{
  "beta": 1.5683131734208395,
  "blocks": 4096,
  "occurrence_mass": 1.0,
  "conditional_entropy_nats": 3.5714104546868244,
  "pair_marginal_l1": 6.792850538862395e-09,
  "reference": {
    "vocab": 4096,
    "original_source": {
      "identity": {
        "fit_report_sha256": "7dafa8fe382295e77ce4ed32683ebe56ce83f0b9d25beed2a4410ee7d73c258e",
        "token_sha256": "f4ec26137d7487429f68a6e977d8386479f205001a6ec7c424bb90f21e6869c9",
        "suffix_sha256": "b3487d310803cd504260137665a1db1361c0d5c0b24e747747a2673dc2e266f2",
        "reconstruction": "merged fourgram prefix counts plus final triples; circular reverse histories v2"
      },
      "entropy": 3.5714023585974424,
      "reference_entropy": 3.571402358583158,
      "observed_pairs": 5910900,
      "occurrences": 1999999998,
      "history_boundary_triples": 2,
      "source_token_count": 2000000000,
      "entropy_difference_from_archive": 1.4284573524037114e-11,
      "note": "Target counts reconstructed from the available 2B natural stream prefix. Matching supported-pair count and near-matching entropy are consistency checks, not proof of byte-identical original source counts. Reverse histories add two wraparound triples to make empirical pair weights exactly stationary."
    },
    "reference_sha256": "535c57b1e3ef35730e26c68987d44cf48df8a5f383387061337dbc7f841ef765",
    "observed_trigrams": 132810622,
    "observed_contexts": 5910900,
    "occurrences": 2000000002,
    "added_supported_triples": [
      [
        480,
        2879,
        294
      ],
      [
        2879,
        294,
        2
      ],
      [
        294,
        2,
        1
      ],
      [
        2,
        1,
        1465
      ]
    ],
    "support_matches_original_empirical": true,
    "original_occurrences": 1999999998,
    "pair_frequency_tvd_upper_bound": 1.999999998e-09,
    "conditional_entropy_nats": 3.5714023607206284,
    "bigram_conditional_entropy_nats": 4.87638457764605,
    "additional_information_nats": 1.3049822169254215,
    "deterministic_contexts": 1457930,
    "deterministic_occurrence_mass": 0.0028618434971381564,
    "pair_flow_count_error": 0,
    "note": "Removed two artificial wrap edges, then added one count along an existing-support return path. Exact stationary reference; probabilities differ minutely from the finite-stream empirical source."
  },
  "identity": {
    "reference": "/notebooks/synthetic_trigrams/outputs/research/natural_language_scaling/trigram_reference_inputs/original",
    "reference_sha256": "535c57b1e3ef35730e26c68987d44cf48df8a5f383387061337dbc7f841ef765",
    "rank": 128,
    "alpha": 0.0,
    "seed": 20261103,
    "tolerance": 1e-08,
    "implementation": "sparse-middle-blocks-v2",
    "feature_bank_rank": 128,
    "context_features": "independent",
    "context_frequency_exponent": 0.0,
    "frequency_pivot_count": 18063.0,
    "frequency_multiplier_bounds": [
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      2.0
    ]
  },
  "target_entropy_nats": 3.5714023607206284,
  "additional_information_nats": 1.3049741229592255,
  "probabilities_directory": "outputs/research/natural_language_scaling/trigram_flat_components_128_source/fits/beta_1.5683131734",
  "note": "Exact empirical support; stationary pair marginals and total conditional information matched. Per-context information is not fitted. Coefficients follow power decay before masking and balancing; no exact final spectrum claim."
}