{"id":"https://openalex.org/W7164034924","doi":"https://doi.org/10.48550/arxiv.2606.08902","title":"A Kernel-Clean Lean Mechanization of Classical Lottery in Action and the Wakker--Debreu--Koopmans Representation Layer","display_name":"A Kernel-Clean Lean Mechanization of Classical Lottery in Action and the Wakker--Debreu--Koopmans Representation Layer","publication_year":2026,"publication_date":"2026-06-08","ids":{"openalex":"https://openalex.org/W7164034924","doi":"https://doi.org/10.48550/arxiv.2606.08902"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.08902","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08902","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.08902","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138257468","display_name":"Jingyuan Li (53885)","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Jingyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138263696","display_name":"Ilia Tsetlin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tsetlin, Ilia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138270841","display_name":"Fan Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Fan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T11182","display_name":"Auction Theory and Applications","score":0.4047999978065491,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.4047999978065491,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.3619000017642975,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.030700000002980232,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7451000213623047},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6225000023841858},{"id":"https://openalex.org/keywords/lottery","display_name":"Lottery","score":0.6069999933242798},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5652999877929688},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.4950999915599823},{"id":"https://openalex.org/keywords/representation-theorem","display_name":"Representation theorem","score":0.38839998841285706}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7451000213623047},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6687999963760376},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6225000023841858},{"id":"https://openalex.org/C2777340749","wikidata":"https://www.wikidata.org/wiki/Q6684955","display_name":"Lottery","level":2,"score":0.6069999933242798},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5652999877929688},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.4950999915599823},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4603999853134155},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C2777152325","wikidata":"https://www.wikidata.org/wiki/Q108163","display_name":"Proposition","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3345000147819519},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C2776542497","wikidata":"https://www.wikidata.org/wiki/Q5266672","display_name":"Development (topology)","level":2,"score":0.2815999984741211}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.08902","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08902","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.08902","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08902","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,58],"present":[1],"a":[2,28,159],"Lean":[3,131],"4/Mathlib":[4],"formalization":[5],"of":[6,45],"the":[7,17,32,42,71,91,153],"additive":[8,46,108,165],"representation":[9],"theory":[10],"behind":[11],"Classical":[12],"Lottery":[13],"in":[14],"Action":[15],"and":[16,55,83,106,148,170],"Wakker-Debreu-Koopmans":[18],"(WDK)":[19],"layer":[20],"it":[21,172],"relies":[22],"on.":[23],"Our":[24],"central":[25],"result":[26],"is":[27,39,125],"machine-checked":[29],"proof":[30],"that":[31],"cross-pair":[33,72],"Thomsen":[34],"/":[35],"double-cancellation":[36],"(hexagon)":[37],"condition":[38],"irreducible":[40,120],"from":[41,98,104],"ordinal":[43,67],"axioms":[44,68],"conjoint":[47,166],"measurement":[48,167],"(weak":[49],"order,":[50],"restricted":[51],"solvability,":[52],"Archimedean":[53],"condition,":[54,73],"tradeoff":[56],"consistency).":[57],"exhibit":[59],"an":[60,80],"explicit":[61],"verified":[62],"counter-model":[63],"(additiveRealBoolPref)":[64],"satisfying":[65],"all":[66],"yet":[69],"failing":[70],"with":[74],"every":[75],"strict":[76],"standard":[77,130],"sequence":[78],"being":[79],"arithmetic":[81],"progression":[82],"hence":[84],"non-dense.":[85],"Around":[86],"this":[87,118],"boundary":[88],"we":[89],"mechanize":[90],"full":[92],"derivable":[93],"construction:":[94],"continuous":[95],"Debreu/Eilenberg":[96],"utility":[97],"separability,":[99],"standard-sequence":[100],"grids,":[101],"bisection":[102],"methods":[103],"connectedness,":[105],"global":[107],"gluing.":[109],"All":[110],"public":[111],"theorems":[112],"are":[113],"sorry-free":[114],"conditional":[115],"wrappers":[116],"over":[117],"single":[119],"structural":[121],"input.":[122],"The":[123,136],"development":[124],"kernel-clean,":[126],"depending":[127],"only":[128],"on":[129],"foundations":[132],"(propext,":[133],"Classical.choice,":[134],"Quot.sound).":[135],"companion":[137],"file":[138],"ClassicalLotteryInAction.lean":[139],"formalizes":[140],"local":[141],"classical-lottery":[142],"constructions,":[143],"average-utility":[144],"results,":[145],"matching-frequency":[146],"lemmas,":[147],"ambiguity-attitude":[149],"statements":[150],"used":[151],"by":[152],"Management":[154],"Science":[155],"paper.":[156],"This":[157],"draws":[158],"precise,":[160],"machine-certified":[161],"line":[162],"between":[163],"what":[164,171],"can":[168],"prove":[169],"must":[173],"assume.":[174]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-10T00:00:00"}