{"id":"https://openalex.org/W7225792247","doi":"https://doi.org/10.5281/zenodo.24131316","title":"Pure Algebraic Formulation of Casimir Variational Decomposition and Non-Commutative Arithmetic Heights: A Formally Verified Framework","display_name":"Pure Algebraic Formulation of Casimir Variational Decomposition and Non-Commutative Arithmetic Heights: A Formally Verified Framework","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225792247","doi":"https://doi.org/10.5281/zenodo.24131316"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24131316","doi":"https://doi.org/10.5281/zenodo.24131316","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24131316","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.24131316","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161374538","display_name":"Reiji Yoshikai","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yoshikai, Reiji","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161374538"],"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.4203999936580658,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.4203999936580658,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.23430000245571136,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.10620000213384628,"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":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8571000099182129},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43720000982284546},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.43130001425743103},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41429999470710754},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37450000643730164},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.3707999885082245},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.3345000147819519},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.3095000088214874},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C196434610","wikidata":"https://www.wikidata.org/wiki/Q1208658","display_name":"Ring theory","level":4,"score":0.2599000036716461},{"id":"https://openalex.org/C199793520","wikidata":"https://www.wikidata.org/wiki/Q4723996","display_name":"Algebraic cycle","level":3,"score":0.2556000053882599},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24131316","doi":"https://doi.org/10.5281/zenodo.24131316","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24131316","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.24131317","doi":"https://doi.org/10.5281/zenodo.24131317","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24131317","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.24131316","doi":"https://doi.org/10.5281/zenodo.24131316","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24131316","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":[],"abstract_inverted_index":{"We":[0,54,170],"establish":[1],"a":[2,45,172],"self-contained,":[3],"purely":[4],"algebraic":[5,125,151],"formulation":[6],"of":[7,11,63,99],"the":[8,15,52,84,96,116,163,178,187],"variational":[9],"decomposition":[10],"finite-dimensional":[12],"representations":[13,62],"over":[14],"complex":[16],"Lie":[17],"algebra":[18],"sl2(C)":[19],"and":[20,127],"construct":[21],"an":[22,158],"arithmetic":[23,159],"bridge":[24],"to":[25,185],"Diophantine":[26],"geometry":[27],"via":[28],"non-commutative":[29,164],"height":[30,160],"functions.First,":[31],"eliminating":[32],"all":[33],"physical":[34],"heuristics":[35],"(such":[36],"as":[37],"D-branes,":[38],"dielectric":[39],"polarizations,":[40],"andgauge":[41],"instantons),":[42],"we":[43,121,148],"define":[44],"canonical":[46],"cubic-Casimir":[47],"trace":[48],"functional":[49,101],"V":[50],"on":[51,162],"categoryRepfd(sl2(C)).":[53],"prove":[55,128],"that":[56,177],"under":[57],"norm-preserving":[58],"bilinear":[59],"decomposition,":[60],"compositedimensional":[61],"rank":[64],"n":[65],"=":[66,168],"ab":[67],"(a,b":[68],"\u2265":[69],"2)":[70],"are":[71,110],"strictly":[72,85],"unstable":[73],"with":[74],"respectto":[75],"V,":[76],"relaxing":[77],"unconditionally":[78],"into":[79,154],"tensor-product":[80],"factors":[81],"governed":[82],"by":[83,156],"positivequartic":[86],"identity":[87],"ab(a2":[88],"\u2212":[89,91],"1)(b2":[90],"1)":[92],">":[93],"0.":[94],"Consequently,":[95],"critical":[97],"points":[98],"minimal":[100],"value":[102],"terminate":[103],"uniquely":[104],"at":[105],"irreducible":[106],"blocks":[107],"whose":[108],"dimensions":[109],"prime":[111,152],"numbersp":[112],"\u2208":[113],"P.":[114],"In":[115],"proof":[117],"assistant":[118],"Lean":[119],"4,":[120],"formalize":[122],"this":[123,150],"entire":[124],"core":[126],"thebi-directional":[129],"logical":[130],"equivalence":[131],"between":[132],"representation-theoretic":[133],"tensor":[134],"irreducibility":[135],"andclassical":[136],"primality":[137],"(IsPrimeDim(p)":[138],"\u2194":[139],"StandardPrime(p))":[140],"without":[141],"axioms":[142],"or":[143],"circular":[144],"hypotheses":[145],"(sorry-free).":[146],"Second,":[147],"translate":[149],"selection":[153],"Diophantinegeometry":[155],"constructing":[157],"function":[161],"direct":[165],"sumalgebra":[166],"An":[167],"\u2a01\ufe01p|nMp(C).":[169],"formulate":[171],"conditional":[173],"characterization":[174],"theorem":[175],"establishing":[176],"bounded":[179],"determinantal":[180],"distortion":[181],"condition":[182],"is":[183],"sufficient":[184],"yield":[186],"classicalDiophantine":[188],"radical":[189],"bound":[190],"c":[191],"\u2264":[192],"C\u03f5rad(abc)1+\u03f5,":[193],"elucidating":[194],"its":[195],"conceptual":[196],"correspondence":[197],"toMochizuki\u2019s":[198],"log-shells":[199],"in":[200],"Inter-Universal":[201],"Teichm\u00a8uller":[202],"theory.":[203]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
