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Tags:
mathematics
information-theory
renyi-entropy
shannon-entropy
hidden-markov-models
bernoulli-convolutions
| { | |
| "name": "variable_phi_q2", | |
| "certificate": { | |
| "order": 2, | |
| "depth": 24, | |
| "interval_nats_per_branch": [ | |
| "9556189083589/70368744177664", | |
| "88503064363261/211106232532992" | |
| ], | |
| "width": "29917248556247/105553116266496", | |
| "spectral_proxy_interval": [ | |
| "88503064362749/211106232532992", | |
| "88503064363261/211106232532992" | |
| ], | |
| "split_bound": 450, | |
| "boundary_fibre_log_error": "29917248555991/105553116266496", | |
| "moment_matrix": [ | |
| [ | |
| "2954828780898362717151025/79228162514264337593543950336", | |
| "280855975038747109285977/79228162514264337593543950336" | |
| ], | |
| [ | |
| "280855975038747109285977/4951760157141521099596496896", | |
| "26695312846852420848577/4951760157141521099596496896" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "14525380908590603280103114449096163/340282366920938463463374607431768211456", | |
| "upper": "7262690454716585602609677888477047/170141183460469231731687303715884105728", | |
| "iterations": 33, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 24, | |
| "order": 2, | |
| "engine": "asynchronous clock-slot replica", | |
| "max_layer_states": 114, | |
| "visited_layer_states": 3915, | |
| "completed_mass_by_total_clock": { | |
| "24": "221573452991312527398225/79228162514264337593543950336", | |
| "25": "1003262711346836821587321/79228162514264337593543950336", | |
| "26": "62024356616955431766435/2475880078570760549798248448", | |
| "27": "4400524549182519229185/154742504910672534362390528", | |
| "28": "98921012088270395997/4835703278458516698824704", | |
| "29": "2937403028009447361/302231454903657293676544", | |
| "30": "29131633875167271/9444732965739290427392", | |
| "31": "381839696855955/590295810358705651712", | |
| "32": "400119271695/4611686018427387904", | |
| "33": "129134199051/18446744073709551616", | |
| "34": "175864689/576460752303423488", | |
| "35": "211383/36028797018963968", | |
| "36": "35/1125899906842624" | |
| }, | |
| "exact": true, | |
| "truncated": false, | |
| "cone": { | |
| "bits": 55, | |
| "inverse_norm_upper": "40281419640972607/40281419640972606", | |
| "embedding_entry_width": "1/36028797018963968", | |
| "absorption_coefficient": "40281419640972607/725645545940155228600478994530304", | |
| "excess_width_upper_beyond_rounded_cone": "3799529406112599450869181436413313/13072068041196572896143442733454300800616430043136", | |
| "radius_rounding_extra_upper": "3/2251799813685248", | |
| "neutral_embeddings": 0, | |
| "retains_every_exact_return": true | |
| } | |
| }, | |
| "probabilistic": false, | |
| "source_stationary": true | |
| }, | |
| "elapsed_seconds_observed": 0.05499064099990392 | |
| } | |