{"id":"https://openalex.org/W7143345772","doi":"https://doi.org/10.5281/zenodo.19341701","title":"Spectral Syzygies, Arithmetic Selection, and Galois Rigidity in Octonionic Flavor Structure","display_name":"Spectral Syzygies, Arithmetic Selection, and Galois Rigidity in Octonionic Flavor Structure","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7143345772","doi":"https://doi.org/10.5281/zenodo.19341701"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.19341701","doi":"https://doi.org/10.5281/zenodo.19341701","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19341701","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.19341701","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008734547","display_name":"M. Bakhtaoui","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bakhtaoui, Michel A.","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0006-6710-7787","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5008734547"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.6294000148773193,"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"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.6294000148773193,"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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.2655999958515167,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.040699999779462814,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/octonions","display_name":"octonions","score":0.972000002861023},{"id":"https://openalex.org/keywords/flavor-symmetry","display_name":"flavor symmetry","score":0.5899999737739563},{"id":"https://openalex.org/keywords/yukawa-couplings","display_name":"Yukawa couplings","score":0.8820000290870667},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"characteristic polynomial","score":0.8029999732971191},{"id":"https://openalex.org/keywords/fano-plane","display_name":"Fano plane","score":0.8610000014305115},{"id":"https://openalex.org/keywords/casimir-operators","display_name":"Casimir operators","score":0.7089999914169312},{"id":"https://openalex.org/keywords/cp-violation","display_name":"CP violation","score":0.8920000195503235},{"id":"https://openalex.org/keywords/vacuum-phase","display_name":"vacuum phase","score":0.9089999794960022}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8337000012397766},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5630999803543091},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4839000105857849},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C39757861","wikidata":"https://www.wikidata.org/wiki/Q1395814","display_name":"Fano plane","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.35100001096725464},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.34369999170303345},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.3418000042438507},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29899999499320984},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28029999136924744},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.25870001316070557}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.19341701","doi":"https://doi.org/10.5281/zenodo.19341701","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19341701","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.19341702","doi":"https://doi.org/10.5281/zenodo.19341702","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19341702","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.19802659","doi":"https://doi.org/10.5281/zenodo.19802659","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19802659","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.19341701","doi":"https://doi.org/10.5281/zenodo.19341701","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19341701","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/W7221568185","https://openalex.org/W7131065003","https://openalex.org/W7140907166","https://openalex.org/W7128953697","https://openalex.org/W7134111344","https://openalex.org/W7155721006","https://openalex.org/W7166811107","https://openalex.org/W7165379666","https://openalex.org/W7164754652","https://openalex.org/W7165531045"],"abstract_inverted_index":{"We":[0],"establish":[1],"exact":[2],"spectral":[3],"laws":[4],"(syzygies)":[5],"for":[6,135],"the":[7,13,18,24,34,45,62,76],"two":[8,70],"physical":[9,103],"Yukawa":[10],"channels":[11],"of":[12,26],"octonionic":[14],"flavor":[15],"framework.":[16],"In":[17,33],"protected":[19],"channel":[20,36],"T_u":[21],"=":[22,38,51,80],"(2,4,6),":[23],"product":[25],"eigenvalues":[27],"is":[28,115],"affine":[29,68],"in":[30,55,117],"their":[31],"sum.":[32],"charged":[35],"T_d":[37],"(3,5,6),":[39],"a":[40,95],"factorized":[41],"characteristic":[42],"polynomial":[43],"selects":[44],"unique":[46],"rational":[47],"interior":[48],"point":[49],"t":[50],"6/7":[52],"with":[53,82,107],"spectrum":[54],"Q(\u221a3).":[56],"A":[57],"three-entry":[58],"Gram":[59],"lemma":[60],"classifies":[61],"seven":[63],"Fano":[64],"lines":[65],"into":[66],"five":[67],"and":[69,109],"radical.":[71],"The":[72,86,102],"Casimir":[73,129],"commutator":[74],"satisfies":[75],"cubic":[77],"law":[78],"C\u2082\u00b3":[79],"\u2212\u03c9\u00b2C\u2082":[81],"\u03c9\u00b2":[83],"\u2208":[84],"Q(\u221a6).":[85],"four-field":[87],"arithmetic":[88],"constellation":[89],"Q(\u221a2),":[90],"Q(\u221a3),":[91],"Q(\u221a5),":[92],"Q(\u221a6)":[93],"forms":[94],"Galois":[96],"sub-complex":[97],"stable":[98],"under":[99],"order-2":[100],"corrections.":[101],"reading,":[104],"including":[105],"comparison":[106],"entanglement-minimization":[108],"vacuum-phase":[110],"approaches":[111],"to":[112],"CP":[113],"violation,":[114],"discussed":[116],"Section":[118],"10.":[119],"v2:":[120],"substantially":[121],"revised":[122],"introduction,":[123],"expanded":[124],"bibliography":[125],"(43":[126],"references),":[127],"explicit":[128],"matrices,":[130],"Fano-plane":[131],"figure":[132],"added.":[133],"Prepared":[134],"journal":[136],"submission.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-03-31T00:00:00"}
