paper_scale_500seed/theorem_reduction_audit.json

{
  "head_counts": [
    80,
    40,
    40,
    40
  ],
  "standardized_columns": true,
  "M": 200,
  "k": 4,
  "n": 30,
  "N": 6000,
  "lambda_k_full": 0.2,
  "lambda_k_ge_1_over_n": true,
  "selected_clients": 160,
  "k_times_lambda_min_AAT": 160,
  "selected_condition_number": 1.0,
  "N_prime": 4800,
  "lambda_1_prime": 0.25,
  "lambda_k_prime": 0.25,
  "sqrt_d_over_N_lambda_k": 0.12909944487358055,
  "subset_split_bound_term": 0.12909944487358055,
  "algebraic_ratio": 1.0,
  "spectral_condition_ratio_normA2_over_M_over_k": 1.6,
  "scope": "Concrete exact witness and proof-reduction check; not a proof of universal existence."
}