{"id":"https://openalex.org/W7224129097","doi":"https://doi.org/10.5281/zenodo.23727137","title":"The sharp Hessian bound for convex four-body central configurations","display_name":"The sharp Hessian bound for convex four-body central configurations","publication_year":2026,"publication_date":"2026-10-28","ids":{"openalex":"https://openalex.org/W7224129097","doi":"https://doi.org/10.5281/zenodo.23727137"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23727137","doi":"https://doi.org/10.5281/zenodo.23727137","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23727137","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","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23727137","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073858793","display_name":"Tejasvi Singh Tomar","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tomar, Tejasvi Singh","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4668-3639","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5073858793"],"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.8852999806404114,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.8852999806404114,"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/T12504","display_name":"Mathematics and Applications","score":0.024800000712275505,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.01850000023841858,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/four-body-problem","display_name":"four-body problem","score":0.7879999876022339},{"id":"https://openalex.org/keywords/central-configurations","display_name":"central configurations","score":0.8569999933242798},{"id":"https://openalex.org/keywords/moment-of-inertia","display_name":"moment of inertia","score":0.8059999942779541},{"id":"https://openalex.org/keywords/isosceles-trapezoid","display_name":"isosceles trapezoid","score":0.8669999837875366},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"computer-assisted proof","score":0.7210000157356262},{"id":"https://openalex.org/keywords/formal-verification","display_name":"formal verification","score":0.6489999890327454},{"id":"https://openalex.org/keywords/lean-theorem-prover","display_name":"Lean theorem prover","score":0.9169999957084656}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.760699987411499},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.677299976348877},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5634999871253967},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5067999958992004},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4650999903678894},{"id":"https://openalex.org/C98653994","wikidata":"https://www.wikidata.org/wiki/Q875937","display_name":"Isosceles triangle","level":2,"score":0.37709999084472656},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.36410000920295715},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.328000009059906},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.32670000195503235},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C10238366","wikidata":"https://www.wikidata.org/wiki/Q165618","display_name":"Moment of inertia","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30979999899864197},{"id":"https://openalex.org/C110407247","wikidata":"https://www.wikidata.org/wiki/Q122508","display_name":"Inertia","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.27239999175071716},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23727137","doi":"https://doi.org/10.5281/zenodo.23727137","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23727137","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.23727138","doi":"https://doi.org/10.5281/zenodo.23727138","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23727138","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.23727137","doi":"https://doi.org/10.5281/zenodo.23727137","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23727137","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W7214643328"],"related_works":["https://openalex.org/W7214722689","https://openalex.org/W7207785420","https://openalex.org/W4385576556","https://openalex.org/W2058527002","https://openalex.org/W2920275260","https://openalex.org/W1660544327","https://openalex.org/W7220712703","https://openalex.org/W3105945846","https://openalex.org/W2622044824","https://openalex.org/W2029062579"],"abstract_inverted_index":{"In":[0,208],"a":[1,58,113,161,226,248],"previous":[2],"paper":[3,178,245],"(arXiv:2609.35632)":[4],"we":[5,39],"proved":[6],"that":[7,33,116],"the":[8,29,41,52,55,62,86,92,109,120,123,132,137,139,142,147,151,158,170,177,180,190,211,214,244,254],"planar":[9],"four-body":[10],"problem":[11],"has":[12],"exactly":[13],"one":[14,90,126,194],"convex":[15,49],"central":[16,50],"configuration":[17],"for":[18,108,146],"each":[19,25],"choice":[20],"of":[21,28,44,54,61,64,69,91,104,112,122,127,150,176,195,213,233,243,253,257,261],"positive":[22],"masses":[23,88],"and":[24,125,144,189,193,205,235],"cyclic":[26],"order":[27],"bodies,":[30],"by":[31,81,182],"proving":[32],"these":[34],"configurations":[35,159],"are":[36,265],"nondegenerate.":[37],"Here":[38],"prove":[40],"sharp":[42],"form":[43],"this":[45],"nondegeneracy:":[46],"at":[47,166,225],"every":[48],"configuration,":[51,124],"Hessian":[53],"potential":[56],"on":[57,89,119],"level":[59],"set":[60],"moment":[63],"inertia":[65],"exceeds":[66],"two":[67,87,100],"thirds":[68],"its":[70],"radial":[71],"part.":[72],"The":[73,184,259],"constant":[74],"2/3":[75],"is":[76,79,129],"optimal;":[77],"it":[78],"approached":[80],"isosceles":[82],"trapezoids":[83],"in":[84,131,169,251],"which":[85],"parallel":[93],"sides":[94],"tend":[95],"to":[96,203,222],"zero.":[97],"We":[98],"give":[99],"independent":[101],"computer-assisted":[102,148],"proofs":[103,264],"an":[105],"equivalent":[106],"inequality":[107],"largest":[110],"eigenvalue":[111],"2\u00d72":[114],"matrix":[115],"depends":[117],"only":[118],"shape":[121],"them":[128,196],"formalized":[130],"Lean":[133,252],"proof":[134,250],"assistant.":[135],"Besides":[136],"paper,":[138],"record":[140],"contains":[141],"programs":[143,185],"data":[145],"part":[149,156],"paper's":[152,171],"first":[153],"proof.":[154],"That":[155],"covers":[157],"with":[160,187,220,237],"relatively":[162],"short":[163],"side":[164],"(roundness":[165],"most":[167],"3/4,":[168],"terms),":[172],"while":[173],"Section":[174,241],"4":[175],"treats":[179],"others":[181],"hand.":[183],"run":[186,206],"Python":[188],"python-flint":[191],"library,":[192],"also":[197,246],"needs":[198],"SymPy.":[199],"README.md":[200],"explains":[201],"how":[202],"check":[204],"them.":[207],"our":[209],"runs":[210],"longest":[212],"checks":[215],"took":[216],"about":[217],"11.5":[218],"hours":[219],"up":[221],"nine":[223],"processes":[224],"time,":[227],"needed":[228],"more":[229],"than":[230],"72":[231],"GiB":[232,239],"memory,":[234],"completed":[236],"120":[238],"available.":[240],"9":[242],"describes":[247],"formal":[249,263],"main":[255],"theorem":[256],"arXiv:2609.35632.":[258],"repositories":[260],"both":[262],"listed":[266],"under":[267],"Related":[268],"works.":[269],"Mathematics":[270],"Subject":[271],"Classification":[272],"(2020):":[273],"70F10,":[274],"70F15,":[275],"65G20,":[276],"68V20.":[277]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-29T00:00:00"}
