{
  "all_points_ordered_floor_le_na_le_orthogonal": true,
  "eps": 0.01,
  "executed": true,
  "explicit_non_claim": "Adds a NEW impossibility axis (energy per bit) with the exact wideband floor and a monotone finite-k characterization; does NOT move the SNR wall banner or any existing artifact, and does NOT claim the finite-k value is an exact converse (it is the NA, labeled).",
  "flagship": {
    "finite_k_na_db": -0.6398,
    "finite_k_penalty_db": 0.9519,
    "floor_db": -1.5917,
    "k": 256,
    "ordering_floor_le_na_le_orthogonal": true,
    "orthogonal_achievable_db": 1.4368
  },
  "floor_db_exact_converse": -1.5917,
  "floor_derivation": "10*log10(ln 2) \u2014 Shannon minimum energy per bit (wideband converse, exact)",
  "honest_scope": "the FLOOR (-1.5917 dB) is the EXACT wideband converse (Shannon minimum energy per bit \u2014 a true converse no code beats); the finite-k value M(k) is a NORMAL APPROXIMATION over the repo's verified rate machinery optimized over bandwidth (an exact finite-k energy converse would need a large-n sphere-packing evaluation the mpmath quadrature does not reach); the orthogonal-signaling ceiling is a VALID achievability upper bound whose union bound is loose (k->inf asymptote ~+1.42 dB, disclosed). MODEL result, NOT OTA / silicon.",
  "k_sweep": [
    {
      "finite_k_na_db": 0.1503,
      "k": 64,
      "ordered": true,
      "orthogonal_achievable_db": 1.5551,
      "penalty_db": 1.742
    },
    {
      "finite_k_na_db": -0.2979,
      "k": 128,
      "ordered": true,
      "orthogonal_achievable_db": 1.4714,
      "penalty_db": 1.2938
    },
    {
      "finite_k_na_db": -0.6398,
      "k": 256,
      "ordered": true,
      "orthogonal_achievable_db": 1.4368,
      "penalty_db": 0.9519
    },
    {
      "finite_k_na_db": -0.8967,
      "k": 512,
      "ordered": true,
      "orthogonal_achievable_db": 1.4235,
      "penalty_db": 0.695
    },
    {
      "finite_k_na_db": -1.0873,
      "k": 1024,
      "ordered": true,
      "orthogonal_achievable_db": 1.4189,
      "penalty_db": 0.5044
    },
    {
      "finite_k_na_db": -1.2272,
      "k": 2048,
      "ordered": true,
      "orthogonal_achievable_db": 1.4177,
      "penalty_db": 0.3645
    },
    {
      "finite_k_na_db": -1.329,
      "k": 4096,
      "ordered": true,
      "orthogonal_achievable_db": 1.4176,
      "penalty_db": 0.2627
    },
    {
      "finite_k_na_db": -1.4026,
      "k": 8192,
      "ordered": true,
      "orthogonal_achievable_db": 1.4178,
      "penalty_db": 0.1891
    },
    {
      "finite_k_na_db": -1.4556,
      "k": 16384,
      "ordered": true,
      "orthogonal_achievable_db": 1.418,
      "penalty_db": 0.1361
    }
  ],
  "na_approaches_exact_floor_as_k_grows": true,
  "penalty_monotone_decreasing_in_k": true,
  "penalty_nonnegative": true,
  "schema": "energy-wall-v65",
  "skipped": false,
  "z3_ordering_lemma_proven": true,
  "z3_ordering_lemma_tier": "z3-lra"
}