{"id":"https://openalex.org/W7166344113","doi":"https://doi.org/10.5281/zenodo.20971615","title":"A Mathematical Framework for Universal Operators","display_name":"A Mathematical Framework for Universal Operators","publication_year":2026,"publication_date":"2026-06-27","ids":{"openalex":"https://openalex.org/W7166344113","doi":"https://doi.org/10.5281/zenodo.20971615"},"language":"en","primary_location":{"id":"pmh:oai:philpapers.org/rec/BAIAMF","doi":null,"is_oa":true,"landing_page_url":"https://philpapers.org/rec/BAIAMF","pdf_url":"https://philpapers.org/archive/BAIAMF.pdf","source":{"id":"https://openalex.org/S4306402130","display_name":"PhilPapers (PhilPapers Foundation)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/article"},"volume":null,"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://philpapers.org/archive/BAIAMF.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133586093","display_name":"Denis Bailey","orcid":"https://orcid.org/0009-0006-9228-1285","observed_orcids":["https://orcid.org/0009-0006-9228-1285"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bailey, Denis","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0006-9228-1285","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133586093"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.5364834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T14299","display_name":"Complex Systems and Dynamics","score":0.9907000064849854,"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/T14299","display_name":"Complex Systems and Dynamics","score":0.9907000064849854,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.005100000184029341,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13898","display_name":"Diverse Interdisciplinary Research Studies","score":0.00139999995008111,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/universal-operators","display_name":"universal operators","score":0.9800000190734863},{"id":"https://openalex.org/keywords/generative-systems","display_name":"generative systems","score":0.8019999861717224},{"id":"https://openalex.org/keywords/state-space","display_name":"state space","score":0.4880000054836273},{"id":"https://openalex.org/keywords/collapse-dynamics","display_name":"collapse dynamics","score":0.9890000224113464},{"id":"https://openalex.org/keywords/emergent-time","display_name":"emergent time","score":0.8510000109672546},{"id":"https://openalex.org/keywords/generative-dynamics","display_name":"generative dynamics","score":0.7730000019073486}],"concepts":[{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.49470001459121704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48660001158714294},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4810999929904938},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.4805999994277954},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4239000082015991},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.4223000109195709},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4050999879837036},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C2778738651","wikidata":"https://www.wikidata.org/wiki/Q16546687","display_name":"Novelty","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3273000121116638},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.30250000953674316},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:philpapers.org/rec/BAIAMF","doi":null,"is_oa":true,"landing_page_url":"https://philpapers.org/rec/BAIAMF","pdf_url":"https://philpapers.org/archive/BAIAMF.pdf","source":{"id":"https://openalex.org/S4306402130","display_name":"PhilPapers (PhilPapers Foundation)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/article"},{"id":"doi:10.5281/zenodo.20971615","doi":"https://doi.org/10.5281/zenodo.20971615","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20971615","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":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.20971616","doi":"https://doi.org/10.5281/zenodo.20971616","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20971616","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:philpapers.org/rec/BAIAMF","doi":null,"is_oa":true,"landing_page_url":"https://philpapers.org/rec/BAIAMF","pdf_url":"https://philpapers.org/archive/BAIAMF.pdf","source":{"id":"https://openalex.org/S4306402130","display_name":"PhilPapers (PhilPapers Foundation)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.41565075516700745}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7166344113.pdf","grobid_xml":"https://content.openalex.org/works/W7166344113.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"Mathematical":[1],"Framework":[2],"for":[3,11],"Universal":[4],"Operators":[5],"develops":[6],"a":[7,34,56,89,99],"substrate\u2011agnostic":[8],"mathematical":[9],"architecture":[10],"generative":[12,78,123],"systems":[13],"by":[14],"formalizing":[15],"the":[16,75],"operator":[17],"stack":[18],"\u2014":[19,29],"orientation,":[20],"separation,":[21],"constraint,":[22],"coherence,":[23],"collapse,":[24],"identity,":[25],"duration,":[26],"and":[27,51,63,69,95,113,116],"evolution":[28],"as":[30,74,88,98],"regime\u2011dependent":[31],"transformations":[32],"over":[33],"state\u2011space.":[35],"The":[36,104],"paper":[37],"defines":[38],"system":[39],"states,":[40],"constraint":[41],"fields,":[42],"coherence":[43,83],"basins,":[44],"collapse":[45,80,102],"dynamics,":[46],"identity":[47,86],"fixed\u2011points,":[48],"duration":[49,91],"integrals,":[50],"emergent":[52],"temporal":[53],"residues,":[54],"establishing":[55],"unified":[57],"model":[58],"of":[59,77,101,118,122],"stability,":[60],"transition,":[61],"persistence,":[62,94],"novelty":[64],"across":[65],"physical,":[66],"cognitive,":[67],"social,":[68],"artificial":[70],"domains.":[71],"Constraint":[72],"acts":[73],"regulator":[76],"behavior,":[79],"provides":[81],"resolution,":[82],"stabilizes":[84],"patterns,":[85],"emerges":[87],"fixed\u2011point,":[90],"measures":[92],"structural":[93],"time":[96],"arises":[97],"residue":[100],"events.":[103],"resulting":[105],"framework":[106],"is":[107],"mathematically":[108],"tractable,":[109],"extensible":[110],"to":[111],"tensor":[112],"manifold":[114],"formulations,":[115],"capable":[117],"supporting":[119],"computational":[120],"modeling":[121],"dynamics.":[124],"Cited":[125],"lines:":[126]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-06-28T00:00:00"}
