Datasets:
Modalities:
Text
Formats:
json
Languages:
English
Size:
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Tags:
mathematics
information-theory
renyi-entropy
shannon-entropy
hidden-markov-models
bernoulli-convolutions
| { | |
| "name": "hidden_clock_q2", | |
| "certificate": { | |
| "order": 2, | |
| "depth": 16, | |
| "interval_nats_per_branch": [ | |
| "15945235707363/70368744177664", | |
| "2871848571221/4398046511104" | |
| ], | |
| "width": "30004341432173/70368744177664", | |
| "spectral_proxy_interval": [ | |
| "91899154278489/140737488355328", | |
| "2871848571221/4398046511104" | |
| ], | |
| "split_bound": 306, | |
| "boundary_fibre_log_error": "60008682863763/140737488355328", | |
| "moment_matrix": [ | |
| [ | |
| "42337/4294967296", | |
| "37705/4294967296", | |
| "9491/1073741824" | |
| ], | |
| [ | |
| "21693/2147483648", | |
| "38801/4294967296", | |
| "38749/4294967296" | |
| ], | |
| [ | |
| "48681/4294967296", | |
| "21693/2147483648", | |
| "43597/4294967296" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "33451127010211/1152921504606846976", | |
| "upper": "133804508049673/4611686018427387904", | |
| "iterations": 31, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 16, | |
| "order": 2, | |
| "engine": "asynchronous clock-slot replica", | |
| "max_layer_states": 2403, | |
| "visited_layer_states": 68686, | |
| "completed_mass_by_total_clock": { | |
| "16": "19/4294967296", | |
| "17": "429/2147483648", | |
| "18": "9527/4294967296", | |
| "19": "4981/536870912", | |
| "20": "4907/268435456", | |
| "21": "45343/2147483648", | |
| "22": "36175/2147483648", | |
| "23": "11167/1073741824", | |
| "24": "22729/4294967296", | |
| "25": "4943/2147483648", | |
| "26": "3757/4294967296", | |
| "27": "315/1073741824", | |
| "28": "377/4294967296", | |
| "29": "25/1073741824", | |
| "30": "3/536870912", | |
| "31": "1/1073741824", | |
| "32": "1/4294967296" | |
| }, | |
| "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": "1/1125899906842624", | |
| "neutral_embeddings": 0, | |
| "retains_every_exact_return": true | |
| } | |
| }, | |
| "probabilistic": false, | |
| "source_stationary": true | |
| }, | |
| "elapsed_seconds_observed": 1.2639873229998102 | |
| } | |