{
  "node": "RH-Parallelogram-RamanujanTail v3.8",
  "status": {
    "beta_zero_axis": "CLOSED_EXACT",
    "full_deterministic_model": "o(N^5)",
    "fixed_eta_M": "OPEN",
    "actual_prime_deviation": "OPEN"
  },
  "exact_spectrum": {
    "phase": "h alpha + d beta",
    "surviving_condition": "beta != 0",
    "alpha_zero_axis": "second pairing channel"
  },
  "weight_multiplier": {
    "exact_formula": "sum_{n<m} w(n)w(m)e((m-n)beta)E_{n-1}(alpha)",
    "bound": "N^3 M_N(alpha) M_N(beta)"
  },
  "candidate_gates": {
    "PRT_eta": "beta-rational coefficient tail << N^(1-eta+o(1))",
    "two_dimensional": "sum |Khat| M_N(alpha)M_N(beta) << N^(2-eta+o(1))",
    "sobolev": "quantitative control of sum |Khat|^2/|1-e(beta)|^2"
  },
  "automatic_reject": [
    "zero total mean treated as fixed eta",
    "o(N^5) treated as fixed eta",
    "finite-q Sobolev numerics promoted as uniform theorem",
    "beta=0 modes reintroduced after pair-square subtraction",
    "adding-fractions theorem cited without translating to the even four-fraction beta-tail"
  ],
  "next_node": "RH-Parallelogram-SobolevConductor v3.9",
  "trust": {
    "rh_claim": false,
    "full_eta_M_positive_proved": false
  }
}