[
  {
    "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
  }
]