{
  "_public_export": {
    "status": "RIEMANN HYPOTHESIS OPEN",
    "record_type": "SANITIZED_HISTORICAL_SOURCE_SNAPSHOT",
    "source_path": "research/local_global_state.json",
    "source_sha256": "4ba6b5027bf8aec5b923ef60f86fd42f9cd3b756285bc8ec2c1a7c5c875b38e0",
    "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": {
      "research/notes/accumulation_spectrum.md": {
        "public_path": "archive/reports/research/notes/accumulation_spectrum.md",
        "status": "EXPORTED"
      }
    }
  },
  "track": "LOCAL_TO_GLOBAL_ZERO_CONFINEMENT_ADELIC_GLUING",
  "date": "2026-09-30",
  "status": "COMPLETED_BOUNDED_AUDIT",
  "rh_status": "OPEN",
  "success_level": 1,
  "success_scope": "Exact conditional theorem stack, normalization, explicit missing comparison proposition, and independent failure tests; no new global confinement bound.",
  "local_rh_mechanism_fixed": true,
  "p_adic_local_mechanism_fixed": true,
  "p_adic_scope": "Kurlberg II: specified Weil-representation vectors, odd residue characteristic. Sauvalle: specified nondegenerate quadratic characters with weak Mellin transforms, including Q_2. Not arbitrary local test functions.",
  "sauvalle_global_gap_identified": true,
  "sauvalle_gap": "The adelic weak Mellin transform equals the actual global L-function times explicit local corrections. For the Q example, off-critical-line zeros are preserved with multiplicity; global confinement is RH-equivalent.",
  "semilocal_stability_scope_fixed": true,
  "semilocal_stability_scope": "Bounded Sonin-space isomorphism and Fourier intertwining; same completed Mellin functions with S-dependent norms. Not a universal real-zero or ground-state stability theorem.",
  "finite_prime_real_zero_property_fixed": true,
  "finite_prime_real_zero_property_scope": "KNOWN CONDITIONAL ON ES: simple lowest eigenvalue and even ground vector of the actual finite Weil matrix.",
  "finite_prime_ES_for_required_cofinal_sequence_proved": false,
  "determinant_convergence_requirement_fixed": true,
  "target_coordinate": "X(z)=xi(1/2+i*z)",
  "sufficient_domain": "Omega={z in C: |Im z|<1/2}",
  "normalization_point": "z_star=i/4",
  "normalization": "F(lambda,N;z)=X(z_star)*exp(i*(z-z_star)*log(lambda))*d(lambda,N;z)/d(lambda,N;z_star)=X(z_star)*vhat(lambda,N;z)/vhat(lambda,N;z_star)",
  "normal_family_bound_found": false,
  "subsequence_limit_identified": false,
  "locally_uniform_convergence_proved": false,
  "preceding_three_flags_scope": "Actual normalized Weil-ground / determinant family, not the separate prolate proxy.",
  "proxy_convergence_known": true,
  "proxy_estimate": "For each 0<r<1/2: sup_{|Im z|<=r}|khat_lambda(z)-X(z)/4| <= C_r*lambda^(-1/2+r)+C_r*lambda^(C_r)*exp(-pi*lambda^2), in the printed h and du/u conventions.",
  "proxy_all_real_zeros_proved": false,
  "new_external_input_found": true,
  "new_external_input_scope": "Explicit CCM Lemmas 7.2-7.3 prolate/Hermite and proxy-transform estimates, not previously quantified in the old audit, were incorporated. Theorem 5.10, CvS Theorem 6.1, and the two Section 8 missing steps were already recorded in research/notes/accumulation_spectrum.md section 4 and are reused, not new inputs. No novelty claim.",
  "new_global_arithmetic_bridge_proved": false,
  "exact_break_proposition": "G*: There exists an ES-admissible sequence (lambda_j,N_j), lambda_j -> infinity, such that for every compact K contained in Omega, sup_K |vhat(lambda_j,N_j;z)/vhat(lambda_j,N_j;z_star) - khat_lambda_j(z)/khat_lambda_j(z_star)| -> 0. ES and the comparison estimate are both unproved obligations.",
  "RH_implies_exact_break_proposition_proved": false,
  "necessary_parameter_condition": "N_j/log(lambda_j) -> infinity; otherwise untouched Dirac-tail zeros force any locally uniform holomorphic limit to vanish identically.",
  "failure_tests": [
    "Actual N=0 family: real zeros and fixed nonreal normalization do not imply local boundedness or normality.",
    "Norm-resolvent convergence need not imply the intended determinant limit without high-spectrum tail control.",
    "Sonin-space stability does not imply actual ground-state or Weil positivity stability.",
    "Local zero-free factors do not transfer the confinement property through an Euler product outside its convergence domain.",
    "Finite simplicity can be lost in an infinite limit.",
    "Raw determinant comparison requires a nonconstant phase correction as well as scalar normalization."
  ],
  "independent_audit_scope": "Core normalization, necessary parameter condition, N=0 counterexample, Hurwitz/Rouche logic, and selected local algebra independently checked; not a second full proof of every cited source.",
  "proof_graph_merged": false,
  "rh_closed": false,
  "next_action": "STOP_THIS_BOUNDED_AUDIT",
  "reopening_condition": "Independent arithmetic control of ES on a cofinal sequence and normalized actual-ground/prolate comparison, or an estimate sufficient for that comparison. Do not substitute more finite zero matching."
}