balanced-numbers.json

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9381 bytes, as of the version from 2026-10-27 01:08 (current). Recorded here, not run.

{
  "0": {
    "number": "0"
  },
  "1": {
    "number": "0.7798934003768228294742064136526901366306257081363209601031335831780717609791088901087787073052785282",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(3)": {
    "number": "0.3210561864106780695711492519171907716293812522996196132842750762216990735320068739850774503808286338",
    "param-latex": "$\\sqrt{3}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(5)": {
    "number": "0.6408068404452539449387670340885006660177122693723308229559796340905947187761399908107259016327543861",
    "param-latex": "$\\sqrt{5}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(7)": {
    "number": "0.3803906937680257451035588977632938813772351339087800676994345687499072937408533364280265396350848459",
    "param-latex": "$\\sqrt{7}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "3": {
    "number": "0.6057207892976856295561610742871546971452241199383242385818462301649969705618914967816623916536859336",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(11)": {
    "number": "0.4042604972448340779400038126726447548156404215231559553035908060459098365012747549669279739971657592",
    "param-latex": "$\\sqrt{11}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(13)": {
    "number": "0.5881276455282872548646524186250949450738871230291278892437900235246723574684006773325911921468084086",
    "param-latex": "$\\sqrt{13}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(15)": {
    "number": "0.4179220936249201378284074258490084379661098672609348201685381174276825144262370111424256314158458830",
    "param-latex": "$\\sqrt{15}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(17)": {
    "number": "0.5771212523718251084740861852596818168962387269255203493649043764189391410558947581961932005675837707",
    "param-latex": "$\\sqrt{17}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(19)": {
    "number": "0.4270356033980088055932374181660509270695730411676597064179221173923750555440937922442829066109424313",
    "param-latex": "$\\sqrt{19}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(21)": {
    "number": "0.5694134117957716337797564849753450163255333018391686653159065150622861348396013410183539703990334806",
    "param-latex": "$\\sqrt{21}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(23)": {
    "number": "0.4336656870944328144943376219021306701444712568373861617383444500322118261770097690401696294329194234",
    "param-latex": "$\\sqrt{23}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "5": {
    "number": "0.5636311887040122311021074044130139641207537623099921078616593412498859935331646182126086015708039804",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(27)": {
    "number": "0.4387666536862618884704143093441028206788304624221276256833151276375718284109515681055274809890590196",
    "param-latex": "$\\sqrt{27}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(29)": {
    "number": "0.5590873872857030846153188143420749372326999429851543935638780557459802347888707036795777760097121916",
    "param-latex": "$\\sqrt{29}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(31)": {
    "number": "0.4428478735796019249207394400063621720815766851985477627300621355516295226680562182282684903053117154",
    "param-latex": "$\\sqrt{31}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(33)": {
    "number": "0.5553952224507595341698130967698284950006714479468794057988204997807302572784322283739065705496595753",
    "param-latex": "$\\sqrt{33}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(35)": {
    "number": "0.4462091213596228693474148195351134201532962204434839918355272509430023108055108602483919943679147763",
    "param-latex": "$\\sqrt{35}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(37)": {
    "number": "0.5523182338562316027242533644802253660769846969368950882698527012535737982339124596715620634572970172",
    "param-latex": "$\\sqrt{37}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(39)": {
    "number": "0.4490397881441164040677890845348449408279643167677654547996577837464688235114934933474097077103523832",
    "param-latex": "$\\sqrt{39}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(2)": {
    "param-latex": "$\\sqrt{2}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.5288915951112465925568670379223205183661948137201804434346521640933897729889879694687112508190553661"
  },
  "2": {
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.4882534060753407545002235033572610376883671545092153829475964426552750821354195848976660360266022599"
  },
  "sqrt(6)": {
    "param-latex": "$\\sqrt{6}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.5066415640626164768562060577083338267447818625568330346873869256708312064182908691057964275464882563"
  },
  "sqrt(8)": {
    "param-latex": "$\\sqrt{8}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.4956196980956746332815740528168459429258915480604570457032555596174794882007245938443022932720795872"
  },
  "sqrt(10)": {
    "param-latex": "$\\sqrt{10}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.5031581047232053626001088552226006006804106408905129160679762467461640264393283885269251211679602222"
  },
  "sqrt(12)": {
    "param-latex": "$\\sqrt{12}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.4975872742888735682098619879159253930134103201906127776078039175417850902102777393713515516891710053"
  },
  "sqrt(14)": {
    "param-latex": "$\\sqrt{14}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.5019196883695551822957099235995135550299109378810951916448616868391966477082837080643474907586855463"
  },
  "4": {
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.4984260330381776155307095868245097300350135211824269469752137903190608739367562440331957986548427861"
  },
  "sqrt(1/2)": {
    "param-latex": "$\\sqrt{1/2}$",
    "comment": "A diagonal-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.6647169317774971062421108635871436685418032702125249400532885991000729886650559725134181751678952585"
  },
  "1*sqrt(2/pi)": {
    "param-latex": "$1\\sqrt{2/\\pi}$",
    "comment": "A unit-quadratic-phase reference; see CITE{balanced-quadratic}.",
    "number": "0.7217059242926050877715858156119067071717932981792008804439748635733424719649134799372303728068514873"
  },
  "sqrt(3/2)": {
    "param-latex": "$\\sqrt{3/2}$",
    "comment": "A diagonal-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.6987932112819265361584551348467379235674862815426546730722502512028371207840897581798178307691106353"
  },
  "2*sqrt(2/pi)": {
    "param-latex": "$2\\sqrt{2/\\pi}$",
    "comment": "A unit-quadratic-phase reference; see CITE{balanced-quadratic}.",
    "number": "0.3681929762809747963106624017460055313715683095106596109382454766741134981461776062195709031405430141"
  },
  "sqrt(5/2)": {
    "param-latex": "$\\sqrt{5/2}$",
    "comment": "A diagonal-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.3781520881155292484301156673523986720651224231088983094500858183493144087541099301334846082838567699"
  },
  "3*sqrt(2/pi)": {
    "param-latex": "$3\\sqrt{2/\\pi}$",
    "comment": "A unit-quadratic-phase reference; see CITE{balanced-quadratic}.",
    "number": "0.5608039810639548648690870450175753068019808627040126373638455097657307372343216104844510926866821862"
  },
  "sqrt(7/2)": {
    "param-latex": "$\\sqrt{7/2}$",
    "comment": "A diagonal-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.3721723365491987891415795946529392440428777120470093329340724850477908026871490549059716233536203720"
  },
  "4*sqrt(2/pi)": {
    "param-latex": "$4\\sqrt{2/\\pi}$",
    "comment": "A unit-quadratic-phase reference; see CITE{balanced-quadratic}.",
    "number": "0.4743107173203279931730365277474657820253877052046737013509757099870111701511661273305742096418884617"
  },
  "1/2": {
    "comment": "A bounded arc-length reference; see CITE{balanced-simple}.",
    "number": "0.4923442258714463928788436651566816377660951457715012532946526193191076795983945814165027047148093055"
  }
}