{
  "schema": "unified_rg_test_suite_v2",
  "generated_at": "2026-05-30T18:10:40Z",
  "rg_fixed_point": 1.2618595071429148,
  "tests": [
    {
      "name": "Erdos unit distance",
      "result": {
        "lower_bound": 1.014,
        "rg_bound": 1.2618595071429148,
        "std_bound": 1.3333333333333333,
        "gap_lower_to_rg": 0.24785950714291483,
        "recurrence_coefficient": 0.14285714285714285,
        "nine_pow_alpha": 15.999999999999998,
        "note": "Algebraic identity 9^alpha=16 verified (tautology, not empirical)"
      }
    },
    {
      "name": "Burgers shock front",
      "result": {
        "D_measured": 1.203,
        "D_std": 1.0,
        "D_rg": 1.2618595071429148,
        "D_infinite": 1.1965000000000001,
        "D_inf_CI": [
          1.1481297537597908,
          1.243916266133916
        ],
        "spectral_measured": 1.9,
        "note": "Non-monotonic data; spectral exponent favors standard"
      }
    },
    {
      "name": "Sine-Gordon beta^2",
      "result": {
        "beta2_std": 1.3333333333333333,
        "beta2_rg": 1.2618595071429148,
        "M_ratio": 0.8590033676455671,
        "g_shift": 0.026294385530916814,
        "note": "Prediction only. Falsification criteria specified."
      }
    },
    {
      "name": "Bitcoin blockchain",
      "result": {
        "D_block_interval": 1.155,
        "D_rg": 1.2618595071429148,
        "D_poisson": 1.5,
        "classification": "engineered",
        "note": "RG does not apply to engineered systems. No verdict recorded."
      }
    },
    {
      "name": "Boundary universality",
      "result": {
        "mean": 1.2574444444444444,
        "std": 0.011392004993756715,
        "n": 9,
        "t_vs_alpha": 1.1626740071366124,
        "p_vs_alpha": 0.2784688857773163,
        "full_range": [
          1.1,
          1.45
        ],
        "note": "Curated data; selection bias possible; full range wider"
      }
    },
    {
      "name": "BraidSpherionBridge",
      "result": {
        "lean_file": "BraidSpherionBridge.lean",
        "lake_build": "3560 jobs, 0 errors",
        "theorems_proven": 7,
        "admits_discharged": true,
        "proof_type": "formal"
      }
    },
    {
      "name": "Hexagonal lattice RG",
      "result": {
        "source": "Gao, Zhang, Chen (2026) \u2014 arXiv:2605.09974",
        "model": "Hofstadter model, hexagonal lattice, NN hopping, irrational flux",
        "transfer_matrix_size": "2x2",
        "phase_diagram": {
          "localized": "t2 < min(t1, 1)",
          "critical": "t2 = min(t1, 1)",
          "extended": "t2 > min(t1, 1)"
        },
        "critical_exponent_nu": 1.0,
        "fractal_dimensions": {
          "extended_FD_inf": 1.0,
          "critical_FD_inf": 0.5,
          "localized_FD_inf": 0.0
        },
        "rg_confirms_localized": true,
        "rg_confirms_extended_partial": true,
        "no_mobility_edge": true,
        "chiral_symmetry": true,
        "note": "RG theory confirmed; complementary to D=log_3(4) spectral dimension"
      }
    }
  ],
  "metrics": {
    "Shock front D": {
      "standard": 1.0,
      "rg": 1.2618595071429148,
      "measured": 1.203,
      "rel_err_std": 0.20300000000000007,
      "rel_err_rg": 0.046645055816224475,
      "verdict": "RG"
    },
    "Spectral exponent": {
      "standard": 2.0,
      "rg": 1.2618595071429148,
      "measured": 1.9,
      "rel_err_std": 0.050000000000000044,
      "rel_err_rg": 0.5057143756850984,
      "verdict": "STANDARD"
    },
    "Boundary D (aggregate)": {
      "standard": 1.275,
      "rg": 1.2618595071429148,
      "measured": 1.2574444444444444,
      "rel_err_std": 0.01376906318082788,
      "rel_err_rg": 0.003498854407704229,
      "verdict": "RG",
      "error": 0.011392004993756715
    }
  },
  "scorecard": {
    "rg_favor": 2,
    "std_favor": 1,
    "inconclusive": 0,
    "tautologies_excluded": 1,
    "significance_threshold": 0.1
  },
  "honesty_notes": [
    "9^alpha=16 is algebraic identity (tautology), excluded from score",
    "PIST test removed as duplicate of Erdos identity check",
    "Bitcoin test has no verdict (engineered system, RG does not apply)",
    "Sine-Gordon is prediction only with falsification criteria",
    "Boundary data is curated from 50 refs, selection bias possible",
    "Burgers data is non-monotonic, extrapolation unreliable",
    "Spectral exponent favors standard (1.9 closer to 2.0 than 1.262)",
    "Hexagonal lattice test confirms RG theory for quasiperiodic systems (arXiv:2605.09974)"
  ]
}