{
  "problem": "3a",
  "name": "GHR sum-difference constant C_3a \u2014 certified lower bound (large-deviation limit of a capped sparse-digit construction)",
  "claim": "C_3a >= 1.187326127925948",
  "alphabet": [
    0,
    8,
    9,
    12,
    16,
    17,
    18,
    20,
    21,
    24,
    25,
    26,
    27,
    28,
    29,
    30,
    32,
    33,
    34,
    35,
    36,
    37,
    38,
    39,
    40,
    41,
    42,
    43,
    44
  ],
  "base": 89,
  "rho": 10.704140799507785,
  "alpha_tilt": 0.06818532818532819,
  "s_tilt": 0.06859160390989587,
  "L_limit_float": 1.1873300680969796,
  "L_lower_rigorous": 1.187326127925948,
  "L_lower_str": "1.187326127925947938",
  "a_exponent": 0.7508285452870895,
  "r_ratio": 1.2494977971640002,
  "record_prev": "1.1835129324218615106564747894020784326947",
  "record_prev_holder": "Mosaic Intelligence 2026 (PR #95), finite d=420",
  "margin_over_record": 0.0038131955040864385,
  "proven_upper_bound": "4/3",
  "digit_lemma_cap": "5/4"
}