{"id":"https://openalex.org/W7213345831","doi":"https://doi.org/10.48550/arxiv.2609.13915","title":"Invariant Algebras of Low-Rank Neutrino Matter Flows: Krylov-Pl\u00fccker Invariants, the $3+1$ Toric Ring, and Controlled Deformations","display_name":"Invariant Algebras of Low-Rank Neutrino Matter Flows: Krylov-Pl\u00fccker Invariants, the $3+1$ Toric Ring, and Controlled Deformations","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213345831","doi":"https://doi.org/10.48550/arxiv.2609.13915"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13915","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13915","pdf_url":"https://arxiv.org/pdf/2609.13915","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/2609.13915","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040915620","display_name":"Jianlong Lu","orcid":"https://orcid.org/0000-0003-4827-7159","observed_orcids":["https://orcid.org/0000-0003-4827-7159"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Lu, Jianlong","raw_affiliation_strings":["Department of Mathematics , National University of Singapore , Singapore 119076"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , National University of Singapore , Singapore 119076","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040915620"],"corresponding_institution_ids":["https://openalex.org/I165932596"],"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/T10921","display_name":"Neutrino Physics Research","score":0.9833999872207642,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10921","display_name":"Neutrino Physics Research","score":0.9833999872207642,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.005499999970197678,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/neutrino-oscillations","display_name":"neutrino oscillations","score":0.8029999732971191},{"id":"https://openalex.org/keywords/matter-potential","display_name":"matter potential","score":0.5329999923706055},{"id":"https://openalex.org/keywords/algebra-of-invariants","display_name":"algebra of invariants","score":0.7680000066757202},{"id":"https://openalex.org/keywords/plucker-relations","display_name":"Pl\u00fccker relations","score":0.7200000286102295},{"id":"https://openalex.org/keywords/exterior-algebra","display_name":"exterior algebra","score":0.4320000112056732},{"id":"https://openalex.org/keywords/maximal-minors","display_name":"maximal minors","score":0.5910000205039978},{"id":"https://openalex.org/keywords/controlled-deformation","display_name":"controlled deformation","score":0.6380000114440918},{"id":"https://openalex.org/keywords/spectral-factorization","display_name":"spectral factorization","score":0.7360000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6661999821662903},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5189999938011169},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.49959999322891235},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4675999879837036},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4140999913215637},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.35760000348091125},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C89890916","wikidata":"https://www.wikidata.org/wiki/Q3738073","display_name":"Jordan matrix","level":3,"score":0.3140999972820282},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.30869999527931213},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.2685000002384186},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2662000060081482},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2619999945163727},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C2776196297","wikidata":"https://www.wikidata.org/wiki/Q17138781","display_name":"Twist","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13915","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13915","pdf_url":"https://arxiv.org/pdf/2609.13915","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.2609.13915","doi":"https://doi.org/10.48550/arxiv.2609.13915","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13915","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":"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":"pmh:oai:arXiv.org:2609.13915","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13915","pdf_url":"https://arxiv.org/pdf/2609.13915","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/W7213345831.pdf","grobid_xml":"https://content.openalex.org/works/W7213345831.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7204778320","https://openalex.org/W4402964890","https://openalex.org/W2090211049","https://openalex.org/W7171921039","https://openalex.org/W7154943526","https://openalex.org/W7218266555","https://openalex.org/W7140907166","https://openalex.org/W4404541071","https://openalex.org/W1544114753","https://openalex.org/W7095817440"],"abstract_inverted_index":{"Matter":[0],"changes":[1],"the":[2,8,14,29,43,51,117,146,151,165,203,209,215],"eigenvalues":[3],"and":[4,68,85,162,190,199,217],"mixing":[5],"matrix":[6],"of":[7,28,46,83,128,150,202,211,220],"neutrino":[9],"propagation":[10],"Hamiltonian":[11,16],"while":[12],"entering":[13],"flavor-basis":[15],"through":[17],"a":[18,24,61,111,126,171,178],"low-dimensional":[19],"additive":[20],"deformation.":[21,36],"We":[22,183],"develop":[23],"unified":[25],"algebraic":[26],"description":[27],"quantities":[30],"that":[31],"are":[32,104],"insensitive":[33],"to":[34],"this":[35,59],"The":[37,132],"invariant":[38,53,204],"algebra":[39,144],"is":[40,110,145],"formulated":[41],"as":[42],"joint":[44],"kernel":[45],"commuting":[47,196],"matter-translation":[48],"derivations":[49],"inside":[50],"flavor-rephasing":[52],"ring.":[54],"For":[55,89],"diagonal":[56,66],"matter":[57,87,90,105,188],"potentials,":[58],"gives":[60],"general":[62],"decomposition":[63],"into":[64],"unaffected":[65],"directions":[67],"an":[69,75,80],"off-diagonal":[70,143,191],"cycle":[71,148],"algebra,":[72],"together":[73],"with":[74,92],"exact":[76,197,212],"dimension":[77],"formula":[78],"for":[79],"arbitrary":[81],"number":[82],"flavors":[84],"independent":[86,129],"parameters.":[88],"spurions":[91],"common":[93],"low-rank":[94],"support,":[95],"block-Krylov":[96],"rows":[97],"generate":[98],"exterior-power":[99],"covariants":[100],"whose":[101],"maximal":[102],"minors":[103],"independent.":[106],"Their":[107],"mass-basis":[108],"form":[109],"Pl\u00fccker":[112,130],"expansion:":[113],"rank":[114,123],"one":[115],"produces":[116,125],"familiar":[118],"Vandermonde":[119],"factorization,":[120],"whereas":[121],"higher":[122],"generically":[124],"sum":[127],"terms.":[131],"standard":[133],"$3+1$":[134],"system":[135,175],"provides":[136],"our":[137],"principal":[138],"nontrivial":[139],"example.":[140],"Its":[141],"global":[142,179],"toric":[147],"ring":[149],"complete":[152],"four-vertex":[153],"flavor":[154],"graph,":[155],"generated":[156],"by":[157],"edge":[158],"moduli,":[159],"triangle":[160],"cycles,":[161],"quadrangle":[163],"cycles;":[164],"commonly":[166],"used":[167],"eleven":[168],"invariants":[169,213],"constitute":[170],"generic":[172],"local":[173],"coordinate":[174],"rather":[176],"than":[177],"polynomial":[180],"generating":[181],"set.":[182],"further":[184],"formulate":[185],"independently":[186],"varying":[187],"compositions":[189],"nonstandard":[192],"interactions":[193],"as,":[194],"respectively,":[195],"flows":[198],"controlled":[200],"deformations":[201],"algebra.":[205],"This":[206],"framework":[207],"separates":[208],"existence":[210],"from":[214],"stronger":[216],"exceptional":[218],"property":[219],"single-monomial":[221],"spectral":[222],"factorization.":[223]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-16T00:00:00"}
