{
  "_public_export": {
    "status": "RIEMANN HYPOTHESIS OPEN",
    "record_type": "SANITIZED_HISTORICAL_SOURCE_SNAPSHOT",
    "source_path": "research/scale_flow/state.json",
    "source_sha256": "4d91bbc02e05deada537264394dab635e134b85293de463d295c0583782a46e2",
    "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/continuous_scale_flow_frobenius.md": {
        "public_path": "archive/reports/research/continuous_scale_flow_frobenius.md",
        "status": "EXPORTED"
      }
    }
  },
  "track": "CONTINUOUS_SCALE_FLOW_FROBENIUS_SECTION",
  "rh_status": "OPEN",
  "status": "BOUNDED_REVIEW_COMPLETE_NO_NEW_METRIC",
  "independent_of": [
    "PHASE_III",
    "PHASE_IV"
  ],
  "active_candidates": [],
  "major_candidates_reviewed": 3,
  "failed_candidates": [
    {
      "id": "SF1",
      "name": "Local Frobenius Haar metric as the full zero metric",
      "reason": "Full local Haar space has infinitely many orthogonal modes in a bounded frequency band; no faithful arithmetic global transfer"
    },
    {
      "id": "SF2",
      "name": "Invariant pairing on the full arithmetic zero quotient",
      "reason": "Exact growth identity exists; positivity of the actual Weil form is RH-equivalent and bare Hilbert completion loses arithmetic quotient"
    },
    {
      "id": "SF3",
      "name": "Stroboscopic or conservation-based metric propagation",
      "reason": "Conditional averaging theorem is valid but no same-space arithmetic unitary return established; symplectic/reversal conservation allows nonzero growth"
    }
  ],
  "additional_falsification": {
    "literal_no_transverse_growth": "FALSE_ON_SPECIFIED_ARITHMETIC_PADIC_NORMAL_MODEL",
    "normal_growth_forward_log_time": 1,
    "normal_model_equals_smooth_ambient_chart": false,
    "normal_model_map_is_topological_embedding": false,
    "normal_growth_identified_with_zero_growth": false,
    "is_counterexample_to_RH": false
  },
  "levels": {
    "1": {
      "achieved": true,
      "scope": "Known exact prime-orbit Frobenius deck monodromy, with inverse positive-time return"
    },
    "2": {
      "achieved": "SPECTRAL_CHARACTER_ONLY",
      "geometric_normal_zero_character_identification": false
    },
    "3": {
      "achieved": "SPECTRAL_CHARACTER_ONLY",
      "identity": "growth = Re(rho)-1/2 on every nonzero arithmetic zero character"
    },
    "4": {
      "achieved": false,
      "reason": "No independent arithmetic invariant positive metric retaining all zero characters"
    },
    "5": {
      "achieved": false
    }
  },
  "component_facts": {
    "exact_mapping_torus": true,
    "prime_power_iteration": true,
    "local_haar_positive_unitary": true,
    "local_haar_compact_resolvent": false,
    "exact_arithmetic_zero_character_growth": true,
    "padic_half_density_fixed_point_weight": true,
    "same_space_unitary_return_sufficient_lemma": true,
    "new_arithmetic_unitary_return": false,
    "new_arithmetic_positive_metric": false,
    "full_zero_hilbert_identification": false
  },
  "current_minimal_gap": "Construct from arithmetic a common invariant positive norm on a faithful completion of the full-zero representation, with every zero character nonzero and bounded; multiplicity/trace identification is a further obligation for a full determinant model",
  "gap_reduced_by_new_arithmetic_bridge": false,
  "strategy_review_completed": true,
  "next_action": "End this round. Reopen only with an independently arithmetic common-space metric or return theorem retaining all zero characters, not another orbit-log recoding or geometric no-transverse-growth claim.",
  "known_programs_compared": [
    "Berry-Keating",
    "Connes spectral realization",
    "Connes-Consani scaling Hamiltonian",
    "Scaling site/adele class space",
    "Deninger flow program",
    "Dynamical zeta functions",
    "Selberg trace formula",
    "Gutzwiller periodic-orbit analogy"
  ],
  "source_audits": [
    "notes/frobenius_mapping_torus.md",
    "notes/spectral_growth.md",
    "notes/program_comparison.md",
    "notes/padic_transverse_audit.md"
  ],
  "independent_audit": "notes/independent_audit.md",
  "experiment": "flow_checks.json",
  "main_log": "research/continuous_scale_flow_frobenius.md",
  "phase3_modified": false,
  "phase4_modified_by_this_track": false,
  "canonical_state_or_graph_modified": false,
  "graph_merges": [],
  "novelty_claimed": false,
  "proof_of_RH": false,
  "refutation_of_RH": false
}