{"id":"https://openalex.org/W7225617815","doi":"https://doi.org/10.5281/zenodo.24083828","title":"Which Bell Causality? Operational Abelianization and a Rideout\u2013Sorkin Theorem for Quantum Sequential Growth","display_name":"Which Bell Causality? Operational Abelianization and a Rideout\u2013Sorkin Theorem for Quantum Sequential Growth","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225617815","doi":"https://doi.org/10.5281/zenodo.24083828"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24083828","doi":"https://doi.org/10.5281/zenodo.24083828","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24083828","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.24083828","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160292797","display_name":"Thomas G Hamilton","orcid":"https://orcid.org/0000-0001-8050-5743","observed_orcids":["https://orcid.org/0000-0001-8050-5743"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hamilton, Thomas G.","raw_affiliation_strings":["Olive Tree International Academy"],"raw_orcid":"https://orcid.org/0000-0001-8050-5743","affiliations":[{"raw_affiliation_string":"Olive Tree International Academy","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160292797"],"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.42480000853538513,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.42480000853538513,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.2468000054359436,"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/T12162","display_name":"Cellular Automata and Applications","score":0.09929999709129333,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.6654999852180481},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.49470001459121704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47360000014305115},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4507000148296356},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.44110000133514404},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4189000129699707},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4169999957084656},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.38960000872612},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3296999931335449},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3296999931335449},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.3003000020980835},{"id":"https://openalex.org/C114852677","wikidata":"https://www.wikidata.org/wiki/Q899044","display_name":"Fock space","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24083828","doi":"https://doi.org/10.5281/zenodo.24083828","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24083828","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.24083829","doi":"https://doi.org/10.5281/zenodo.24083829","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24083829","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.24083828","doi":"https://doi.org/10.5281/zenodo.24083828","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24083828","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/W7225410441","https://openalex.org/W7225620553","https://openalex.org/W7202023390","https://openalex.org/W7202160862","https://openalex.org/W3086918131","https://openalex.org/W7134199664","https://openalex.org/W7213036957","https://openalex.org/W4245472834","https://openalex.org/W7163999939","https://openalex.org/W7169657248"],"abstract_inverted_index":{"Classical":[0],"Rideout\u2013Sorkin":[1,80],"growth":[2,284],"is":[3],"constrained":[4],"by":[5],"Bell-type":[6],"spectator":[7],"independence,":[8],"whose":[9],"equivalent":[10,16],"scalar":[11],"formulations":[12],"need":[13],"not":[14,169,269],"remain":[15],"for":[17,27],"noncommuting":[18],"quantum":[19,33,282,304],"transitions.":[20],"We":[21],"ask":[22],"which":[23],"comparison":[24],"domains":[25],"matter":[26],"the":[28,73,89,98,124,146,181,206,223,227,232,243,259,261],"finite-cylinder":[29,152,165],"predictions":[30],"of":[31,57,126,178],"causal-past-ordered":[32],"sequential":[34,283,305],"growth.":[35],"Four":[36],"conventions":[37,91],"are":[38,105,256,263],"distinguished:":[39],"own-core,":[40],"direct,":[41],"source-faithful,":[42],"and":[43,54,67,139,163,184,188,211,219,249,291,297,300],"broad.":[44],"With":[45],"invertible":[46],"finite-dimensional":[47],"transitions,":[48],"an":[49,78,112,171],"operator":[50,99,158],"Markov":[51],"sum":[52],"rule,":[53],"strict":[55],"covariance":[56],"reached":[58,74,108,161],"vectors,":[59],"direct":[60],"Bell":[61],"implies":[62],"a":[63,68,83,119,131,140,189,275],"parent-independent":[64],"precursor":[65],"factorization":[66],"faithful":[69],"commutative":[70],"algebra":[71],"on":[72,107],"module.":[75],"This":[76],"yields":[77],"algebra-valued":[79],"reconstruction":[81],"with":[82,215],"single":[84],"exceptional":[85],"junction":[86,147],"correction.":[87],"Although":[88],"four":[90],"have":[92],"strictly":[93],"different":[94],"full-matrix":[95],"solution":[96],"classes,":[97],"defects":[100],"in":[101,205,258,274,303],"three":[102],"separating":[103],"examples":[104],"invisible":[106],"states.":[109],"By":[110],"contrast,":[111],"explicit":[113],"all-stage":[114,136,254],"rank-two":[115],"own-core":[116],"model":[117],"violates":[118],"direct-Bell":[120],"graft":[121],"constraint":[122],"at":[123],"level":[125],"its":[127,185,236],"Gram":[128],"kernel,":[129],"establishing":[130],"genuine":[132],"predictive":[133],"separation.":[134],"An":[135],"broad-Bell":[137],"example":[138],"general":[141],"visibility":[142],"criterion":[143],"show":[144],"that":[145,199],"correction":[148],"can":[149],"also":[150],"affect":[151],"interference.":[153],"These":[154],"results":[155],"distinguish":[156],"full":[157],"identities":[159],"from":[160],"dynamics":[162],"coherent":[164],"data;":[166],"they":[167],"do":[168],"claim":[170],"extension":[172],"to":[173],"covariant":[174],"infinite-history":[175],"events.":[176],"Contents":[177],"this":[179],"record:":[180],"manuscript":[182],"(PDF)":[183],"LaTeX":[186],"source,":[187],"certificates":[190,248],"bundle.":[191],"The":[192,253],"bundle":[193,233],"holds":[194],"ten":[195,247],"standalone":[196],"Python":[197,228],"scripts":[198,224,262],"check":[200],"every":[201],"finite":[202,264],"computation":[203],"cited":[204],"paper":[207,273],"using":[208],"exact":[209],"integer":[210],"rational":[212],"arithmetic,":[213],"together":[214],"their":[216],"result":[217],"files":[218],"SHA-256":[220],"checksums.":[221],"Reproducibility:":[222],"use":[225],"only":[226],"standard":[229],"library.":[230],"Unzip":[231],"and,":[234],"inside":[235],"folder,":[237],"run:":[238],"python3":[239],"run_all.py.":[240],"It":[241],"verifies":[242],"checksums,":[244],"runs":[245],"all":[246],"reports":[250],"ALL":[251],"PASS.":[252],"theorems":[255],"proved":[257],"manuscript;":[260],"checks.":[265],"Status:":[266],"research":[267],"preprint,":[268],"peer":[270],"reviewed.":[271],"Third":[272],"series,":[276],"following":[277],"T.":[278],"G.":[279],"Hamilton,":[280],"\"Noncommutative":[281],"under":[285],"state-level":[286],"covariance:":[287],"existence,":[288],"fixed-seed":[289],"rigidity,":[290],"geometric":[292],"limits\",":[293],"Zenodo":[294,307],"(2026),":[295,308],"doi:10.5281/zenodo.23953788,":[296],"\"Bell":[298],"causality":[299],"operational":[301],"rigidity":[302],"growth\",":[306],"doi:10.5281/zenodo.24006143.----":[309]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}