{
  "project": "CSM_RH",
  "paper": 48,
  "version": "0.1",
  "date": "2026-09-07",
  "state_transition": "v1.38 -> v1.39",
  "campaign": "44",
  "tracks": "PK1 EXACT_PESC_TRIANGULAR_KERNEL_NORMALIZATION; PK2 ROOT_SPECTRAL_REPRESENTATION",
  "status": "PASS",
  "checks": {
    "utf8_all_source_files": true,
    "nul_bytes_absent": true,
    "json_parse": true,
    "csv_parse": true,
    "canonical_math_delimiters_only": "$...$ and $$...$$",
    "backslash_math_delimiters_absent": true,
    "unicode_math_operator_substitution_absent": true,
    "math_delimiters_balanced": true,
    "numeric_positive_lag_identity_max_abs_error": 8.242295734817162e-13,
    "numeric_prefix_gram_identity_max_abs_error": 6.821210263296962e-13,
    "numeric_root_quotient_identity_max_abs_error": 3.410605131648481e-13,
    "numeric_brownian_spectrum_identity_max_abs_error": 4.718003765447065e-12,
    "numeric_lag_mass_formula_max_abs_error": 0.0,
    "pure_prefix_first_mode_fraction_error_at_N_10000": 4.052514029029286e-05,
    "root_claims": {
      "RH_PROVED": false,
      "RH_DISPROVED": false,
      "GLOBAL_RH_CERTIFICATE": false
    },
    "PK1_closure": "CLOSED_AS_EXACT_LAG_POSITION_NORMALIZATION_WITH_PREFIX_GRAM_COMPLETION",
    "PK2_closure": "CLOSED_AS_EXACT_BROWNIAN_SPECTRAL_REPRESENTATION_WITH_LOW_MODE_PRESERVED",
    "next": "Campaign 44 / PK3 TRANSLATED_WINDOW_SYNTHESIS",
    "fixed_power_proved": false,
    "automatic_root_promotion": false
  },
  "new_certified_ids": [
    "B-RH-032",
    "B-RH-033",
    "B-RH-034",
    "B-RH-035",
    "O-RH-125",
    "O-RH-126",
    "O-RH-127"
  ],
  "notes": [
    "The PSD completion and Brownian spectrum are exact finite-dimensional identities.",
    "The k=1 low-frequency witness is a root-kernel quotient observability statement, not a claim that the actual prime-error sequence has 8/pi^2 of its energy in that mode.",
    "The Theta(N^2) spectral spread is a conditioning ledger for PK3, not a proof that every possible synthesis fails.",
    "No new external theorem is used for the linear-algebraic claims."
  ]
}