{"id":"https://openalex.org/W7222938545","doi":"https://doi.org/10.48550/arxiv.2610.23209","title":"Regular Additive Scalar Invariants of ${\\mathcal N}=1$ Hyperbolic Spin Supertriangles","display_name":"Regular Additive Scalar Invariants of ${\\mathcal N}=1$ Hyperbolic Spin Supertriangles","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222938545","doi":"https://doi.org/10.48550/arxiv.2610.23209"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.23209","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23209","pdf_url":"https://arxiv.org/pdf/2610.23209","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.23209","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014003200","display_name":"Ilia Gaiur","orcid":"https://orcid.org/0009-0007-3615-9848","observed_orcids":["https://orcid.org/0009-0007-3615-9848"]},"institutions":[{"id":"https://openalex.org/I84909340","display_name":"Institut des Hautes \u00c9tudes Scientifiques","ror":"https://ror.org/05d5m2r55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I84909340"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gaiur, Ilia","raw_affiliation_strings":["Institut des Hautes \u00c9tudes Scientifiques 35 route de Chartres , 91440 Bures-sur-Yvette , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut des Hautes \u00c9tudes Scientifiques 35 route de Chartres , 91440 Bures-sur-Yvette , France","institution_ids":["https://openalex.org/I84909340"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159078454","display_name":"Robert Penner","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I84909340","display_name":"Institut des Hautes \u00c9tudes Scientifiques","ror":"https://ror.org/05d5m2r55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I84909340"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Penner, Robert","raw_affiliation_strings":["Institut des Hautes \u00c9tudes Scientifiques 35 route de Chartres , 91440 Bures-sur-Yvette , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut des Hautes \u00c9tudes Scientifiques 35 route de Chartres , 91440 Bures-sur-Yvette , France","institution_ids":["https://openalex.org/I84909340"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I84909340"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T12504","display_name":"Mathematics and Applications","score":0.19699999690055847,"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/T12504","display_name":"Mathematics and Applications","score":0.19699999690055847,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.17749999463558197,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.14560000598430634,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"hyperbolic geometry","score":0.7739999890327454},{"id":"https://openalex.org/keywords/n-1-supersymmetry","display_name":"N=1 supersymmetry","score":0.8790000081062317},{"id":"https://openalex.org/keywords/body-area","display_name":"body area","score":0.6269999742507935}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7200000286102295},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.63919997215271},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6236000061035156},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.5814999938011169},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5324000120162964},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4717000126838684},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45750001072883606},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4056999981403351},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40310001373291016},{"id":"https://openalex.org/C82673646","wikidata":"https://www.wikidata.org/wiki/Q2246553","display_name":"Hyperbolic triangle","level":4,"score":0.3569999933242798},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C117855890","wikidata":"https://www.wikidata.org/wiki/Q3042004","display_name":"Hyperbolic set","level":2,"score":0.3255999982357025},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3230000138282776},{"id":"https://openalex.org/C2988735580","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic flow","level":3,"score":0.30469998717308044},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.29679998755455017},{"id":"https://openalex.org/C139966315","wikidata":"https://www.wikidata.org/wiki/Q1003216","display_name":"Hyperbolic angle","level":5,"score":0.2922999858856201},{"id":"https://openalex.org/C40976572","wikidata":"https://www.wikidata.org/wiki/Q2330873","display_name":"Gauge (firearms)","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C136005978","wikidata":"https://www.wikidata.org/wiki/Q1362077","display_name":"First variation","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C39308205","wikidata":"https://www.wikidata.org/wiki/Q7880612","display_name":"Ultraparallel theorem","level":5,"score":0.26989999413490295},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.26489999890327454},{"id":"https://openalex.org/C31836371","wikidata":"https://www.wikidata.org/wiki/Q1856609","display_name":"Scalar potential","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.23209","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23209","pdf_url":"https://arxiv.org/pdf/2610.23209","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.23209","doi":"https://doi.org/10.48550/arxiv.2610.23209","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.23209","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.23209","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23209","pdf_url":"https://arxiv.org/pdf/2610.23209","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222938545.pdf","grobid_xml":"https://content.openalex.org/works/W7222938545.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4293578207","https://openalex.org/W2099422107","https://openalex.org/W3088261827","https://openalex.org/W3197700937","https://openalex.org/W7168276573","https://openalex.org/W2004713430","https://openalex.org/W4407205159","https://openalex.org/W2084334256","https://openalex.org/W4310054751","https://openalex.org/W7098651043"],"abstract_inverted_index":{"We":[0],"classify":[1],"regular":[2],"cyclic":[3],"scalar":[4,51],"invariants":[5,52],"of":[6,44,49,92,115],"non-degenerate":[7],"hyperbolic":[8,60],"${\\mathcal":[9],"N}=1$":[10],"spin":[11,22,117],"supertriangles":[12,127],"which":[13],"are":[14,123],"additive":[15,50],"under":[16,113],"geodesic":[17],"subdivision.":[18],"After":[19],"fixing":[20],"the":[21,24,32,78,88,96,116,120],"lift,":[23,118],"common-first":[25],"gauge":[26],"(introduced":[27],"in":[28,62,68,75],"earlier":[29],"work":[30],"by":[31],"second-named":[33],"author":[34],"and":[35,71,80],"further":[36],"developed":[37],"here)":[38],"gives":[39],"a":[40],"complete":[41],"$3|4$":[42],"modulus":[43],"such":[45],"supertriangles..":[46],"The":[47,108],"space":[48],"is":[53,87],"proved":[54],"to":[55,104],"have":[56],"superdimension":[57],"$3|1$:":[58],"ordinary":[59,100,126],"area":[61],"degree":[63,69,76],"zero,":[64],"two":[65],"even":[66,131],"generators":[67,122],"two,":[70],"one":[72],"odd":[73],"generator":[74,86,110],"three;":[77],"degree-one":[79],"degree-four":[81],"sectors":[82],"vanish.":[83],"One":[84],"degree-two":[85],"fermionic":[89],"first":[90],"variation":[91],"body":[93,101],"area,":[94],"equivalently":[95],"nilpotent":[97],"correction":[98],"from":[99],"angle":[102,106],"defect":[103],"super":[105],"defect.":[107],"degree-three":[109],"changes":[111],"sign":[112],"reversal":[114],"while":[119],"other":[121],"fixed,":[124],"so":[125],"carry":[128],"only":[129],"three":[130],"invariants.":[132]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-20T00:00:00"}
