{
  "_public_export": {
    "status": "RIEMANN HYPOTHESIS OPEN",
    "record_type": "SANITIZED_HISTORICAL_SOURCE_SNAPSHOT",
    "source_path": "research/common_parent_state.json",
    "source_sha256": "b0e3575ae929b73c9da5afd9d37040677e37f8d67e80ea737bd27667fd9b8080",
    "exported_on": "2026-09-30",
    "public_credit": "@ykbballer91",
    "license": "CC-BY-4.0",
    "ai_assisted": true,
    "original_fields_are_historical": true,
    "checks_rerun_in_public_export": false,
    "scope": "Historical claims and verification records retain their original scope. Priority 1 cyclicity is even L2 only; full-ground capture and RH remain open.",
    "references": {}
  },
  "rh_status": "OPEN",
  "date": "2026-09-30",
  "status": "COMPLETED_LIMITED_AUDIT_STOPPED_AFTER_THREE_MECHANISMS",
  "A_exact_variational_problem_fixed": true,
  "B_exact_variational_problem_fixed": true,
  "B_scope": "The prescribed proxy is the arithmetic image of a mean-zero combination of prolate modes 0 and 4; it is not the minimizer or a stationary point of the ordinary full even mean-zero concentration problem.",
  "common_parent_found": false,
  "proxy_rayleigh_excess_bound_found": false,
  "ground_gap_bound_found": false,
  "excess_over_gap_goes_to_zero": false,
  "common_limit_functional_found": false,
  "common_limit_equation_found": false,
  "G_star_proved": false,
  "rh_closed": false,
  "finite_step31_scoring_performed": true,
  "finite_diagnostic_cases": 18,
  "high_precision_matrix_cases": 9,
  "numerical_scope": "288-bit Arb matrix midpoints and 75-digit eigenscoring of rounded floating-point trial coefficients; eigenvalues, gaps, scores, and the exact prolate proxy are not interval-certified.",
  "proxy_error_interval_certified": false,
  "known_radical_relation_verified": true,
  "known_radical_relation_source": "Connes-Consani, Spectral triples and zeta-cycles, Section 3, pp.118-120",
  "radical_relation_is_new": false,
  "abstract_gap_lemma_proved": true,
  "gap_lemma_is_new": false,
  "gap_ratio_alone_implies_G_star": false,
  "G_star_sufficient_rate": "For every 0<r<1/2, sqrt((lambda^(2r)-1)/r) * (||P_N k_lambda||_2 sqrt(excess/gap) + ||(I-P_N)k_lambda||_2) -> 0, together with the actual ES condition and known proxy convergence.",
  "simple_leakage_parent_on_full_source": "FALSE_BY_KERNEL_TEST",
  "ordinary_concentration_minimizer_identification": "FALSE_FOR_PRESCRIBED_MODE_0_4_PROXY",
  "global_Weil_unique_minimizer_candidate": "FAILS_INFINITE_DIMENSIONAL_RADICAL_OR_NONMINIMAL_ZERO_ENERGY",
  "success_level": 1,
  "current_obstruction": "No RH-independent quantitative control of the actual proxy energy excess relative to the full Weil ground gap, with projection and growing-window Fourier losses; the known arithmetic radical relation does not select a unique ground state.",
  "recommended_next_action": "STOP_THIS_LIMITED_TRACK; no fourth renamed mechanism and no automatic proof-graph merge.",
  "final_verdict": "NO COMMON PARENT IDENTIFIED.",
  "proof_graph_merged": false
}