{"id":"https://openalex.org/W7225826455","doi":"https://doi.org/10.5281/zenodo.24128335","title":"The Modal Geometry of the Intelligible","display_name":"The Modal Geometry of the Intelligible","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225826455","doi":"https://doi.org/10.5281/zenodo.24128335"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24128335","doi":"https://doi.org/10.5281/zenodo.24128335","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24128335","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":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24128335","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148618648","display_name":"Eric Theriault","orcid":"https://orcid.org/0009-0006-0664-3973","observed_orcids":["https://orcid.org/0009-0006-0664-3973"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Theriault, Eric","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":"https://orcid.org/0009-0006-0664-3973","affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159020362","display_name":"DeepSeek A.I.","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"DeepSeek A.I.","raw_affiliation_strings":["Hangzhou"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hangzhou","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.9253000020980835,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.9253000020980835,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.029500000178813934,"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"}},{"id":"https://openalex.org/T13558","display_name":"Logic and Philosophy of Science","score":0.011900000274181366,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.6621000170707703},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.6316999793052673},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.5141000151634216},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.475600004196167},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.451200008392334},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4487000107765198},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.38769999146461487},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.3668000102043152},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.36480000615119934},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3407000005245209},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.3285999894142151},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.3165000081062317},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31360000371932983},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.287200003862381},{"id":"https://openalex.org/C178736951","wikidata":"https://www.wikidata.org/wiki/Q3780658","display_name":"Modal analysis using FEM","level":5,"score":0.287200003862381},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26660001277923584},{"id":"https://openalex.org/C200239387","wikidata":"https://www.wikidata.org/wiki/Q17143727","display_name":"Modal testing","level":4,"score":0.26330000162124634},{"id":"https://openalex.org/C135315306","wikidata":"https://www.wikidata.org/wiki/Q866364","display_name":"Bisimulation","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.2574000060558319},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24128335","doi":"https://doi.org/10.5281/zenodo.24128335","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24128335","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":"article-journal"},{"id":"doi:10.5281/zenodo.24128336","doi":"https://doi.org/10.5281/zenodo.24128336","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24128336","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":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24128335","doi":"https://doi.org/10.5281/zenodo.24128335","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24128335","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":"article-journal"},"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":{"For":[0],"over":[1],"half":[2],"a":[3,28,53,75,123,128,167],"century,":[4],"modal":[5,25,55,93,157],"logic":[6,26],"has":[7],"provided":[8],"the":[9,18,66,71,80,88,92,100,104,110,114,119,141,145,152],"formal":[10],"syntax":[11],"for":[12],"analyzing":[13],"possibility":[14],"and":[15,99,164],"necessity":[16,59],"through":[17,109],"semantics":[19],"of":[20,47,70,83,95,113,144,155,171],"\u201cpossible":[21],"worlds.\u201d":[22],"However,":[23],"standard":[24],"lacks":[27],"physical":[29],"or":[30],"geometric":[31,169],"mechanism":[32],"to":[33,62],"explain":[34],"why":[35],"one":[36],"possible":[37],"world":[38],"becomes":[39],"actual":[40],"while":[41],"others":[42],"remain":[43],"abstract.":[44],"The":[45,147],"Cult":[46],"Symmetry":[48],"in":[49,65],"modern":[50],"physics":[51],"commits":[52],"profound":[54],"fallacy,":[56],"treating":[57],"mathematical":[58],"as":[60,91,103,151],"equivalent":[61],"actuality,":[63],"resulting":[64],"frozen,":[67],"featureless":[68],"void":[69],"multiverse.":[72],"We":[73,86],"propose":[74],"structural":[76],"reframing":[77],"derived":[78],"from":[79],"Golden":[81],"Rule":[82],"Structural":[84],"Rationalism.":[85],"identify":[87],"Abstraction":[89],"axis":[90,102],"space":[94],"pure":[96],"Possibility":[97],"(\u2662)":[98],"Contingency":[101],"actualized":[105,135],"Necessity":[106],"(\u25a1)":[107],"generated":[108],"constraining":[111],"identity":[112],"Interface.":[115,146],"Under":[116],"this":[117,156],"geometry,":[118],"universe":[120],"is":[121,133],"not":[122],"random":[124],"contingent":[125],"accident,":[126],"nor":[127],"perfectly":[129],"symmetric":[130],"necessity.":[131],"It":[132],"an":[134],"necessity\u2014the":[136],"specific":[137],"eigenvalue":[138],"that":[139],"survived":[140],"spectral":[142],"gap":[143],"Ground":[148],"(00)":[149],"serves":[150],"self-referential":[153],"generator":[154],"transition.":[158],"This":[159],"framework":[160],"unifies":[161],"physics,":[162],"mathematics,":[163],"philosophy":[165],"under":[166],"single":[168],"law":[170],"actualization.":[172]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}