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mathematics
information-theory
renyi-entropy
shannon-entropy
hidden-markov-models
bernoulli-convolutions
| { | |
| "name": "phi_markov_q2", | |
| "certificate": { | |
| "order": 2, | |
| "depth": 128, | |
| "interval_nats_per_branch": [ | |
| "440495377338643/1125899906842624", | |
| "118004085817165/281474976710656" | |
| ], | |
| "width": "31520965930017/1125899906842624", | |
| "spectral_proxy_interval": [ | |
| "118004085817037/281474976710656", | |
| "118004085817165/281474976710656" | |
| ], | |
| "split_bound": 18, | |
| "boundary_fibre_log_error": "31520965929505/1125899906842624", | |
| "moment_matrix": [ | |
| [ | |
| "58021936384783931945423462154945200408643822586773593064809585183534478670438306546827342174149783827428767436092988115141448233969/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096", | |
| "5514975223718445220396051167750089790440322584981534036290522609749223455583069098723666334144282425996168191589087740745936245529/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096" | |
| ], | |
| [ | |
| "5514975223718445220396051167750089790440322584981534036290522609749223455583069098723666334144282425996168191589087740745936245529/837987995621412318723376562387865382967460363787024586107722590232610251879596686050117143635431464230626991136655378178359617675746660621652103062880256", | |
| "524197460707370310116187602824649518417557457621236671137180105986966723136917791144646572928202624591453356986949903026751376513/837987995621412318723376562387865382967460363787024586107722590232610251879596686050117143635431464230626991136655378178359617675746660621652103062880256" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "285224894413937447024608214971918668255460181617373558971696637323212363300079053189412576252563255178365781092685886551817561074912285706275/57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097345724416", | |
| "upper": "142612447215241186347881775316553410879355225494347263363320619716041965564663361778080891774367127090399314185337195563292412148575047221431/28793048285076456849987446449190283896766061557132266451844835664715760516297522370041860391064901485759493828054533728788532902755163518009654497157537048672862208", | |
| "iterations": 33, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 128, | |
| "order": 2, | |
| "engine": "unit-clock integer replica", | |
| "max_layer_states": 14, | |
| "visited_layer_states": 3535, | |
| "exact": true, | |
| "truncated": false, | |
| "cone": { | |
| "bits": 57, | |
| "inverse_norm_upper": "161125678563890425/161125678563890424", | |
| "embedding_entry_width": "1/144115188075855872", | |
| "absorption_coefficient": "161125678563890425/11610328735042483657607663912484864", | |
| "excess_width_upper_beyond_rounded_cone": "60792470497801589598634485257919025/836612354636580665353180334941075251239451522760704", | |
| "radius_rounding_extra_upper": "1/1125899906842624", | |
| "neutral_embeddings": 0, | |
| "retains_every_exact_return": true | |
| } | |
| }, | |
| "probabilistic": false, | |
| "source_stationary": true | |
| }, | |
| "elapsed_seconds_observed": 0.022212707999869963 | |
| } | |