Datasets:
Modalities:
Text
Formats:
json
Languages:
English
Size:
< 1K
Tags:
mathematics
information-theory
renyi-entropy
shannon-entropy
hidden-markov-models
bernoulli-convolutions
Download evidence/example_certificates.json from PureOne/VELORYN-Boundary-Kernel-Entropy: direct link, hf CLI and curl.
- Browser
- Download file 26 kB
-
https://huggingface.co/datasets/PureOne/VELORYN-Boundary-Kernel-Entropy/resolve/main/evidence/example_certificates.json
- Command line
-
hf download hf://datasets/PureOne/VELORYN-Boundary-Kernel-Entropy/evidence/example_certificates.json
-
curl -L -o example_certificates.json https://huggingface.co/datasets/PureOne/VELORYN-Boundary-Kernel-Entropy/resolve/main/evidence/example_certificates.json
26 kB
| [ | |
| { | |
| "name": "phi_fair_q2", | |
| "certificate": { | |
| "order": 2, | |
| "depth": 128, | |
| "interval_nats_per_branch": [ | |
| "258123688130423/562949953421312", | |
| "270835677556033/562949953421312" | |
| ], | |
| "width": "6355994712805/281474976710656", | |
| "spectral_proxy_interval": [ | |
| "4231807461813/8796093022208", | |
| "270835677556033/562949953421312" | |
| ], | |
| "split_bound": 18, | |
| "boundary_fibre_log_error": "12711989425609/562949953421312", | |
| "moment_matrix": [ | |
| [ | |
| "11860760135078791270761230734708730107/6582018229284824168619876730229402019930943462534319453394436096" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "11860760135078791270761230734708730107/6582018229284824168619876730229402019930943462534319453394436096", | |
| "upper": "11860760135078791270761230734708730107/6582018229284824168619876730229402019930943462534319453394436096", | |
| "iterations": 0, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 128, | |
| "order": 2, | |
| "engine": "unit-clock integer replica", | |
| "max_layer_states": 7, | |
| "visited_layer_states": 892, | |
| "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": 0.00847616700002618 | |
| }, | |
| { | |
| "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 | |
| }, | |
| { | |
| "name": "salem_fair_q2", | |
| "certificate": { | |
| "order": 2, | |
| "depth": 64, | |
| "interval_nats_per_branch": [ | |
| "222897977129737/562949953421312", | |
| "1195246264631/2199023255552" | |
| ], | |
| "width": "83085066615799/562949953421312", | |
| "spectral_proxy_interval": [ | |
| "165479535719849/281474976710656", | |
| "82739767859925/140737488355328" | |
| ], | |
| "split_bound": 216452, | |
| "boundary_fibre_log_error": "108061094309961/562949953421312", | |
| "moment_matrix": [ | |
| [ | |
| "121338835637214357477/2658455991569831745807614120560689152" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "121338835637214357477/2658455991569831745807614120560689152", | |
| "upper": "121338835637214357477/2658455991569831745807614120560689152", | |
| "iterations": 0, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 64, | |
| "order": 2, | |
| "engine": "unit-clock integer replica", | |
| "max_layer_states": 1477, | |
| "visited_layer_states": 32580, | |
| "exact": true, | |
| "truncated": false, | |
| "cone": { | |
| "bits": 56, | |
| "inverse_norm_upper": "6212796517718380984166984953967970864316256054411264/4212241431760505290622594754183488816285843165187257", | |
| "embedding_entry_width": "1/72057594037927936", | |
| "absorption_coefficient": "344879487064097044699938762966516296/4212241431760505290622594754183488816285843165187257", | |
| "excess_width_upper_beyond_rounded_cone": "44144574344204421721592161659714085888/4212241431760505290622594754183488816285843165187257", | |
| "radius_rounding_extra_upper": "1/1125899906842624", | |
| "neutral_embeddings": 2, | |
| "retains_every_exact_return": true | |
| } | |
| }, | |
| "probabilistic": false, | |
| "source_stationary": true | |
| }, | |
| "elapsed_seconds_observed": 0.3204310040000564 | |
| }, | |
| { | |
| "name": "salem_markov_q2", | |
| "certificate": { | |
| "order": 2, | |
| "depth": 64, | |
| "interval_nats_per_branch": [ | |
| "60925045122905/281474976710656", | |
| "236008171634569/562949953421312" | |
| ], | |
| "width": "114158081388759/562949953421312", | |
| "spectral_proxy_interval": [ | |
| "236008171634057/562949953421312", | |
| "236008171634569/562949953421312" | |
| ], | |
| "split_bound": 216452, | |
| "boundary_fibre_log_error": "114158081388247/562949953421312", | |
| "moment_matrix": [ | |
| [ | |
| "225153361430428056633255339247267861845861014466973408330323719665/115792089237316195423570985008687907853269984665640564039457584007913129639936", | |
| "21400788860114134120993586160712437370851365107205789468376687897/115792089237316195423570985008687907853269984665640564039457584007913129639936" | |
| ], | |
| [ | |
| "21400788860114134120993586160712437370851365107205789468376687897/7237005577332262213973186563042994240829374041602535252466099000494570602496", | |
| "2034141355587553096519566487553495344262420531382581444683345537/7237005577332262213973186563042994240829374041602535252466099000494570602496" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "1106811453431227725215335329230731877356373287125782650539794694191156162083/497323236409786642155382248146820840100456150797347717440463976893159497012533375533056", | |
| "upper": "553405726747715045897838865796856317919255299619168372930706031298143112887/248661618204893321077691124073410420050228075398673858720231988446579748506266687766528", | |
| "iterations": 33, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 64, | |
| "order": 2, | |
| "engine": "unit-clock integer replica", | |
| "max_layer_states": 10, | |
| "visited_layer_states": 1219, | |
| "exact": true, | |
| "truncated": false, | |
| "cone": { | |
| "bits": 56, | |
| "inverse_norm_upper": "6212796517718380984166984953967970864316256054411264/4212241431760505290622594754183488816285843165187257", | |
| "embedding_entry_width": "1/72057594037927936", | |
| "absorption_coefficient": "344879487064097044699938762966516296/4212241431760505290622594754183488816285843165187257", | |
| "excess_width_upper_beyond_rounded_cone": "44144574344204421721592161659714085888/4212241431760505290622594754183488816285843165187257", | |
| "radius_rounding_extra_upper": "1/1125899906842624", | |
| "neutral_embeddings": 2, | |
| "retains_every_exact_return": true | |
| } | |
| }, | |
| "probabilistic": false, | |
| "source_stationary": true | |
| }, | |
| "elapsed_seconds_observed": 0.017152975999806586 | |
| }, | |
| { | |
| "name": "salem_fair_q3", | |
| "certificate": { | |
| "order": 3, | |
| "depth": 16, | |
| "interval_nats_per_branch": [ | |
| "8096426502693/281474976710656", | |
| "1195246264631/2199023255552" | |
| ], | |
| "width": "144895095370075/281474976710656", | |
| "spectral_proxy_interval": [ | |
| "175444994055579/281474976710656", | |
| "43861248513895/70368744177664" | |
| ], | |
| "split_bound": 13530, | |
| "boundary_fibre_log_error": "83674283776443/140737488355328", | |
| "moment_matrix": [ | |
| [ | |
| "153121/70368744177664" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "153121/70368744177664", | |
| "upper": "153121/70368744177664", | |
| "iterations": 0, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 16, | |
| "order": 3, | |
| "engine": "unit-clock integer replica", | |
| "max_layer_states": 2493, | |
| "visited_layer_states": 10982, | |
| "exact": true, | |
| "truncated": false, | |
| "cone": { | |
| "bits": 54, | |
| "inverse_norm_upper": "24268736397337427264075309831609710619681475264512/16454068092814472066527784151935828148751697428707", | |
| "embedding_entry_width": "1/18014398509481984", | |
| "absorption_coefficient": "5388741985376516666422854713671622/16454068092814472066527784151935828148751697428707", | |
| "excess_width_upper_beyond_rounded_cone": "172439743532048533325531350837491904/16454068092814472066527784151935828148751697428707", | |
| "radius_rounding_extra_upper": "1/1125899906842624", | |
| "neutral_embeddings": 2, | |
| "retains_every_exact_return": true | |
| } | |
| }, | |
| "probabilistic": false, | |
| "source_stationary": true | |
| }, | |
| "elapsed_seconds_observed": 0.3680168539999613 | |
| }, | |
| { | |
| "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 | |
| }, | |
| { | |
| "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 | |
| }, | |
| { | |
| "name": "mixture_cusp_q2", | |
| "certificate": { | |
| "order": 2, | |
| "depth": 16, | |
| "interval_nats_per_branch": [ | |
| "0", | |
| "0" | |
| ], | |
| "width": "0", | |
| "spectral_proxy_interval": [ | |
| "0", | |
| "0" | |
| ], | |
| "split_bound": 3, | |
| "boundary_fibre_log_error": "15760482964753/140737488355328", | |
| "moment_matrix": [ | |
| [ | |
| "1/65536", | |
| "0" | |
| ], | |
| [ | |
| "0", | |
| "1" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "1", | |
| "upper": "1", | |
| "iterations": 0, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 16, | |
| "order": 2, | |
| "engine": "unit-clock integer replica", | |
| "max_layer_states": 3, | |
| "visited_layer_states": 64, | |
| "exact": true, | |
| "truncated": false, | |
| "cone": { | |
| "bits": 54, | |
| "inverse_norm_upper": "1", | |
| "embedding_entry_width": "0", | |
| "absorption_coefficient": "0", | |
| "excess_width_upper_beyond_rounded_cone": "0", | |
| "radius_rounding_extra_upper": "1/1125899906842624", | |
| "neutral_embeddings": 0, | |
| "retains_every_exact_return": true | |
| } | |
| }, | |
| "probabilistic": false, | |
| "source_stationary": true | |
| }, | |
| "elapsed_seconds_observed": 0.001080258000001777 | |
| }, | |
| { | |
| "name": "salem_correlated_q2", | |
| "certificate": { | |
| "order": 2, | |
| "depth": 64, | |
| "interval_nats_per_branch": [ | |
| "160079265574253/562949953421312", | |
| "137118673481575/281474976710656" | |
| ], | |
| "width": "114158081388897/562949953421312", | |
| "spectral_proxy_interval": [ | |
| "68559336740625/140737488355328", | |
| "137118673481575/281474976710656" | |
| ], | |
| "split_bound": 216452, | |
| "boundary_fibre_log_error": "114158081388247/562949953421312", | |
| "moment_matrix": [ | |
| [ | |
| "2960819646724759885797509729085862798965505954793747742626093005/115792089237316195423570985008687907853269984665640564039457584007913129639936", | |
| "529013130495137511591331241820863665046623333539701122193747013/115792089237316195423570985008687907853269984665640564039457584007913129639936" | |
| ], | |
| [ | |
| "529013130495137511591331241820863665046623333539701122193747013/28948022309329048855892746252171976963317496166410141009864396001978282409984", | |
| "94519533364906908244866202860367727559690794188297657269672445/28948022309329048855892746252171976963317496166410141009864396001978282409984" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "7170227357961695745342310538335906062961428017630938400309498396488586837/248661618204893321077691124073410420050228075398673858720231988446579748506266687766528", | |
| "upper": "3585113679245354437918724024963618652391145841338780866924599759341166925/124330809102446660538845562036705210025114037699336929360115994223289874253133343883264", | |
| "iterations": 31, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 64, | |
| "order": 2, | |
| "engine": "unit-clock integer replica", | |
| "max_layer_states": 3286, | |
| "visited_layer_states": 143872, | |
| "exact": true, | |
| "truncated": false, | |
| "cone": { | |
| "bits": 56, | |
| "inverse_norm_upper": "6212796517718380984166984953967970864316256054411264/4212241431760505290622594754183488816285843165187257", | |
| "embedding_entry_width": "1/72057594037927936", | |
| "absorption_coefficient": "344879487064097044699938762966516296/4212241431760505290622594754183488816285843165187257", | |
| "excess_width_upper_beyond_rounded_cone": "44144574344204421721592161659714085888/4212241431760505290622594754183488816285843165187257", | |
| "radius_rounding_extra_upper": "1/1125899906842624", | |
| "neutral_embeddings": 2, | |
| "retains_every_exact_return": true | |
| } | |
| }, | |
| "probabilistic": false, | |
| "source_stationary": true | |
| }, | |
| "elapsed_seconds_observed": 1.8505300279998664 | |
| }, | |
| { | |
| "name": "phi_correlated_q2", | |
| "certificate": { | |
| "order": 2, | |
| "depth": 128, | |
| "interval_nats_per_branch": [ | |
| "224613882718947/562949953421312", | |
| "480748731368083/1125899906842624" | |
| ], | |
| "width": "31520965930189/1125899906842624", | |
| "spectral_proxy_interval": [ | |
| "480748731367399/1125899906842624", | |
| "480748731368083/1125899906842624" | |
| ], | |
| "split_bound": 18, | |
| "boundary_fibre_log_error": "31520965929505/1125899906842624", | |
| "moment_matrix": [ | |
| [ | |
| "21480909372898357400527329973574795544140153201504654202980446807977178044485282443274424079317922564819677456223527565078104677341/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096", | |
| "4098027382324387576487048536606615639527543964481048048740444863996583710221865629527104908287770106956338833661941459416690154485/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096" | |
| ], | |
| [ | |
| "4098027382324387576487048536606615639527543964481048048740444863996583710221865629527104908287770106956338833661941459416690154485/3351951982485649274893506249551461531869841455148098344430890360930441007518386744200468574541725856922507964546621512713438470702986642486608412251521024", | |
| "781802489584942987649461207122422649134866017505928542091945511281552409553605669845487444607132078996480031279933255435673412429/3351951982485649274893506249551461531869841455148098344430890360930441007518386744200468574541725856922507964546621512713438470702986642486608412251521024" | |
| ] | |
| ], | |
| "spectral_radius": { | |
| "lower": "52845533869027585301098676985219302960312758619678275153998657967099928427284494965750885893933048584975243380424509866844240409443035637533/28793048285076456849987446449190283896766061557132266451844835664715760516297522370041860391064901485759493828054533728788532902755163518009654497157537048672862208", | |
| "upper": "26422766936562806341711532280853175748459687129602909559239853007920186645640539337986375761730076746631506743690424350253090934429862896009/14396524142538228424993723224595141948383030778566133225922417832357880258148761185020930195532450742879746914027266864394266451377581759004827248578768524336431104", | |
| "iterations": 31, | |
| "method": "exact rational positive-resolvent bisection" | |
| }, | |
| "diagnostics": { | |
| "depth": 128, | |
| "order": 2, | |
| "engine": "unit-clock integer replica", | |
| "max_layer_states": 18, | |
| "visited_layer_states": 4564, | |
| "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": 0.040081848999989234 | |
| }, | |
| { | |
| "name": "variable_shannon_demo", | |
| "certificate": { | |
| "order": 1, | |
| "depth": 12, | |
| "samples": 128, | |
| "confidence": "99/100", | |
| "interval_nats_per_branch": [ | |
| "0", | |
| "2362036049594252892388675/3626777458843887524118528" | |
| ], | |
| "width": "2362036049594252892388675/3626777458843887524118528", | |
| "sampling_mode": "seeded pseudorandom demonstration", | |
| "independent_exact_draws_required": true, | |
| "sampled_quantity": "H(X_n,Z_n | Z_0)/n", | |
| "surprisal_range_upper": "12193974156573/8796093022208", | |
| "hoeffding_margin": "241103831240303432722881/1208925819614629174706176", | |
| "finite_block_bias_upper": "18027499691663/35184372088832", | |
| "mean_surprisal_interval": [ | |
| "31050235355/68719476736", | |
| "93150706327/206158430208" | |
| ], | |
| "maximum_fibre_layer_states": 4, | |
| "probabilistic": true | |
| }, | |
| "elapsed_seconds_observed": 0.11917953900001521 | |
| } | |
| ] | |