{ "Q": [ [ -2, 2 ], [ 1, -1 ] ], "six_rate_time_checks": [ { "t": 0.0, "nu": 2, "absolute_entry_error": 0.0, "analytic": [ [ 1.0, 0.0 ], [ 0.0, 1.0 ] ], "R": [ [ "0", "1" ], [ "1/2", "1/2" ] ], "matrix": [ [ 1.0, 0.0 ], [ 0.0, 1.0 ] ], "trace": [ { "k": 0, "poisson_weight": 1.0, "R_power": [ [ "1", "0" ], [ "0", "1" ] ] }, { "k": 1, "poisson_weight": 0.0, "R_power": [ [ "0", "1" ], [ "1/2", "1/2" ] ] }, { "k": 2, "poisson_weight": 0.0, "R_power": [ [ "1/2", "1/2" ], [ "1/4", "3/4" ] ] }, { "k": 3, "poisson_weight": 0.0, "R_power": [ [ "1/4", "3/4" ], [ "3/8", "5/8" ] ] }, { "k": 4, "poisson_weight": 0.0, "R_power": [ [ "3/8", "5/8" ], [ "5/16", "11/16" ] ] }, { "k": 5, "poisson_weight": 0.0, "R_power": [ [ "5/16", "11/16" ], [ "11/32", "21/32" ] ] }, { "k": 6, "poisson_weight": 0.0, "R_power": [ [ "11/32", "21/32" ], [ "21/64", "43/64" ] ] }, { "k": 7, "poisson_weight": 0.0, "R_power": [ [ "21/64", "43/64" ], [ "43/128", "85/128" ] ] }, { "k": 8, "poisson_weight": 0.0, "R_power": [ [ "43/128", "85/128" ], [ "85/256", "171/256" ] ] }, { "k": 9, "poisson_weight": 0.0, "R_power": [ [ "85/256", "171/256" ], [ "171/512", "341/512" ] ] }, { "k": 10, "poisson_weight": 0.0, "R_power": [ [ "171/512", "341/512" ], [ "341/1024", "683/1024" ] ] }, { "k": 11, "poisson_weight": 0.0, "R_power": [ [ "341/1024", "683/1024" ], [ "683/2048", "1365/2048" ] ] }, { "k": 12, "poisson_weight": 0.0, "R_power": [ [ "683/2048", "1365/2048" ], [ "1365/4096", "2731/4096" ] ] }, { "k": 13, "poisson_weight": 0.0, "R_power": [ [ "1365/4096", "2731/4096" ], [ "2731/8192", "5461/8192" ] ] }, { "k": 14, "poisson_weight": 0.0, "R_power": [ [ "2731/8192", "5461/8192" ], [ "5461/16384", "10923/16384" ] ] }, { "k": 15, "poisson_weight": 0.0, "R_power": [ [ "5461/16384", "10923/16384" ], [ "10923/32768", "21845/32768" ] ] }, { "k": 16, "poisson_weight": 0.0, "R_power": [ [ "10923/32768", "21845/32768" ], [ "21845/65536", "43691/65536" ] ] }, { "k": 17, "poisson_weight": 0.0, "R_power": [ [ "21845/65536", "43691/65536" ], [ "43691/131072", "87381/131072" ] ] }, { "k": 18, "poisson_weight": 0.0, "R_power": [ [ "43691/131072", "87381/131072" ], [ "87381/262144", "174763/262144" ] ] }, { "k": 19, "poisson_weight": 0.0, "R_power": [ [ "87381/262144", "174763/262144" ], [ "174763/524288", "349525/524288" ] ] } ], "rowmass": 1.0, "omitted_poisson_mass_float": 0.0, "analytic_poisson_tail_upper": 0.0 }, { "t": 0.0, "nu": 3, "absolute_entry_error": 0.0, "analytic": [ [ 1.0, 0.0 ], [ 0.0, 1.0 ] ], "R": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ], "matrix": [ [ 1.0, 0.0 ], [ 0.0, 1.0 ] ], "trace": [ { "k": 0, "poisson_weight": 1.0, "R_power": [ [ "1", "0" ], [ "0", "1" ] ] }, { "k": 1, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 2, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 3, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 4, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 5, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 6, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 7, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 8, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 9, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 10, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 11, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 12, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 13, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 14, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 15, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 16, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 17, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 18, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 19, "poisson_weight": 0.0, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] } ], "rowmass": 1.0, "omitted_poisson_mass_float": 0.0, "analytic_poisson_tail_upper": 0.0 }, { "t": 0.5, "nu": 2, "absolute_entry_error": 1.1102230246251565e-16, "analytic": [ [ 0.48208677343228656, 0.5179132265677134 ], [ 0.2589566132838567, 0.7410433867161432 ] ], "R": [ [ "0", "1" ], [ "1/2", "1/2" ] ], "matrix": [ [ 0.4820867734322865, 0.5179132265677133 ], [ 0.25895661328385666, 0.7410433867161432 ] ], "trace": [ { "k": 0, "poisson_weight": 0.36787944117144233, "R_power": [ [ "1", "0" ], [ "0", "1" ] ] }, { "k": 1, "poisson_weight": 0.36787944117144233, "R_power": [ [ "0", "1" ], [ "1/2", "1/2" ] ] }, { "k": 2, "poisson_weight": 0.18393972058572117, "R_power": [ [ "1/2", "1/2" ], [ "1/4", "3/4" ] ] }, { "k": 3, "poisson_weight": 0.061313240195240384, "R_power": [ [ "1/4", "3/4" ], [ "3/8", "5/8" ] ] }, { "k": 4, "poisson_weight": 0.015328310048810096, "R_power": [ [ "3/8", "5/8" ], [ "5/16", "11/16" ] ] }, { "k": 5, "poisson_weight": 0.0030656620097620196, "R_power": [ [ "5/16", "11/16" ], [ "11/32", "21/32" ] ] }, { "k": 6, "poisson_weight": 0.0005109436682936699, "R_power": [ [ "11/32", "21/32" ], [ "21/64", "43/64" ] ] }, { "k": 7, "poisson_weight": 7.299195261338141e-05, "R_power": [ [ "21/64", "43/64" ], [ "43/128", "85/128" ] ] }, { "k": 8, "poisson_weight": 9.123994076672677e-06, "R_power": [ [ "43/128", "85/128" ], [ "85/256", "171/256" ] ] }, { "k": 9, "poisson_weight": 1.0137771196302974e-06, "R_power": [ [ "85/256", "171/256" ], [ "171/512", "341/512" ] ] }, { "k": 10, "poisson_weight": 1.0137771196302975e-07, "R_power": [ [ "171/512", "341/512" ], [ "341/1024", "683/1024" ] ] }, { "k": 11, "poisson_weight": 9.216155633002704e-09, "R_power": [ [ "341/1024", "683/1024" ], [ "683/2048", "1365/2048" ] ] }, { "k": 12, "poisson_weight": 7.68012969416892e-10, "R_power": [ [ "683/2048", "1365/2048" ], [ "1365/4096", "2731/4096" ] ] }, { "k": 13, "poisson_weight": 5.907792072437631e-11, "R_power": [ [ "1365/4096", "2731/4096" ], [ "2731/8192", "5461/8192" ] ] }, { "k": 14, "poisson_weight": 4.2198514803125934e-12, "R_power": [ [ "2731/8192", "5461/8192" ], [ "5461/16384", "10923/16384" ] ] }, { "k": 15, "poisson_weight": 2.8132343202083955e-13, "R_power": [ [ "5461/16384", "10923/16384" ], [ "10923/32768", "21845/32768" ] ] }, { "k": 16, "poisson_weight": 1.7582714501302472e-14, "R_power": [ [ "10923/32768", "21845/32768" ], [ "21845/65536", "43691/65536" ] ] }, { "k": 17, "poisson_weight": 1.0342773236060278e-15, "R_power": [ [ "21845/65536", "43691/65536" ], [ "43691/131072", "87381/131072" ] ] }, { "k": 18, "poisson_weight": 5.745985131144598e-17, "R_power": [ [ "43691/131072", "87381/131072" ], [ "87381/262144", "174763/262144" ] ] }, { "k": 19, "poisson_weight": 3.0242027006024198e-18, "R_power": [ [ "87381/262144", "174763/262144" ], [ "174763/524288", "349525/524288" ] ] } ], "rowmass": 1.0, "omitted_poisson_mass_float": 0.0, "analytic_poisson_tail_upper": 1.5877064178162703e-19 }, { "t": 0.5, "nu": 3, "absolute_entry_error": 4.440892098500626e-16, "analytic": [ [ 0.48208677343228656, 0.5179132265677134 ], [ 0.2589566132838567, 0.7410433867161432 ] ], "R": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ], "matrix": [ [ 0.48208677343228634, 0.517913226567713 ], [ 0.2589566132838565, 0.7410433867161429 ] ], "trace": [ { "k": 0, "poisson_weight": 0.22313016014842982, "R_power": [ [ "1", "0" ], [ "0", "1" ] ] }, { "k": 1, "poisson_weight": 0.33469524022264474, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 2, "poisson_weight": 0.25102143016698353, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 3, "poisson_weight": 0.12551071508349176, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 4, "poisson_weight": 0.04706651815630941, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 5, "poisson_weight": 0.014119955446892823, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 6, "poisson_weight": 0.0035299888617232058, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 7, "poisson_weight": 0.0007564261846549727, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 8, "poisson_weight": 0.00014182990962280736, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 9, "poisson_weight": 2.3638318270467892e-05, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 10, "poisson_weight": 3.5457477405701838e-06, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 11, "poisson_weight": 4.835110555322977e-07, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 12, "poisson_weight": 6.043888194153722e-08, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 13, "poisson_weight": 6.973717147100448e-09, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 14, "poisson_weight": 7.471839800464765e-10, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 15, "poisson_weight": 7.471839800464766e-11, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 16, "poisson_weight": 7.0048498129357185e-12, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 17, "poisson_weight": 6.180749834943282e-13, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 18, "poisson_weight": 5.1506248624527345e-14, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 19, "poisson_weight": 4.0662827861468955e-15, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] } ], "rowmass": 0.9999999999999996, "omitted_poisson_mass_float": 4.440892098500626e-16, "analytic_poisson_tail_upper": 3.2843053272724923e-16 }, { "t": 1.0, "nu": 2, "absolute_entry_error": 4.285460875053104e-14, "analytic": [ [ 0.36652471224524263, 0.6334752877547574 ], [ 0.3167376438773787, 0.6832623561226213 ] ], "R": [ [ "0", "1" ], [ "1/2", "1/2" ] ], "matrix": [ [ 0.36652471224522126, 0.6334752877547145 ], [ 0.31673764387735726, 0.6832623561225785 ] ], "trace": [ { "k": 0, "poisson_weight": 0.1353352832366127, "R_power": [ [ "1", "0" ], [ "0", "1" ] ] }, { "k": 1, "poisson_weight": 0.2706705664732254, "R_power": [ [ "0", "1" ], [ "1/2", "1/2" ] ] }, { "k": 2, "poisson_weight": 0.2706705664732254, "R_power": [ [ "1/2", "1/2" ], [ "1/4", "3/4" ] ] }, { "k": 3, "poisson_weight": 0.18044704431548358, "R_power": [ [ "1/4", "3/4" ], [ "3/8", "5/8" ] ] }, { "k": 4, "poisson_weight": 0.09022352215774179, "R_power": [ [ "3/8", "5/8" ], [ "5/16", "11/16" ] ] }, { "k": 5, "poisson_weight": 0.036089408863096716, "R_power": [ [ "5/16", "11/16" ], [ "11/32", "21/32" ] ] }, { "k": 6, "poisson_weight": 0.012029802954365572, "R_power": [ [ "11/32", "21/32" ], [ "21/64", "43/64" ] ] }, { "k": 7, "poisson_weight": 0.0034370865583901633, "R_power": [ [ "21/64", "43/64" ], [ "43/128", "85/128" ] ] }, { "k": 8, "poisson_weight": 0.0008592716395975408, "R_power": [ [ "43/128", "85/128" ], [ "85/256", "171/256" ] ] }, { "k": 9, "poisson_weight": 0.00019094925324389796, "R_power": [ [ "85/256", "171/256" ], [ "171/512", "341/512" ] ] }, { "k": 10, "poisson_weight": 3.8189850648779595e-05, "R_power": [ [ "171/512", "341/512" ], [ "341/1024", "683/1024" ] ] }, { "k": 11, "poisson_weight": 6.943609208869018e-06, "R_power": [ [ "341/1024", "683/1024" ], [ "683/2048", "1365/2048" ] ] }, { "k": 12, "poisson_weight": 1.1572682014781697e-06, "R_power": [ [ "683/2048", "1365/2048" ], [ "1365/4096", "2731/4096" ] ] }, { "k": 13, "poisson_weight": 1.7804126176587226e-07, "R_power": [ [ "1365/4096", "2731/4096" ], [ "2731/8192", "5461/8192" ] ] }, { "k": 14, "poisson_weight": 2.5434465966553178e-08, "R_power": [ [ "2731/8192", "5461/8192" ], [ "5461/16384", "10923/16384" ] ] }, { "k": 15, "poisson_weight": 3.391262128873757e-09, "R_power": [ [ "5461/16384", "10923/16384" ], [ "10923/32768", "21845/32768" ] ] }, { "k": 16, "poisson_weight": 4.2390776610921964e-10, "R_power": [ [ "10923/32768", "21845/32768" ], [ "21845/65536", "43691/65536" ] ] }, { "k": 17, "poisson_weight": 4.987150189520231e-11, "R_power": [ [ "21845/65536", "43691/65536" ], [ "43691/131072", "87381/131072" ] ] }, { "k": 18, "poisson_weight": 5.541277988355812e-12, "R_power": [ [ "43691/131072", "87381/131072" ], [ "87381/262144", "174763/262144" ] ] }, { "k": 19, "poisson_weight": 5.832924198269276e-13, "R_power": [ [ "87381/262144", "174763/262144" ], [ "174763/524288", "349525/524288" ] ] } ], "rowmass": 0.9999999999999357, "omitted_poisson_mass_float": 6.428191312579656e-14, "analytic_poisson_tail_upper": 6.446916219139726e-14 }, { "t": 1.0, "nu": 3, "absolute_entry_error": 5.542954983894788e-11, "analytic": [ [ 0.36652471224524263, 0.6334752877547574 ], [ 0.3167376438773787, 0.6832623561226213 ] ], "R": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ], "matrix": [ [ 0.36652471221752786, 0.6334752876993279 ], [ 0.31673764384966396, 0.6832623560671918 ] ], "trace": [ { "k": 0, "poisson_weight": 0.049787068367863944, "R_power": [ [ "1", "0" ], [ "0", "1" ] ] }, { "k": 1, "poisson_weight": 0.14936120510359183, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 2, "poisson_weight": 0.22404180765538773, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 3, "poisson_weight": 0.22404180765538773, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 4, "poisson_weight": 0.1680313557415408, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 5, "poisson_weight": 0.10081881344492448, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 6, "poisson_weight": 0.05040940672246224, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 7, "poisson_weight": 0.021604031452483817, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 8, "poisson_weight": 0.00810151179468143, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 9, "poisson_weight": 0.0027005039315604767, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 10, "poisson_weight": 0.000810151179468143, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 11, "poisson_weight": 0.0002209503216731299, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 12, "poisson_weight": 5.5237580418282474e-05, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 13, "poisson_weight": 1.2747133942680572e-05, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 14, "poisson_weight": 2.7315287020029796e-06, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 15, "poisson_weight": 5.463057404005959e-07, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 16, "poisson_weight": 1.0243232632511172e-07, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 17, "poisson_weight": 1.807629288090207e-08, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 18, "poisson_weight": 3.0127154801503447e-09, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] }, { "k": 19, "poisson_weight": 4.756919179184755e-10, "R_power": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ] } ], "rowmass": 0.9999999999168558, "omitted_poisson_mass_float": 8.314415822496812e-11, "analytic_poisson_tail_upper": 8.324608563573319e-11 } ], "one_term_not_renormalized": { "R": [ [ "1/3", "2/3" ], [ "1/3", "2/3" ] ], "matrix": [ [ 0.22313016014842982, 0.0 ], [ 0.0, 0.22313016014842982 ] ], "trace": [ { "k": 0, "poisson_weight": 0.22313016014842982, "R_power": [ [ "1", "0" ], [ "0", "1" ] ] } ], "rowmass": 0.22313016014842982, "omitted_poisson_mass_float": 0.7768698398515702, "analytic_poisson_tail_upper": 1.338780960890579 }, "allzero_generator_policy": { "matrix": [ [ 1.0, 0.0 ], [ 0.0, 1.0 ] ], "trace": [], "omitted_poisson_mass_float": 0.0, "analytic_poisson_tail_upper": 0.0, "rowmass": 1.0 }, "invalid_cases_rejected": [ "bad_rate", "negative_offdiag", "row_sum", "negative_time", "nonfinite_time", "zero_nu_nonzero_Q", "term_budget", "bool_time" ], "scope": "Poisson truncation bound in exact-real theory is distinct from float roundoff; +3e-15 is observed test tolerance, not universal guarantee. 2states, no SciPy expm/queue/customer rate fit. Common tick may be a dummy self-transition, not real jump." }