{"id":"https://openalex.org/W7225314247","doi":"https://doi.org/10.5281/zenodo.23984804","title":"Spheres and projective spaces determined by the one-form spectrum","display_name":"Spheres and projective spaces determined by the one-form spectrum","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225314247","doi":"https://doi.org/10.5281/zenodo.23984804"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23984804","doi":"https://doi.org/10.5281/zenodo.23984804","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23984804","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.23984804","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133211680","display_name":"Anass NIFA","orcid":"https://orcid.org/0000-0002-8986-7123","observed_orcids":["https://orcid.org/0000-0002-8986-7123"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nifa, Anass","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8986-7123","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133211680"],"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.48410001397132874,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.48410001397132874,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.29420000314712524,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.14499999582767487,"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/riemannian-manifolds","display_name":"Riemannian manifolds","score":0.7609999775886536},{"id":"https://openalex.org/keywords/sphere","display_name":"sphere","score":0.8920000195503235},{"id":"https://openalex.org/keywords/projective-space","display_name":"projective space","score":0.9129999876022339},{"id":"https://openalex.org/keywords/cayley-plane","display_name":"Cayley plane","score":0.9700000286102295},{"id":"https://openalex.org/keywords/complex-projective-space","display_name":"complex projective space","score":0.6909999847412109},{"id":"https://openalex.org/keywords/spectral-rigidity","display_name":"spectral rigidity","score":0.492000013589859},{"id":"https://openalex.org/keywords/curvature-bounds","display_name":"curvature bounds","score":0.5979999899864197},{"id":"https://openalex.org/keywords/jacobi-operator","display_name":"Jacobi operator","score":0.8799999952316284},{"id":"https://openalex.org/keywords/non-orientable-manifolds","display_name":"non-orientable manifolds","score":0.7829999923706055}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8698999881744385},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6876000165939331},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.6416000127792358},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.6287999749183655},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5579000115394592},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5573999881744385},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.5439000129699707},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.46209999918937683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45910000801086426},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.44130000472068787},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.4115999937057495},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.39910000562667847},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.39169999957084656},{"id":"https://openalex.org/C132702353","wikidata":"https://www.wikidata.org/wiki/Q2538404","display_name":"Complex projective space","level":4,"score":0.36959999799728394},{"id":"https://openalex.org/C37470923","wikidata":"https://www.wikidata.org/wiki/Q633815","display_name":"Real projective plane","level":5,"score":0.35690000653266907},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C90685605","wikidata":"https://www.wikidata.org/wiki/Q764115","display_name":"Projective line","level":4,"score":0.3564000129699707},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35589998960494995},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3402999937534332},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C163434512","wikidata":"https://www.wikidata.org/wiki/Q390741","display_name":"Collineation","level":4,"score":0.31949999928474426},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C84407019","wikidata":"https://www.wikidata.org/wiki/Q2724480","display_name":"Quaternionic projective space","level":5,"score":0.29510000348091125},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.2766999900341034},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2689000070095062},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.2506999969482422}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.23984804","doi":"https://doi.org/10.5281/zenodo.23984804","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23984804","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.23984805","doi":"https://doi.org/10.5281/zenodo.23984805","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23984805","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.24106555","doi":"https://doi.org/10.5281/zenodo.24106555","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24106555","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.23984804","doi":"https://doi.org/10.5281/zenodo.23984804","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23984804","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":0,"referenced_works":[],"related_works":["https://openalex.org/W2141824804","https://openalex.org/W7225178756","https://openalex.org/W1601441812","https://openalex.org/W1533921740","https://openalex.org/W1816535155","https://openalex.org/W2091222571","https://openalex.org/W2046525801","https://openalex.org/W4205180506","https://openalex.org/W2521857619","https://openalex.org/W7221549086"],"abstract_inverted_index":{"The":[0,23],"ordinary":[1],"one-form":[2],"spectrum":[3],"determines":[4,96,150],"the":[5,15,28,36,62,90,111,151],"standard":[6],"spheres,":[7],"real,":[8],"complex":[9,37],"and":[10,14,60,72,127],"quaternionic":[11],"projective":[12,38,136],"spaces,":[13],"Cayley":[16],"plane":[17,39],"among":[18,117],"closed":[19],"connected":[20],"Riemannian":[21],"manifolds.":[22],"same":[24],"conclusion":[25],"holds":[26,41],"in":[27,42,57,61,100,144],"complementary":[29,63],"degree":[30,44,58,64],"without":[31],"an":[32],"orientability":[33],"assumption;":[34],"for":[35,134],"it":[40],"each":[43],"0":[45],"\u2264":[46,48],"p":[47],"4.":[49],"Above":[50],"dimension":[51,139],"four,":[52,142],"partial":[53],"spectral":[54],"matchings":[55],"suffice":[56],"one":[59],"under":[65],"quantitative":[66],"bounds":[67],"on":[68],"omitted":[69],"eigenvalue":[70,92],"copies":[71],"matching":[73,80],"cost.":[74],"In":[75],"sufficiently":[76],"large":[77],"dimension,":[78],"a":[79,101,145],"after":[81],"independent":[82],"finite":[83],"omissions":[84],"with":[85],"error":[86],"o(\u03bd\u207b\u00b9),":[87],"uniformly":[88],"as":[89],"model":[91,99],"\u03bd":[93],"\u2192":[94,109],"\u221e,":[95,110],"every":[97],"d-dimensional":[98],"common":[102],"set":[103],"of":[104,114,138],"form":[105],"degrees.":[106],"As":[107],"d":[108,120],"lower":[112],"limit":[113],"their":[115],"proportion":[116],"0,":[118],"\u2026,":[119],"is":[121],"at":[122],"least":[123],"\u221a(8/21).":[124],"Heat":[125],"identities":[126],"geodesic":[128],"returns":[129],"give":[130],"averaged":[131],"curvature":[132],"bounds;":[133],"nonreal":[135],"targets":[137],"greater":[140],"than":[141],"equality":[143],"periodic":[146],"index":[147],"estimate":[148],"then":[149],"Jacobi":[152],"operators.":[153],"First":[154],"published":[155],"5":[156],"November":[157,163],"2026.":[158],"Version":[159],"2,":[160],"revised":[161],"10":[162],"2026":[164],"(39":[165],"pages).":[166]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-06T00:00:00"}
