{"id":"https://openalex.org/W7203441471","doi":"https://doi.org/10.33774/coe-2026-8k0nq","title":"\u03c7\u2011Spectral Reality: Foundations of the Operator\u2011Geometric Univers","display_name":"\u03c7\u2011Spectral Reality: Foundations of the Operator\u2011Geometric Univers","publication_year":2026,"publication_date":"2026-08-19","ids":{"openalex":"https://openalex.org/W7203441471","doi":"https://doi.org/10.33774/coe-2026-8k0nq"},"language":"en","primary_location":{"id":"doi:10.33774/coe-2026-8k0nq","doi":"https://doi.org/10.33774/coe-2026-8k0nq","is_oa":true,"landing_page_url":"https://doi.org/10.33774/coe-2026-8k0nq","pdf_url":"https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6a818e13d1922e37d56d4b2d/original/spectral-reality-foundations-of-the-operator-geometric-univers.pdf","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6a818e13d1922e37d56d4b2d/original/spectral-reality-foundations-of-the-operator-geometric-univers.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147190751","display_name":"Anatolii Mukha","orcid":"https://orcid.org/0009-0005-4614-6667","observed_orcids":["https://orcid.org/0009-0005-4614-6667"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anatolii Mukha","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0005-4614-6667","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5147190751"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":41,"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":0.7407000064849854,"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":0.7407000064849854,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.17159999907016754,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.03700000047683716,"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/quantum-measurement-problem","display_name":"measurement problem","score":0.6890000104904175},{"id":"https://openalex.org/keywords/wave-function-collapse","display_name":"wave function collapse","score":0.7850000262260437},{"id":"https://openalex.org/keywords/quantum-to-classical-transition","display_name":"quantum-to-classical transition","score":0.6489999890327454},{"id":"https://openalex.org/keywords/entanglement","display_name":"entanglement","score":0.8450000286102295},{"id":"https://openalex.org/keywords/spectral-curvature","display_name":"spectral curvature","score":0.531000018119812},{"id":"https://openalex.org/keywords/spectral-integration","display_name":"spectral integration","score":0.47200000286102295},{"id":"https://openalex.org/keywords/unification-of-physics","display_name":"unification of physics","score":0.5479999780654907}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.6811000108718872},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.5609999895095825},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5485000014305115},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.545799970626831},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4390000104904175},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3564000129699707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3337000012397766},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.3334999978542328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3271999955177307},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.32120001316070557},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3199000060558319},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C124967146","wikidata":"https://www.wikidata.org/wiki/Q3457898","display_name":"Spectral resolution","level":3,"score":0.3001999855041504},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.29269999265670776},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C194969405","wikidata":"https://www.wikidata.org/wiki/Q170519","display_name":"Virtual reality","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.27320000529289246},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.26980000734329224},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.267300009727478},{"id":"https://openalex.org/C191015642","wikidata":"https://www.wikidata.org/wiki/Q1132459","display_name":"Fragmentation (computing)","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C169402740","wikidata":"https://www.wikidata.org/wiki/Q2590381","display_name":"Measurement problem","level":3,"score":0.26510000228881836},{"id":"https://openalex.org/C23358344","wikidata":"https://www.wikidata.org/wiki/Q46079","display_name":"Copenhagen interpretation","level":5,"score":0.26269999146461487},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.2578999996185303}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.33774/coe-2026-8k0nq","doi":"https://doi.org/10.33774/coe-2026-8k0nq","is_oa":true,"landing_page_url":"https://doi.org/10.33774/coe-2026-8k0nq","pdf_url":"https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6a818e13d1922e37d56d4b2d/original/spectral-reality-foundations-of-the-operator-geometric-univers.pdf","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"doi:10.5281/zenodo.21937653","doi":"https://doi.org/10.5281/zenodo.21937653","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21937653","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":"Book"},{"id":"doi:10.5281/zenodo.21937654","doi":"https://doi.org/10.5281/zenodo.21937654","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21937654","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":"Book"}],"best_oa_location":{"id":"doi:10.33774/coe-2026-8k0nq","doi":"https://doi.org/10.33774/coe-2026-8k0nq","is_oa":true,"landing_page_url":"https://doi.org/10.33774/coe-2026-8k0nq","pdf_url":"https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6a818e13d1922e37d56d4b2d/original/spectral-reality-foundations-of-the-operator-geometric-univers.pdf","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203441471.pdf","grobid_xml":"https://content.openalex.org/works/W7203441471.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W7155490298","https://openalex.org/W7165040429","https://openalex.org/W7166889454","https://openalex.org/W7168085259","https://openalex.org/W7168866147","https://openalex.org/W7169811659","https://openalex.org/W7169868013","https://openalex.org/W7170137504","https://openalex.org/W7170181506","https://openalex.org/W7170269061","https://openalex.org/W7170719390","https://openalex.org/W7170859179","https://openalex.org/W7171028780","https://openalex.org/W7171212509","https://openalex.org/W7171288768","https://openalex.org/W7171302312","https://openalex.org/W7171395507","https://openalex.org/W7171462713","https://openalex.org/W7171675873","https://openalex.org/W7171785337","https://openalex.org/W7171953369","https://openalex.org/W7172158244","https://openalex.org/W7172256447","https://openalex.org/W7172306464","https://openalex.org/W7172326767","https://openalex.org/W7172393216","https://openalex.org/W7172445213","https://openalex.org/W7172505633","https://openalex.org/W7172525520","https://openalex.org/W7196944395","https://openalex.org/W7197001812","https://openalex.org/W7201848561","https://openalex.org/W7201856184","https://openalex.org/W7201871161","https://openalex.org/W7202177043","https://openalex.org/W7202389402","https://openalex.org/W7203459730","https://openalex.org/W7203464791"],"related_works":["https://openalex.org/W7204159158","https://openalex.org/W7206204692","https://openalex.org/W7204042064","https://openalex.org/W7214102409","https://openalex.org/W7204453639","https://openalex.org/W7171953369","https://openalex.org/W7203687219","https://openalex.org/W7172204052","https://openalex.org/W7204722358","https://openalex.org/W7203914267"],"abstract_inverted_index":{"\u03c7\u2011Spectral":[0,96,100,104,109,113,168],"Reality":[1,169],"presents":[2],"a":[3,86,154,171],"unified":[4,143],"operator\u2011spectral":[5,66,156,166],"reconstruction":[6],"of":[7,23,58,187,193,201,213],"physics,":[8],"defining":[9],"reality":[10,120],"not":[11],"through":[12,19,132,138,141,144,148],"spacetime,":[13,160],"fields,":[14,161],"or":[15],"quantum":[16,163,199],"states,":[17,54,130],"but":[18],"the":[20,27,178,198,208,214],"internal":[21],"organization":[22],"entanglement":[24,194],"governed":[25],"by":[26,50,123,126,129,135],"operator":[28],"triad":[29],"D,":[30],"T\u03c7,":[31],"and":[32,42,56,60,77,90,106,146,162,174,185,210],"M\u1d62.":[33],"Geometry,":[34],"time,":[35],"matter,":[36],"dynamics,":[37],"interactions,":[38],"measurement,":[39],"collapse,":[40],"integration,":[41,145],"completion":[43],"emerge":[44],"as":[45,85,153],"derived":[46],"spectral":[47,52,72,92],"phenomena":[48],"produced":[49],"coherent":[51],"layers,":[53,73,127],"transitions,":[55,133],"gradients":[57],"curvature":[59],"connectivity.":[61],"The":[62,115,190],"monograph":[63],"develops":[64],"an":[65],"architecture":[67],"in":[68,112],"which":[69],"D":[70],"generates":[71],"T\u03c7":[74],"transports":[75],"coherence,":[76],"M\u1d62":[78],"stabilizes":[79],"curvature.":[80],"Together":[81],"they":[82],"define":[83],"\u03c7\u2011Reality":[84],"coherent,":[87],"hierarchical,":[88],"modular,":[89],"self\u2011consistent":[91],"universe.":[93],"Measurement":[94],"becomes":[95,99,108],"Reconstruction,":[97],"collapse":[98,181],"Reduction,":[101],"interactions":[102],"become":[103],"Gradients,":[105],"unity":[107],"Integration,":[110],"culminating":[111],"Finalization.":[114],"\u03c7\u2011Final":[116],"Law":[117],"shows":[118],"that":[119],"is":[121],"generated":[122],"operators,":[124],"structured":[125],"configured":[128],"evolved":[131],"influenced":[134],"gradients,":[136],"observed":[137],"reconstruction,":[139],"stabilized":[140],"reduction,":[142],"completed":[147],"finalization":[149],"\u2014":[150,196,206],"establishing":[151],"\u03c7\u2011Unification":[152],"comprehensive":[155],"ontology.":[157],"By":[158],"replacing":[159],"states":[164],"with":[165],"foundations,":[167],"provides":[170],"new":[172],"mathematical":[173],"physical":[175],"ontology":[176],"resolving":[177],"measurement":[179],"problem,":[180],"paradox,":[182],"quantum\u2013classical":[183],"discontinuity,":[184],"fragmentation":[186],"modern":[188],"theory.":[189],"\u03c7\u2011spectral":[191],"interpretation":[192],"extremes":[195],"including":[197],"resolution":[200],"Euler\u2019s":[202],"36":[203],"Officers":[204],"Problem":[205],"demonstrates":[207],"universality":[209],"explanatory":[211],"power":[212],"framework.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":41}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-08-15T00:00:00"}