{
  "_public_export": {
    "status": "RIEMANN HYPOTHESIS OPEN",
    "record_type": "SANITIZED_HISTORICAL_SOURCE_SNAPSHOT",
    "source_path": "research/hierarchical_selection_state.json",
    "source_sha256": "b4f57fe270afe210ad4ed3883bd3dbe4bdd3aa5d3778c5e8aad155c608b51294",
    "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": {}
  },
  "date": "2026-09-30",
  "rh_status": "OPEN",
  "status": "COMPLETED_LIMITED_AUDIT",
  "support_m2_selection_proved": true,
  "support_m3_selection_proved": true,
  "support_fixed_m_selection_pattern_found": true,
  "support_all_fixed_finite_m_selection_proved": true,
  "higher_order_effective_forms_found": true,
  "gamma_hierarchy_proved": true,
  "gamma_small_parameter": "epsilon=Y^-6 after dividing by s_m=a*kappa_Y*16^m*Y^(4*m+4)",
  "support_minimum_asymptotic": "mu_(a,m) ~ a*(m!)^2/(sqrt(pi)*||k||_2^2) * Y^(7/2-2*m)*exp(-2*Y)",
  "exact_schur_pivot_asymptotic": "d_j ~ a*kappa_Y*16^j*((m-j)!)^2*Y^(6*j+4-2*m)",
  "boundary_resolution_scale_fixed": true,
  "boundary_scale": "beta=2*Y, v=beta*(t-a), Omega=pi*N/a, h=Omega/beta",
  "critical_scaled_full_operator_found": true,
  "critical_full_form": "J_h(F)=||F||_L2(R+)^2 + (1/2)||1_{|frequency|>h} Fourier(even_extension(F))||_Plancherel^2",
  "critical_form_scope": "Fixed finite jet-profile space; h_N -> h>2/pi, or h_N -> infinity. Derived from the actual periodic P_N, not a substituted projector.",
  "resolved_full_selector_is_k": true,
  "resolved_full_selector_scope": "Only the lowest direction restricted to P_N R_a span{k,k'',...,k^(2m)}, for each fixed finite m. Not the full finite Weil ground.",
  "sufficient_path_condition": "liminf N/(a*Y)>4/pi^2; in particular N/(a*Y)->infinity",
  "sharp_necessary_transition_constant_identified": false,
  "all_under_resolved_paths_classified": false,
  "prime_rank_one_closed_flow_found": false,
  "prime_finite_update_rank_one_claim_refuted": true,
  "prime_boundary_covector_dictionary_found": true,
  "sonine_exact_dictionary_found": false,
  "sonine_dictionary_scope": "No energy/selection-preserving identification of current two-cutoff realization with the Sonine chain. An exact Gamma/Sonine/Suzuki dictionary and a trivial support/PW dictionary exist separately.",
  "gamma_sonine_rkhs_dictionary_found": true,
  "canonical_one_parameter_filtration_found": false,
  "filtration_scope": "False concerns a replacement of the current two-parameter selection problem, not existence of classical Sonine or Paley-Wiener chains.",
  "actual_full_ground_to_k_comparison_proved": false,
  "uniform_m_to_infinity_control_proved": false,
  "G_star_proved": false,
  "rh_closed": false,
  "restricted_success_level": 4,
  "novelty_claimed": false,
  "proof_graph_merged": false,
  "current_obstruction": "The actual ground of the full finite Weil matrix is not identified with the selected fixed-m radical trial state. Uniform complement/gap control, ES and the faithful G_star comparison remain unproved. Small critical ratios and under-resolved selector behavior are not classified.",
  "next_action": "STOP_AFTER_REQUESTED_THREE_DIRECTIONS; preserve this bounded result without automatic merge or a fourth mechanism.",
  "final_verdict": "HIERARCHICAL SELECTION IDENTIFIED: fixed-finite-m boundary hierarchy selects k, and sufficiently resolved canonical Fourier projection preserves that restricted selection."
}