' UNSAT certificate (exhaustive 1-bit corroboration in artifacts/automata_max_v83.json)",
      "multi_bit_memory_closed": true,
      "q1_gmin_safe": true,
      "q2_every_blocked_state_escapes": true,
      "randomized_argument": "Q2' -> every g_min-blocked state escapes deterministically, so a randomized policy firing with p>0 there has a p>0 escape from I; any a.s.-safe policy puts zero mass on g_min-blocked states -> support subset g_min",
      "randomized_policy_closed": true,
      "randomized_skolem_witness": {
        "adone": "False",
        "ar1": "False",
        "ar2": "False",
        "bdone": "False",
        "br1": "False",
        "br2": "False"
      }
    },
    "cxl_forward_progress::B_get_r2": {
      "deterministic_learned_closed": true,
      "deterministic_learned_proof": "proven",
      "k_bits_required": 1,
      "multi_bit_argument": "no finite-memory guard of any width beats g_min: the memoryless invariant makes pi a simulation, so by WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) a memory-augmented guard is safe iff its base guard is; a behaviorally-weaker one projects to a base escape forbidden by the Q2' UNSAT certificate (exhaustive 1-bit corroboration in artifacts/automata_max_v83.json)",
      "multi_bit_memory_closed": true,
      "q1_gmin_safe": true,
      "q2_every_blocked_state_escapes": true,
      "randomized_argument": "Q2' -> every g_min-blocked state escapes deterministically, so a randomized policy firing with p>0 there has a p>0 escape from I; any a.s.-safe policy puts zero mass on g_min-blocked states -> support subset g_min",
      "randomized_policy_closed": true,
      "randomized_skolem_witness": {
        "adone": "False",
        "ar1": "False",
        "ar2": "False",
        "bdone": "False",
        "br1": "False",
        "br2": "False"
      }
    },
    "emlsr_switch::SwitchAhead": {
      "deterministic_learned_closed": true,
      "deterministic_learned_proof": "proven",
      "k_bits_required": 2,
      "multi_bit_argument": "no finite-memory guard of any width beats g_min: the memoryless invariant makes pi a simulation, so by WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) a memory-augmented guard is safe iff its base guard is; a behaviorally-weaker one projects to a base escape forbidden by the Q2' UNSAT certificate (exhaustive 1-bit corroboration in artifacts/automata_max_v83.json)",
      "multi_bit_memory_closed": true,
      "q1_gmin_safe": true,
      "q2_every_blocked_state_escapes": true,
      "randomized_argument": "Q2' -> every g_min-blocked state escapes deterministically, so a randomized policy firing with p>0 there has a p>0 escape from I; any a.s.-safe policy puts zero mass on g_min-blocked states -> support subset g_min",
      "randomized_policy_closed": true,
      "randomized_skolem_witness": {
        "crit": "True",
        "cur": "1",
        "missed": "False",
        "pressure": "True",
        "stall": "False"
      }
    },
    "multiap_token::TxA": {
      "deterministic_learned_closed": true,
      "deterministic_learned_proof": "proven",
      "k_bits_required": 1,
      "multi_bit_argument": "no finite-memory guard of any width beats g_min: the memoryless invariant makes pi a simulation, so by WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) a memory-augmented guard is safe iff its base guard is; a behaviorally-weaker one projects to a base escape forbidden by the Q2' UNSAT certificate (exhaustive 1-bit corroboration in artifacts/automata_max_v83.json)",
      "multi_bit_memory_closed": true,
      "q1_gmin_safe": true,
      "q2_every_blocked_state_escapes": true,
      "randomized_argument": "Q2' -> every g_min-blocked state escapes deterministically, so a randomized policy firing with p>0 there has a p>0 escape from I; any a.s.-safe policy puts zero mass on g_min-blocked states -> support subset g_min",
      "randomized_policy_closed": true,
      "randomized_skolem_witness": {
        "harm": "False",
        "served": "1",
        "tA": "False",
        "tB": "True",
        "wA": "True",
        "wB": "False"
      }
    },
    "pqc_wifi_handshake::ConfirmKey": {
      "deterministic_learned_closed": true,
      "deterministic_learned_proof": "proven",
      "k_bits_required": 2,
      "multi_bit_argument": "no finite-memory guard of any width beats g_min: the memoryless invariant makes pi a simulation, so by WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) a memory-augmented guard is safe iff its base guard is; a behaviorally-weaker one projects to a base escape forbidden by the Q2' UNSAT certificate (exhaustive 1-bit corroboration in artifacts/automata_max_v83.json)",
      "multi_bit_memory_closed": true,
      "q1_gmin_safe": true,
      "q2_every_blocked_state_escapes": true,
      "randomized_argument": "Q2' -> every g_min-blocked state escapes deterministically, so a randomized policy firing with p>0 there has a p>0 escape from I; any a.s.-safe policy puts zero mass on g_min-blocked states -> support subset g_min",
      "randomized_policy_closed": true,
      "randomized_skolem_witness": {
        "bnd": "False",
        "dg": "True",
        "ds": "False",
        "insec": "False",
        "kc": "False"
      }
    },
    "pqc_wifi_handshake::SendData": {
      "deterministic_learned_closed": true,
      "deterministic_learned_proof": "proven",
      "k_bits_required": 1,
      "multi_bit_argument": "no finite-memory guard of any width beats g_min: the memoryless invariant makes pi a simulation, so by WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) a memory-augmented guard is safe iff its base guard is; a behaviorally-weaker one projects to a base escape forbidden by the Q2' UNSAT certificate (exhaustive 1-bit corroboration in artifacts/automata_max_v83.json)",
      "multi_bit_memory_closed": true,
      "q1_gmin_safe": true,
      "q2_every_blocked_state_escapes": true,
      "randomized_argument": "Q2' -> every g_min-blocked state escapes deterministically, so a randomized policy firing with p>0 there has a p>0 escape from I; any a.s.-safe policy puts zero mass on g_min-blocked states -> support subset g_min",
      "randomized_policy_closed": true,
      "randomized_skolem_witness": {
        "bnd": "False",
        "dg": "False",
        "ds": "False",
        "insec": "False",
        "kc": "False"
      }
    },
    "smd_bss_transition::Commit": {
      "deterministic_learned_closed": true,
      "deterministic_learned_proof": "proven",
      "k_bits_required": 1,
      "multi_bit_argument": "no finite-memory guard of any width beats g_min: the memoryless invariant makes pi a simulation, so by WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41) a memory-augmented guard is safe iff its base guard is; a behaviorally-weaker one projects to a base escape forbidden by the Q2' UNSAT certificate (exhaustive 1-bit corroboration in artifacts/automata_max_v83.json)",
      "multi_bit_memory_closed": true,
      "q1_gmin_safe": true,
      "q2_every_blocked_state_escapes": true,
      "randomized_argument": "Q2' -> every g_min-blocked state escapes deterministically, so a randomized policy firing with p>0 there has a p>0 escape from I; any a.s.-safe policy puts zero mass on g_min-blocked states -> support subset g_min",
      "randomized_policy_closed": true,
      "randomized_skolem_witness": {
        "committed": "False",
        "crit": "False",
        "fresh": "False",
        "lost": "False",
        "served": "0",
        "staged": "False"
      }
    }
  },
  "reduction_theorem": "WrflMathlib.Refinement.refinement_sound (lean-mathlib/WrflMathlib/Refinement.lean:41)",
  "schema": "mechanism-family-closure-v90",
  "skipped": false,
  "thesis": "Closes the OPEN 'change the mechanism family' design-around route (ii). Multi-bit / arbitrary finite memory and randomized policies are closed by REUSING the memoryless Q2' UNSAT certificate + the Lean-kernel refinement_sound reduction (no infeasible enumeration); deterministic learned policies were already closed by v14; the FBL converse bounds any continuous/soft controller on the reliability axis. The one genuinely-hard corner (continuous state + nonlinear controller) is disclosed OPEN.",
  "title": "v90 \u2014 mechanism-family closure (multi-bit memory + randomized/learned policies + physics ceiling)"
}