{
 "artifact": "fleet_optimality_certificate",
 "status": "MEASURED",
 "honesty_tag": "\ud83d\udfe2 PROVEN fleet counting wall (SubmodularCover.lean: fleet_miss_lower \u2200 routings/policies/traces; pooled attains it; per-instance pays more; capacitated (1\u22121/e) finite core + cited NWF'78 + non-submodular foil) + \ud83d\udfe1 CP-SAT-CERTIFIED optimum on the exact committed instance + \ud83d\udfe1 the committed measured hit rates (untouched) \u2014 pooled equals the certified optimum, per-instance structurally cannot",
 "lean_source": "serving_limits/formal/lean/SubmodularCover.lean",
 "lean_theorems": [
  "SubmodularCover.fleet_miss_lower",
  "SubmodularCover.pooled_attains_wall_witness",
  "SubmodularCover.per_instance_pays_more_witness",
  "SubmodularCover.greedy_budget2_witness",
  "SubmodularCover.greedy_below_opt_witness",
  "SubmodularCover.greedy_foil"
 ],
 "quantifier_census": {
  "forall_theorems": [
   "fleet_miss_lower (\u2200 routings, \u2200 demand policies, \u2200 traces)"
  ],
  "finite_witnesses_decide": [
   "pooled_attains_wall_witness",
   "per_instance_pays_more_witness",
   "greedy_budget2_witness (exact-\u211a: 4\u00b7greedy \u2265 3\u00b7OPT at k=2, greedy STRICTLY below OPT so the 3/4 rate is genuinely exercised \u2014 NWF'78 rate, not exhibited-tight)",
   "greedy_below_opt_witness (greedy 5 < OPT 6)",
   "greedy_foil"
  ],
  "cited": "Nemhauser\u2013Wolsey\u2013Fisher 1978 (the general (1\u22121/e) \u2200-statement)"
 },
 "instance": {
  "k_prefixes": 32,
  "m_per_prefix": 16,
  "seed": 7,
  "n_requests": 512,
  "n_distinct": 32,
  "replicates": "run_multihost_fleet_floor.py verbatim"
 },
 "cpsat": {
  "status": "OPTIMAL",
  "objective_min_prefills": 32,
  "best_objective_bound": 32,
  "bound_is_proven_optimal": true,
  "n_hosts": 16
 },
 "pooled_misses_measured": 32,
 "pooled_equals_certified_optimum": true,
 "pooled_pct_of_certified_optimum": 100.0,
 "committed_hit_rates_untouched": {
  "2": {
   "pooled": 0.9375,
   "per_instance": 0.875
  },
  "4": {
   "pooled": 0.9375,
   "per_instance": 0.752
  },
  "8": {
   "pooled": 0.9375,
   "per_instance": 0.5527
  },
  "16": {
   "pooled": 0.9375,
   "per_instance": 0.3398
  }
 },
 "scope_note": "the CP-SAT optimum and the counting wall are for the UNCAPACITATED committed instance (hosts hold what they fetch); the capacitated regime is covered by the greedy (1\u22121/e) finite core + citation, not claimed beyond it"
}