{
 "artifact": "entropy_ceiling_certificate",
 "status": "MEASURED",
 "honesty_tag": "\ud83d\udfe2 PROVEN counting wall (CacheCeiling.lean: cold_miss_lower \u2200-trace \u2200-demand-policy, prefetch foil pins the model boundary, tightness witness) + \ud83d\udfe1 MEASURED policy positions + \ud83d\udfe0 MODELED LZ76 entropy line (cited Ziv\u2013Lempel'76/Kaspar\u2013Schuster'87, finite-sample bias disclosed) \u2014 the three tags are NEVER blended",
 "lean_source": "serving_limits/formal/lean/CacheCeiling.lean",
 "lean_theorems": [
  "CacheCeiling.cold_miss_lower",
  "CacheCeiling.hits_upper_wall",
  "CacheCeiling.wall_attained_witness",
  "CacheCeiling.prefetch_beats_wall_foil",
  "CacheCeiling.prefetch_not_demand",
  "CacheCeiling.lru_not_always_at_wall"
 ],
 "quantifier_census": {
  "forall_theorems": [
   "cold_miss_lower (\u2200-trace \u2200-demand-policy)",
   "hits_upper_wall (\u2200-trace \u2200-demand-policy)"
  ],
  "finite_witnesses_decide": [
   "wall_attained_witness",
   "prefetch_beats_wall_foil",
   "lru_not_always_at_wall"
  ],
  "hypothesis": "DemandStep (no prefetch/fabrication) \u2014 load-bearing, machine-foiled"
 },
 "traces": [
  {
   "trace": "mooncake",
   "label": "real production trace (Mooncake FAST'25)",
   "n_test_refs": 21069,
   "n_distinct": 16930,
   "wall_hit_rate_proven": 0.19645,
   "lz76_entropy_bits_per_ref_modeled": 11.5413,
   "max_entropy_bits": 14.0473,
   "normalized_entropy": 0.8216,
   "belady_crosschecks_agree": true,
   "per_capacity": [
    {
     "capacity_blocks": 423,
     "wall_hit_rate_proven": 0.19645,
     "belady_hit_rate": 0.12687,
     "belady_pct_of_wall": 64.58,
     "lru_hit_rate": 0.04059,
     "learned_hit_rate": 0.04628,
     "evolved_hit_rate": 0.0599,
     "evolved_pct_of_wall": 30.49
    },
    {
     "capacity_blocks": 846,
     "wall_hit_rate_proven": 0.19645,
     "belady_hit_rate": 0.16,
     "belady_pct_of_wall": 81.45,
     "lru_hit_rate": 0.04352,
     "learned_hit_rate": 0.04856,
     "evolved_hit_rate": 0.06014,
     "evolved_pct_of_wall": 30.62
    },
    {
     "capacity_blocks": 1693,
     "wall_hit_rate_proven": 0.19645,
     "belady_hit_rate": 0.19645,
     "belady_pct_of_wall": 100.0,
     "lru_hit_rate": 0.05497,
     "learned_hit_rate": 0.0588,
     "evolved_hit_rate": 0.06613,
     "evolved_pct_of_wall": 33.66
    },
    {
     "capacity_blocks": 3386,
     "wall_hit_rate_proven": 0.19645,
     "belady_hit_rate": 0.19645,
     "belady_pct_of_wall": 100.0,
     "lru_hit_rate": 0.07504,
     "learned_hit_rate": 0.0775,
     "evolved_hit_rate": 0.08919,
     "evolved_pct_of_wall": 45.4
    }
   ]
  },
  {
   "trace": "oasst_derived",
   "label": "DERIVED from real oasst1 text (NOT a production capture)",
   "n_test_refs": 2650,
   "n_distinct": 1858,
   "wall_hit_rate_proven": 0.29887,
   "lz76_entropy_bits_per_ref_modeled": 8.2349,
   "max_entropy_bits": 10.8595,
   "normalized_entropy": 0.7583,
   "belady_crosschecks_agree": true,
   "per_capacity": [
    {
     "capacity_blocks": 64,
     "wall_hit_rate_proven": 0.29887,
     "belady_hit_rate": 0.06038,
     "belady_pct_of_wall": 20.2,
     "lru_hit_rate": 0.0,
     "learned_hit_rate": 0.00075,
     "evolved_hit_rate": 0.00415,
     "evolved_pct_of_wall": 1.39
    },
    {
     "capacity_blocks": 92,
     "wall_hit_rate_proven": 0.29887,
     "belady_hit_rate": 0.08151,
     "belady_pct_of_wall": 27.27,
     "lru_hit_rate": 0.0,
     "learned_hit_rate": 0.00076,
     "evolved_hit_rate": 0.00415,
     "evolved_pct_of_wall": 1.39
    },
    {
     "capacity_blocks": 185,
     "wall_hit_rate_proven": 0.29887,
     "belady_hit_rate": 0.15094,
     "belady_pct_of_wall": 50.5,
     "lru_hit_rate": 0.01208,
     "learned_hit_rate": 0.01321,
     "evolved_hit_rate": 0.01208,
     "evolved_pct_of_wall": 4.04
    },
    {
     "capacity_blocks": 371,
     "wall_hit_rate_proven": 0.29887,
     "belady_hit_rate": 0.22113,
     "belady_pct_of_wall": 73.99,
     "lru_hit_rate": 0.02264,
     "learned_hit_rate": 0.02264,
     "evolved_hit_rate": 0.02718,
     "evolved_pct_of_wall": 9.09
    }
   ]
  }
 ],
 "mooncake_wall_hit_rate": 0.19645,
 "mooncake_belady_pct_of_wall_mid": 81.45,
 "mooncake_evolved_pct_of_wall_mid": 30.62,
 "headline_reframe": "the trace admits at most wall_hit_rate (PROVEN); Belady captures belady_pct_of_wall of it; the evolved policy captures evolved_pct_of_wall \u2014 the policy gap is bounded by the trace's own structure, not engineering shortfall"
}