{"id":"https://openalex.org/W7225828938","doi":"https://doi.org/10.5281/zenodo.24135155","title":"The probability that a Gaussian tetrahedron is acute","display_name":"The probability that a Gaussian tetrahedron is acute","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225828938","doi":"https://doi.org/10.5281/zenodo.24135155"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24135155","doi":"https://doi.org/10.5281/zenodo.24135155","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24135155","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24135155","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5146246459","display_name":"Sungsoo Na","orcid":"https://orcid.org/0009-0005-5257-3374","observed_orcids":["https://orcid.org/0009-0005-5257-3374"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Na, Sungsoo","raw_affiliation_strings":["TEAM42 Inc., Seoul, Republic of Korea"],"raw_orcid":"https://orcid.org/0009-0005-5257-3374","affiliations":[{"raw_affiliation_string":"TEAM42 Inc., Seoul, Republic of Korea","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5146246459"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.6538000106811523,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.6538000106811523,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.06769999861717224,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.062300000339746475,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7615000009536743},{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.5896000266075134},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.5669999718666077},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4302999973297119},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4169999957084656},{"id":"https://openalex.org/C104416048","wikidata":"https://www.wikidata.org/wiki/Q302518","display_name":"Propagator","level":2,"score":0.3912999927997589},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3774999976158142},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3353999853134155},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3061000108718872},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.2874999940395355},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C65574998","wikidata":"https://www.wikidata.org/wiki/Q386272","display_name":"Feynman diagram","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C152022596","wikidata":"https://www.wikidata.org/wiki/Q7268361","display_name":"Quadratic form (statistics)","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C4285052","wikidata":"https://www.wikidata.org/wiki/Q3406268","display_name":"Moment problem","level":3,"score":0.27480000257492065},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2606000006198883},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24135155","doi":"https://doi.org/10.5281/zenodo.24135155","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24135155","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24135156","doi":"https://doi.org/10.5281/zenodo.24135156","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24135156","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24135155","doi":"https://doi.org/10.5281/zenodo.24135155","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24135155","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,14],"four":[3],"independent":[4],"standard":[5],"normal":[6],"points":[7,41],"of":[8,42,60,75,117,125,133,142,148,161,188,194],"\u211d3":[9],"span":[10],"an":[11],"acute":[12],"tetrahedron,":[13],"is,":[15],"a":[16,57,72,115,130,146],"tetrahedron":[17],"whose":[18],"six":[19],"dihedral":[20],"angles":[21],"are":[22,89,102],"all":[23],"smaller":[24],"than":[25],"\u03c0/2,":[26],"with":[27,137,155],"probability":[28,110],"(2/\u03c0)":[29],"arctan(1/3)":[30],"\u2212":[31,35,62],"1/6":[32],"+":[33],"(40\u221a3":[34],"72)/(45\u03c0)":[36],"=":[37],"0.0189404094\u2026":[38],".":[39],"For":[40,52],"\u211dn,":[43],"n":[44,92,99],"\u2265":[45],"3,":[46],"let":[47],"pn":[48,55,111],"be":[49],"this":[50],"probability.":[51],"odd":[53],"n,":[54,69],"is":[56,71,83,112,129,145],"rational":[58,73,107,191],"combination":[59,74],"arctan(1/3)/\u03c0":[61],"1/12,":[63],"1/\u03c0":[64],"and":[65,78,158,182,185,193],"\u221a3/\u03c0;":[66],"for":[67,91,96],"even":[68],"\u03c02pn":[70],"1,":[76],"ln(4/3)":[77],"\u221a5":[79],"Cl2(arccos(1/9)),":[80],"where":[81,127],"Cl2":[82],"the":[84,118,122,177,183,189,195,201],"Clausen":[85],"function.":[86],"The":[87,109,140,174],"coefficients":[88],"given":[90],"\u2264":[93,98,100],"8;":[94],"those":[95],"4":[97],"8":[101],"computer-assisted,":[103],"obtained":[104],"in":[105,200],"exact":[106,190],"arithmetic.":[108],"written":[113],"as":[114],"moment":[116],"weight":[119],"exp(\u2212\u03a6)":[120],"over":[121],"positive":[123],"orthant":[124],"\u211d6,":[126],"\u03a6":[128],"quadratic":[131],"form":[132],"signature":[134],"(1,":[135],"5)":[136],"zero":[138],"diagonal.":[139],"evaluation":[141],"such":[143],"moments":[144],"translation":[147],"known":[149],"results":[150],"on":[151,159],"one-loop":[152],"Feynman":[153],"integrals":[154],"massless":[156],"propagators":[157],"volumes":[160],"ideal":[162],"hyperbolic":[163],"simplices.":[164],"MSC":[165],"2020:":[166],"Primary":[167],"60D05;":[168],"Secondary":[169],"52A22,":[170],"51M10,":[171],"33B30,":[172],"81Q30.":[173],"record":[175],"contains":[176],"paper,":[178],"its":[179],"LaTeX":[180],"source,":[181],"programs":[184],"recorded":[186],"outputs":[187],"computations":[192],"Monte":[196],"Carlo":[197],"runs":[198],"reported":[199],"paper.":[202]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}