{"id":"https://openalex.org/W7212266175","doi":"https://doi.org/10.48550/arxiv.2609.11469","title":"A proof of the Hodge universality conjecture at nonzero dispersion","display_name":"A proof of the Hodge universality conjecture at nonzero dispersion","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212266175","doi":"https://doi.org/10.48550/arxiv.2609.11469"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11469","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11469","pdf_url":"https://arxiv.org/pdf/2609.11469","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/2609.11469","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000060017","display_name":"Francisco Hern\u00e1ndez Iglesias","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Iglesias, Francisco Hern\u00e1ndez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5000060017"],"corresponding_institution_ids":[],"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.45649999380111694,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.45649999380111694,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.4503999948501587,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.011500000022351742,"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/miura-transformation","display_name":"Miura transformation","score":0.6740000247955322},{"id":"https://openalex.org/keywords/hodge-classes","display_name":"Hodge classes","score":0.6549999713897705},{"id":"https://openalex.org/keywords/dispersion","display_name":"dispersion","score":0.42800000309944153},{"id":"https://openalex.org/keywords/integrable-hierarchies","display_name":"integrable hierarchies","score":0.777999997138977},{"id":"https://openalex.org/keywords/gromov-witten-invariants","display_name":"Gromov-Witten invariants","score":0.6100000143051147}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8202999830245972},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.7718999981880188},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5899999737739563},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.45419999957084656},{"id":"https://openalex.org/C81265862","wikidata":"https://www.wikidata.org/wiki/Q225527","display_name":"Ramification","level":2,"score":0.4510999917984009},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4368000030517578},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42969998717308044},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3743000030517578},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3140000104904175},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29190000891685486},{"id":"https://openalex.org/C18556879","wikidata":"https://www.wikidata.org/wiki/Q753035","display_name":"Riemann surface","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C2779148545","wikidata":"https://www.wikidata.org/wiki/Q6382014","display_name":"KdV hierarchy","level":4,"score":0.26820001006126404},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.25450000166893005}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11469","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11469","pdf_url":"https://arxiv.org/pdf/2609.11469","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.2609.11469","doi":"https://doi.org/10.48550/arxiv.2609.11469","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11469","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:2609.11469","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11469","pdf_url":"https://arxiv.org/pdf/2609.11469","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/W7212266175.pdf","grobid_xml":"https://content.openalex.org/works/W7212266175.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1570788505","https://openalex.org/W2036639310","https://openalex.org/W2047218706","https://openalex.org/W2088578613","https://openalex.org/W2093785095","https://openalex.org/W2097619526","https://openalex.org/W2141227353","https://openalex.org/W2282914807","https://openalex.org/W2520657557","https://openalex.org/W4385681994","https://openalex.org/W4398229806","https://openalex.org/W4415309250","https://openalex.org/W7104951757","https://openalex.org/W7125145667"],"related_works":["https://openalex.org/W4415309250","https://openalex.org/W4414381867","https://openalex.org/W2138945228","https://openalex.org/W7099471801","https://openalex.org/W4393970454","https://openalex.org/W2122744474","https://openalex.org/W2963207207","https://openalex.org/W2512767861","https://openalex.org/W1970621705","https://openalex.org/W1448727407"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"a":[3],"scalar":[4],"tau-symmetric":[5],"Hamiltonian":[6,34],"deformation":[7],"of":[8,23,28,50],"the":[9,20,26,38,48],"Riemann":[10],"hierarchy":[11,40],"in":[12,31],"generalized":[13],"standard":[14],"form":[15],"is":[16],"uniquely":[17],"determined":[18],"by":[19,55],"nonzero":[21,62],"coefficient":[22],"$u_x^2$":[24],"and":[25],"coefficients":[27],"$u_{xx}^g$,":[29],"$g\\ge2$,":[30],"its":[32],"first":[33],"density.":[35],"This":[36],"determines":[37],"original":[39],"up":[41],"to":[42],"normal":[43],"Miura":[44],"transformations.":[45],"Combined":[46],"with":[47],"construction":[49],"Hodge-class":[51],"double":[52],"ramification":[53],"hierarchies":[54],"Buryak--Rossi,":[56],"this":[57],"establishes":[58],"Hodge":[59],"universality":[60],"at":[61],"dispersion.":[63]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}