{
  "format": "FH2024_KAMEXAMPLE_V1",
  "status": "VALIDATED",
  "reason": "All specialized theorem hypotheses and quantitative tests passed",
  "theorem": "Figueras-Haro 2024, Theorem 2.18, d=n=2",
  "epsilon_exact": "1/100",
  "frequency_exact": "(1,(1+sqrt(5))/2)",
  "action_offset": "exact frequency",
  "real_domain": "real slice of U0 intersect {I1>0}",
  "candidate": "results/eps0p01.json.torus",
  "candidate_fingerprint": "fnv1a64:6c443ca42bd2ba62",
  "precision_bits": 256,
  "mpfi_version": "1.5.4",
  "mpfr_version": "4.2.0",
  "modes": 64,
  "grid": 256,
  "refinement_steps": 2,
  "bound_semantics": "Intervals enclose computed quantities; norm bounds are majorants, not two-sided estimates of the actual norms",
  "parameters_exact": {
    "rho_radian": "1/10",
    "rho_final_radian": "1/20",
    "rho_wide_radian": "1/2",
    "domain_margin": "1/10",
    "sigma_factor": "2"
  },
  "bounds": {
    "C_DE": ["3.8667379255149694945820998567816e2","3.8667379255149694945820998567817e2"],
    "C_DEt": ["1.4895542008528885929527323081634e3","1.4895542008528885929527323081635e3"],
    "C_Delta": ["1.7919835902930283431048196093813e4","1.7919835902930283431048196093814e4"],
    "C_E": ["1.4285242338274801220026908637304e1","1.4285242338274801220026908637305e1"],
    "C_E_L": ["1.4285149733165331320206954873986e1","1.4285149733165331320206954873987e1"],
    "C_E_N": ["4.3870838207399285026752823010290e-1","4.3870838207399285026752823010291e-1"],
    "C_Et": ["2.8570484676549602440053817274608e1","2.8570484676549602440053817274609e1"],
    "C_Et_L": ["2.8570299466330662640413909747973e1","2.8570299466330662640413909747974e1"],
    "C_Et_N": ["8.7741676414798570053505646020581e-1","8.7741676414798570053505646020582e-1"],
    "C_LieB": ["1.5397203561208435928556890480581e0","1.5397203561208435928556890480582e0"],
    "C_LieG": ["4.0813100587637655336329974913676e2","4.0813100587637655336329974913677e2"],
    "C_LieK": ["1.8454313533716275045815310023071e0","1.8454313533716275045815310023072e0"],
    "C_LieL": ["1.4285149734297259136149736495584e1","1.4285149734297259136149736495585e1"],
    "C_LieLt": ["1.4285149737528157395611104157634e1","1.4285149737528157395611104157635e1"],
    "C_LieN": ["2.2872552598550688971306598779506e1","2.2872552598550688971306598779507e1"],
    "C_LieXiL": ["1.6772264426080360900892185110794e1","1.6772264426080360900892185110795e1"],
    "C_OmegaL": ["6.5095040355248169753702427543324e-1","6.5095040355248169753702427543325e-1"],
    "C_OmegaN": ["2.4557839829459721316010930698079e-3","2.4557839829459721316010930698080e-3"],
    "C_T": ["1.9928751720703539221180824632736e-1","1.9928751720703539221180824632737e-1"],
    "C_barDK_common": ["1.3931161788473468937820033991874e2","1.3931161788473468937820033991875e2"],
    "C_barE": ["1.8592145981715800783120847251296e3","1.8592145981715800783120847251297e3"],
    "C_barK": ["3.4720812946807976376102688738471e1","3.4720812946807976376102688738472e1"],
    "C_deltaB": ["8.4084354954595213878623750267924e0","8.4084354954595213878623750267925e0"],
    "C_deltaDK_common": ["7.8011412669779267921890956328566e1","7.8011412669779267921890956328567e1"],
    "C_deltaG": ["2.2288094217669651833964453090039e3","2.2288094217669651833964453090040e3"],
    "C_deltaInvT": ["7.0743212286975602409519969282270e5","7.0743212286975602409519969282271e5"],
    "C_deltaK": ["1.9502830561944800714257990262758e1","1.9502830561944800714257990262759e1"],
    "C_deltaN_common": ["1.2490734592013056916556555954379e2","1.2490734592013056916556555954380e2"],
    "C_deltaT": ["1.1348103528480501703181620697383e2","1.1348103528480501703181620697384e2"],
    "C_dist": ["1.9502830561944800714257990262758e2","1.9502830561944800714257990262759e2"],
    "C_grid": ["7.1421197077820067609631038299972e-21","7.1421197077820067609631038299973e-21"],
    "C_meanXiN_L": ["7.8955201007624792528522910143356e1","7.8955201007624792528522910143357e1"],
    "C_meanXiN_N": ["1.0669338836559510328118368716848e-1","1.0669338836559510328118368716849e-1"],
    "C_newE": ["2.0988089068623662929891005393323e3","2.0988089068623662929891005393324e3"],
    "C_redLL_L": ["1.4534029853465094761425688082552e1","1.4534029853465094761425688082553e1"],
    "C_redLL_N": ["3.8493008898005902411491771945659e-1","3.8493008898005902411491771945660e-1"],
    "C_redLN": ["1.6012936694509492424776937746231e0","1.6012936694509492424776937746232e0"],
    "C_redLN_L": ["1.5397203558247184357944447117960e0","1.5397203558247184357944447117961e0"],
    "C_redLN_N": ["6.1573313626230806683249062827103e-2","6.1573313626230806683249062827104e-2"],
    "C_redNL_L": ["4.0813100579788317127852057011019e2","4.0813100579788317127852057011020e2"],
    "C_redNL_N": ["1.4534029854242652326201680999173e1","1.4534029854242652326201680999174e1"],
    "C_redNN": ["1.4534111106740584365549126195739e1","1.4534111106740584365549126195740e1"],
    "C_redNN_L": ["1.4534029853465094761425688082552e1","1.4534029853465094761425688082553e1"],
    "C_redNN_N": ["3.8493008898005902411491771945659e-1","3.8493008898005902411491771945660e-1"],
    "C_sym": ["6.5095040355248169753702427543324e-1","6.5095040355248169753702427543325e-1"],
    "C_xiL": ["1.3647390370807429700602416196388e0","1.3647390370807429700602416196389e0"],
    "C_xiL_L": ["1.3616894608312014515663322804509e0","1.3616894608312014515663322804510e0"],
    "C_xiL_N": ["3.0495762495415184939093391878474e-3","3.0495762495415184939093391878475e-3"],
    "C_xiN": ["7.9143263196434447843996221864954e1","7.9143263196434447843996221864955e1"],
    "C_xiN_L": ["7.8955201007624792528522910143356e1","7.8955201007624792528522910143357e1"],
    "C_xiN_N": ["1.8806218880965531547331172159763e-1","1.8806218880965531547331172159764e-1"],
    "M_E_wide": ["3.1318614953972089662010196933726e-1","3.1318614953972089662010196933727e-1"],
    "M_T_wide": ["1.3422402503125397684126881249893e-1","1.3422402503125397684126881249894e-1"],
    "Q_barEtaN": ["2.6016115920792470477150264395203e5","2.6016115920792470477150264395204e5"],
    "Q_eta": ["1.5609671917682472722248406609644e6","1.5609671917682472722248406609645e6"],
    "Q_etaL": ["2.6467010132591021686914421847268e5","2.6467010132591021686914421847269e5"],
    "Q_etaL1": ["1.2675275311634708976913654018120e2","1.2675275311634708976913654018121e2"],
    "Q_etaL2": ["2.2263070567087443290632647753921e3","2.2263070567087443290632647753922e3"],
    "Q_etaL3": ["2.8711736378658510490785360752345e2","2.8711736378658510490785360752346e2"],
    "Q_etaL4": ["0","0"],
    "Q_etaL5": ["2.6215665014970868811578823520071e5","2.6215665014970868811578823520072e5"],
    "Q_etaN": ["7.8048359588412363611242033048222e5","7.8048359588412363611242033048223e5"],
    "U0_radius_0": ["2.4538675326681857152400951919590e-1","2.4538675326681857152400951919591e-1"],
    "U0_radius_1": ["2.3736662524187946287976985358254e-1","2.3736662524187946287976985358255e-1"],
    "U0_radius_2": ["1.1319901893230200231763764540556e0","1.1319901893230200231763764540557e0"],
    "U0_radius_3": ["1.7454313533715720009552527513054e0","1.7454313533715720009552527513055e0"],
    "U_radius_0": ["3.4538675326681857152400951919590e-1","3.4538675326681857152400951919591e-1"],
    "U_radius_1": ["3.3736662524187946287976985358254e-1","3.3736662524187946287976985358255e-1"],
    "U_radius_2": ["1.2319901893230200231763764540556e0","1.2319901893230200231763764540557e0"],
    "U_radius_3": ["1.8454313533715720009552527513054e0","1.8454313533715720009552527513055e0"],
    "a": ["2.0000000000000000000000000000000e0","2.0000000000000000000000000000000e0"],
    "average_T_00": ["2.5386448196200821973661981530581e-2","2.5386448196200821973661981530582e-2"],
    "average_T_01": ["-5.2195447822991306220383736879824e-5","-5.2195447822991306220383736879823e-5"],
    "average_T_10": ["-5.2195447822991306220383736879824e-5","-5.2195447822991306220383736879823e-5"],
    "average_T_11": ["2.5383008583032057881969995749052e-2","2.5383008583032057881969995749053e-2"],
    "b_B": ["3.0710800393519389566942604742202e-2","3.0710800393519389566942604742203e-2"],
    "b_DK": ["6.8043144163877140647436396990168e0","6.8043144163877140647436396990169e0"],
    "b_DKt": ["7.1425748665822473593011714917257e0","7.1425748665822473593011714917258e0"],
    "b_Du": ["8.2940273719549655845577635415424e-2","8.2940273719549655845577635415425e-2"],
    "b_E": ["1.1482539868878989811132564638811e-19","1.1482539868878989811132564638812e-19"],
    "b_N": ["2.0896594185642946465796953464495e-1","2.0896594185642946465796953464496e-1"],
    "b_Nt": ["2.1935419102337578363565891595347e-1","2.1935419102337578363565891595348e-1"],
    "b_etaL": ["2.5187432438316102544809690746301e-20","2.5187432438316102544809690746302e-20"],
    "b_etaN": ["8.2014900671983686737190754952526e-19","8.2014900671983686737190754952527e-19"],
    "b_invT": ["3.9477600503812396264261455071678e1","3.9477600503812396264261455071679e1"],
    "c_D2X": ["6.0293294210950736736322485898600e-2","6.0293294210950736736322485898601e-2"],
    "c_DTh": ["6.0293294210950736736322485898600e-2","6.0293294210950736736322485898601e-2"],
    "c_DX": ["1.0000000000000000000000000000000e0","1.0000000000000000000000000000000e0"],
    "c_DXt": ["1.0000000000000000000000000000000e0","1.0000000000000000000000000000000e0"],
    "c_R": ["8.1368800444060212192128034429155e-2","8.1368800444060212192128034429156e-2"],
    "c_R1": ["3.2547520177624084876851213771662e-1","3.2547520177624084876851213771663e-1"],
    "c_Th": ["1.0354478536476992750810184283826e0","1.0354478536476992750810184283827e0"],
    "c_X": ["1.8454313533715720009552527513054e0","1.8454313533715720009552527513055e0"],
    "chi": ["1.3878286323427095104488458739808e-8","1.3878286323427095104488458739809e-8"],
    "delta": ["1.3262911924324611314073646947709e-3","1.3262911924324611314073646947710e-3"],
    "distance_B": ["1.2776614853691324366749824471583e-7","1.2776614853691324366749824471584e-7"],
    "distance_DK": ["1.1853831481639670689846864015226e-6","1.1853831481639670689846864015227e-6"],
    "distance_DKt": ["1.1853831481639670689846864015226e-6","1.1853831481639670689846864015227e-6"],
    "distance_K": ["3.7523980741938037759712317188263e-10","3.7523980741938037759712317188264e-10"],
    "distance_N": ["1.8979666931857518455326110101427e-6","1.8979666931857518455326110101428e-6"],
    "distance_Nt": ["1.8979666931857518455326110101427e-6","1.8979666931857518455326110101428e-6"],
    "distance_invT": ["1.0749428682561537124105085940175e-2","1.0749428682561537124105085940176e-2"],
    "domain_distance": ["9.9999999999999999999999999999999e-2","1.0000000000000000000000000000000e-1"],
    "final_angular_derivative_bound": ["8.2940462379137143973493568854501e-2","8.2940462379137143973493568854502e-2"],
    "final_regular_action_lower": ["9.6800981030174016940424316834726e-1","9.6800981030174016940424316834727e-1"],
    "gamma": ["1.5915494309189533576888376337251e-1","1.5915494309189533576888376337252e-1"],
    "gap_B": ["3.0710800393519389566942604742202e-2","3.0710800393519389566942604742203e-2"],
    "gap_DK": ["7.4808353167767806538587032844346e0","7.4808353167767806538587032844347e0"],
    "gap_DKt": ["7.1425748665822473593011714917257e0","7.1425748665822473593011714917258e0"],
    "gap_N": ["2.2974244019032210261334829726199e-1","2.2974244019032210261334829726200e-1"],
    "gap_Nt": ["2.1935419102337578363565891595347e-1","2.1935419102337578363565891595348e-1"],
    "gap_invT": ["3.9477600503812396264261455071678e1","3.9477600503812396264261455071679e1"],
    "gram_defect_rho": ["1.7519909653902552793335134192921e-1","1.7519909653902552793335134192922e-1"],
    "gram_defect_wide": ["4.4241077857827670721311393991280e-1","4.4241077857827670721311393991281e-1"],
    "kappa": ["8.6654198515342662998685518023674e-2","8.6654198515342662998685518023675e-2"],
    "nu": ["1.9069651704780711189153581461366e-12","1.9069651704780711189153581461367e-12"],
    "regular_action_lower": ["9.6800981067697997682362354594438e-1","9.6800981067697997682362354594439e-1"],
    "residual_finite_part": ["1.1258858571795789482991544301076e-19","1.1258858571795789482991544301077e-19"],
    "residual_interpolation_error": ["2.2368129708320032814102033773471e-21","2.2368129708320032814102033773472e-21"],
    "rho": ["1.5915494309189533576888376337251e-2","1.5915494309189533576888376337252e-2"],
    "rho_final": ["7.9577471545947667884441881686257e-3","7.9577471545947667884441881686258e-3"],
    "rho_final_radian": ["4.9999999999999999999999999999999e-2","5.0000000000000000000000000000001e-2"],
    "rho_radian": ["9.9999999999999999999999999999999e-2","1.0000000000000000000000000000001e-1"],
    "rho_wide_radian": ["5.0000000000000000000000000000000e-1","5.0000000000000000000000000000000e-1"],
    "sigma_B": ["6.1421600787038779133885209484404e-2","6.1421600787038779133885209484405e-2"],
    "sigma_L": ["1.4285149733164494718602342983451e1","1.4285149733164494718602342983452e1"],
    "sigma_N": ["4.3870838204675156727131783190695e-1","4.3870838204675156727131783190696e-1"],
    "sigma_invT": ["7.8955201007624792528522910143356e1","7.8955201007624792528522910143357e1"],
    "tau": ["1.0000000000000000000000000000000e0","1.0000000000000000000000000000000e0"],
    "test_domain": ["4.3327102847488881878256845501902e-2","4.3327102847488881878256845501903e-2"],
    "test_geometry": ["8.6902895128872358181036525760847e-2","8.6902895128872358181036525760848e-2"],
    "test_phase": ["1.8940239113364738369706928241323e-8","1.8940239113364738369706928241324e-8"],
    "test_sym": ["1.9069651704780711189153581461366e-12","1.9069651704780711189153581461367e-12"],
    "theorem_C": ["6.2617886029759193723304108399515e6","6.2617886029759193723304108399516e6"],
    "theorem_condition": ["8.6902895128872358181036525760847e-2","8.6902895128872358181036525760848e-2"],
    "torsion_average_alias_error_per_entry": ["1.3810091808767263037661657788973e-56","1.3810091808767263037661657788974e-56"],
    "weighted_error": ["3.8853821982101605932935022503417e-15","3.8853821982101605932935022503418e-15"]
  }
}
