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