{"id":"https://openalex.org/W7165378682","doi":"https://doi.org/10.5281/zenodo.20759883","title":"The Prime Phase Equation and the Incommensurability of Reality","display_name":"The Prime Phase Equation and the Incommensurability of Reality","publication_year":2026,"publication_date":"2026-06-19","ids":{"openalex":"https://openalex.org/W7165378682","doi":"https://doi.org/10.5281/zenodo.20759883"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.20759883","doi":"https://doi.org/10.5281/zenodo.20759883","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20759883","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":"Report"},"volume":null,"type":"report","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.20759883","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140826550","display_name":"Seongil Lee","orcid":"https://orcid.org/0009-0007-8708-7637","observed_orcids":["https://orcid.org/0009-0007-8708-7637"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lee, Seongil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5140826550"],"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9965999722480774,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9965999722480774,"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/T11166","display_name":"Analytic Number Theory Research","score":0.00139999995008111,"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/T14299","display_name":"Complex Systems and Dynamics","score":0.000699999975040555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/prime-numbers","display_name":"prime numbers","score":0.9909999966621399},{"id":"https://openalex.org/keywords/phase-equilibria","display_name":"phase equilibria","score":0.953000009059906},{"id":"https://openalex.org/keywords/incommensurability","display_name":"incommensurability","score":0.9559999704360962},{"id":"https://openalex.org/keywords/mathematical-structures","display_name":"mathematical structures","score":0.4580000042915344},{"id":"https://openalex.org/keywords/geometric-asymmetry","display_name":"geometric asymmetry","score":0.8029999732971191},{"id":"https://openalex.org/keywords/emergence","display_name":"emergence","score":0.8080000281333923},{"id":"https://openalex.org/keywords/complexity","display_name":"complexity","score":0.9649999737739563},{"id":"https://openalex.org/keywords/structural-organization","display_name":"structural organization","score":0.6740000247955322}],"concepts":[{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.7531999945640564},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5151000022888184},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5019999742507935},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49140000343322754},{"id":"https://openalex.org/C71104824","wikidata":"https://www.wikidata.org/wiki/Q1476639","display_name":"Structural equation modeling","level":2,"score":0.45509999990463257},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.3880000114440918},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35569998621940613},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33820000290870667},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3010999858379364},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.25380000472068787}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.20759883","doi":"https://doi.org/10.5281/zenodo.20759883","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20759883","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":"Report"},{"id":"doi:10.5281/zenodo.20759884","doi":"https://doi.org/10.5281/zenodo.20759884","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20759884","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":"Report"},{"id":"doi:10.5281/zenodo.20785935","doi":"https://doi.org/10.5281/zenodo.20785935","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20785935","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":"Report"}],"best_oa_location":{"id":"doi:10.5281/zenodo.20759883","doi":"https://doi.org/10.5281/zenodo.20759883","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20759883","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":"Report"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7165519737","https://openalex.org/W6930695682","https://openalex.org/W6949371592","https://openalex.org/W6968149858","https://openalex.org/W6930829158","https://openalex.org/W7127929857","https://openalex.org/W7163780738","https://openalex.org/W6893279274","https://openalex.org/W6968261598","https://openalex.org/W6902169908"],"abstract_inverted_index":{"The":[0,31],"Prime":[1,35],"Phase":[2,36],"Equation":[3,37],"and":[4,15,28,52,88,102,111],"the":[5,10,34,97],"Incommensurability":[6],"of":[7,23,96],"Reality":[8],"investigates":[9],"possibility":[11],"that":[12],"prime-number":[13],"structures":[14,47,76],"phase":[16,71],"relationships":[17,72],"may":[18,48],"represent":[19],"a":[20,39,58,79],"fundamental":[21],"source":[22],"incommensurability":[24],"observed":[25],"across":[26],"mathematics":[27],"physical":[29,64],"systems.":[30],"paper":[32],"introduces":[33],"as":[38,94],"conceptual":[40],"framework":[41,82],"for":[42,60,83],"examining":[43],"how":[44],"discrete":[45],"numerical":[46],"generate":[49],"persistent":[50],"geometric":[51],"dynamical":[53],"asymmetries.":[54],"Rather":[55],"than":[56],"proposing":[57],"replacement":[59],"established":[61],"mathematical":[62],"or":[63],"theories,":[65],"this":[66],"work":[67],"explores":[68],"whether":[69],"recurring":[70],"associated":[73],"with":[74],"prime":[75],"can":[77],"provide":[78],"useful":[80],"interpretive":[81],"understanding":[84],"structural":[85],"organization,":[86],"emergence,":[87],"complexity.":[89],"This":[90],"publication":[91],"is":[92,103],"presented":[93],"part":[95],"broader":[98],"E-LOGOS":[99],"research":[100],"program":[101],"intended":[104],"to":[105],"encourage":[106],"further":[107],"analysis,":[108],"criticism,":[109],"verification,":[110],"discussion.":[112]},"counts_by_year":[],"updated_date":"2026-10-08T09:06:37.294493","created_date":"2026-06-20T00:00:00"}