{
  "node": "RH-Parallelogram-SobolevConductor v3.9",
  "status": {
    "uniform_finite_conductor_sobolev": "CLOSED",
    "finite_q_le_N_weighted_model": "N^4",
    "full_B2_antiderivative": "CLOSED_IN_HILBERT_COMPLETION",
    "full_fixed_eta_M": "OPEN",
    "actual_prime_deviation": "OPEN"
  },
  "main_theorem": "sup_{squarefree q} H_d(q) < infinity",
  "key_tools": [
    "Young l^(4/3) convolution inequality",
    "CRT factorization",
    "coprime csc^2 / Jordan J_2 identity",
    "discrete summation by parts",
    "Besicovitch B^2 weak compactness"
  ],
  "automatic_reject": [
    "finite-q Sobolev growth cited as remaining obstruction",
    "B2 equality promoted to pointwise equality",
    "full O(N^4) claimed without quantitative finite-box transfer",
    "finite q<=N bound promoted directly to infinite-conductor theorem"
  ],
  "canonical_open_gap": "quantitative Besicovitch/rational-spectrum to finite-box transfer",
  "next_node": "RH-Parallelogram-SobolevTailTransfer v3.10",
  "trust": {
    "rh_claim": false,
    "full_eta_M_positive_proved": false
  }
}