{
  "_public_export": {
    "status": "RIEMANN HYPOTHESIS OPEN",
    "record_type": "SANITIZED_HISTORICAL_SOURCE_SNAPSHOT",
    "source_path": "research/rate_history_state.json",
    "source_sha256": "6bd023a13702cb75a2b31969e37d06e3b96d879826c712e508c642315f5b2efd",
    "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",
  "radical_finite_splitting_fixed": true,
  "distinct_decay_rates_found": false,
  "distinct_decay_rates_scope": "Distinct leading asymptotics are proved for support-only actual Weil defects. The leading asymptotics of the full canonical support-plus-Fourier system are not identified; only unconditional upper bounds are proved.",
  "support_only_distinct_asymptotics_proved": true,
  "support_only_effective_boundary_form": "After diagonal endpoint rescaling, the leading matrix is rank one, proportional to 1*1^T. By itself this does not identify a selector for the full canonical system or all m; the restricted support-only R1 selection is recorded separately.",
  "support_only_boundary_cancellation_example_proved": true,
  "support_only_cancellation_gain": "For g_a=k-k(a)/k''(a)*k'', Q(R_a g_a)/Q(R_a k) ~ 2/(pi^2*lambda^4), and g_a -> k in L2.",
  "full_projection_recognition_upper_bound_proved": true,
  "full_projection_bound": "For fixed m, a=log(lambda)>=1 and Omega=pi(N+1)/a>=1: |Q(P_N R_a f_i,P_N R_a f_j)| <= C_m [a(1+Omega)^(4m+8) exp(a-pi*Omega/2) + lambda^(8m+24) exp(-2*pi*lambda^2)].",
  "recognition_vanishes_on_both_tested_cofinal_paths_proved": true,
  "recognition_vanishes_on_every_N_over_a_to_infinity_path_proved": false,
  "rate_selected_direction_found": false,
  "rate_selected_direction_scope": "False refers to the requested full support-plus-Fourier canonical system. A restricted support-only R1 result is proved separately below.",
  "support_only_R1_lowest_direction_selection_proved": true,
  "support_only_R1_selected_direction_is_k": true,
  "support_only_R1_gap_asymptotic": "s_a=(a/Y)*[k''(a)]^2; gap/s_a -> (G_infinity^-1)_(1,1)>0 in raw basis (k,k''), indices 0,1.",
  "rate_selected_direction_is_k": false,
  "actual_ground_tracks_selected_direction": false,
  "path_independent_limit_found": false,
  "path_dependence_found": false,
  "same_simple_finite_endpoint_is_history_independent": true,
  "prime_power_derivative_corner_fixed": true,
  "fixed_m_gram_convergence_proved": true,
  "canonical_probability_measure_found": false,
  "probability_scope": "No canonical arithmetic state-selecting probability law without an extra input vector or scale. Standard projection-valued and finite counting spectral measures exist but do not solve selection.",
  "G_star_proved": false,
  "rh_closed": false,
  "finite_endpoints": 11,
  "restricted_generalized_eigenproblems": 33,
  "m_values": [
    1,
    2,
    3
  ],
  "cofinal_paths": [
    "N=max(4,ceil((log lambda)^2))",
    "N=max(4,ceil((log lambda)^3))"
  ],
  "numerical_scope": "448-bit Arb matrix midpoints; 100-digit non-interval eigenscoring; high-precision quadrature resolution comparison; floating-point prolate comparison. Diagnostics are not asymptotic proofs or interval certificates.",
  "full_track_success_level": 1,
  "partial_success": "Support-only component has distinct leading asymptotics and a proven lowest-direction selection toward k within R1, with its restricted gap asymptotic. Full canonical recognition has a rigorous upper bound, but no full leading rate or selector.",
  "novelty_claimed": false,
  "current_obstruction": "Full actual whitened next-order splitting matrix, uniform remainder and unique minimal direction are not identified. Restricted energy recognition does not control the full ground gap or the transform comparison G*.",
  "next_action": "STOP_AFTER_THREE_MECHANISMS; do not invent another order, path action, metric, or probability law.",
  "proof_graph_merged": false,
  "final_verdict": "NO FINITE-SCALE SELECTION PRINCIPLE IDENTIFIED.",
  "final_verdict_scope": "Full canonical support-plus-Fourier system, not the proved restricted support-only R1 selection."
}