{"id":"https://openalex.org/W7222874009","doi":"https://doi.org/10.5281/zenodo.23459859","title":"Theory of Fractal Resonance: A Unified Framework (Papers I\u2013IV)","display_name":"Theory of Fractal Resonance: A Unified Framework (Papers I\u2013IV)","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7222874009","doi":"https://doi.org/10.5281/zenodo.23459859"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23459859","doi":"https://doi.org/10.5281/zenodo.23459859","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23459859","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","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23459859","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159016375","display_name":"Filipp Egorov","orcid":"https://orcid.org/0009-0003-4978-6817","observed_orcids":["https://orcid.org/0009-0003-4978-6817"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Egorov, Filipp","raw_affiliation_strings":["Independent Researcher, Moscow, Russia"],"raw_orcid":"https://orcid.org/0009-0003-4978-6817","affiliations":[{"raw_affiliation_string":"Independent Researcher, Moscow, Russia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159016375"],"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.4749000072479248,"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"}},"topics":[{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.4749000072479248,"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":0.4262999892234802,"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.029400000348687172,"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":[],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.628000020980835},{"id":"https://openalex.org/C172790937","wikidata":"https://www.wikidata.org/wiki/Q18343","display_name":"Dark energy","level":3,"score":0.5400999784469604},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.4350999891757965},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4185999929904938},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.396699994802475},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.36419999599456787},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C122527463","wikidata":"https://www.wikidata.org/wiki/Q578430","display_name":"Quantum decoherence","level":3,"score":0.3303999900817871},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C166126730","wikidata":"https://www.wikidata.org/wiki/Q725309","display_name":"Planck","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C46451288","wikidata":"https://www.wikidata.org/wiki/Q1080745","display_name":"Unified field theory","level":2,"score":0.3052999973297119},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C98444146","wikidata":"https://www.wikidata.org/wiki/Q318","display_name":"Galaxy","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C184497039","wikidata":"https://www.wikidata.org/wiki/Q911473","display_name":"Holographic principle","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2858999967575073},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C159249277","wikidata":"https://www.wikidata.org/wiki/Q79925","display_name":"Dark matter","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.2597000002861023},{"id":"https://openalex.org/C207297109","wikidata":"https://www.wikidata.org/wiki/Q15605","display_name":"Cosmic microwave background","level":3,"score":0.257999986410141},{"id":"https://openalex.org/C83764196","wikidata":"https://www.wikidata.org/wiki/Q17014577","display_name":"Fractal derivative","level":5,"score":0.2563000023365021},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2524000108242035},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23459859","doi":"https://doi.org/10.5281/zenodo.23459859","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23459859","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.23459860","doi":"https://doi.org/10.5281/zenodo.23459860","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23459860","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":"doi:10.5281/zenodo.23459859","doi":"https://doi.org/10.5281/zenodo.23459859","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23459859","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":[],"sustainable_development_goals_aurora":[],"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":{"This":[0],"record":[1],"contains":[2],"the":[3,8,123,150,238],"unified":[4,184],"English":[5],"edition":[6],"of":[7,10,61,110,117,149,157,172,201,214],"Theory":[9],"Fractal":[11,15,27],"Resonance":[12,16,28],"(TFR)":[13],"/":[14],"Calculus":[17],"(FRC)":[18],"series,":[19],"comprising":[20],"four":[21],"interconnected":[22],"papers.":[23],"Paper":[24,100,131,166],"I":[25],"-":[26,102,133,168],"Calculus:":[29],"Core":[30],"Formalism.":[31],"Unified":[32],"variational":[33],"principle":[34],"over":[35],"spacetime":[36],"and":[37,50,163],"scale":[38,62,113],"parameter;":[39],"five":[40],"fundamental":[41],"operators":[42],"derived":[43],"strictly":[44],"from":[45,177,237],"variation;":[46],"emergent":[47],"Hilbert":[48],"space":[49],"Born":[51,239],"rule":[52,240],"via":[53],"Gleason's":[54],"theorem":[55],"after":[56],"macroscopic":[57],"decoherence":[58],"(S-transition);":[59],"reduction":[60],"aberrations":[63],"to":[64],"Yang-Mills":[65],"gauge":[66],"fields":[67],"SU(3)xSU(2)xU(1);":[68],"modified":[69,140],"Navier-Stokes":[70],"equations":[71,142],"with":[72,90,122,143,180],"scale-dependent":[73],"Reynolds":[74],"tensor":[75],"establishing":[76],"dA/dr":[77],"=":[78,232],"0":[79],"as":[80,106,119,128,136,146,170,199],"a":[81,107,120,137],"primary":[82],"topological":[83],"attractor;":[84],"observational":[85,129],"confirmation":[86],"on":[87],"28":[88],"galaxies":[89,98],"nuclear":[91],"rings":[92],"(AINUR,":[93],"DensePak)":[94],"versus":[95],"5":[96],"control":[97],"(SPARC).":[99],"II":[101],"Conceptual":[103],"Foundations.":[104],"K-invariant":[105],"universal":[108],"measure":[109],"structural":[111],"stability;":[112],"selection":[114],"principle;":[115],"status":[116],"log-periodicity":[118],"postulate":[121],"comb":[124,195],"shape":[125],"in":[126,197],"P(k)":[127,198],"arbiter.":[130],"III":[132],"Chronodynamics.":[134],"Time":[135],"dynamical":[138],"field;":[139,152],"Friedmann":[141],"dark":[144],"energy":[145,148],"potential":[147],"time":[151,212],"CMB":[153],"peak":[154],"smoothing;":[155],"absence":[156],"gravitational":[158],"slip;":[159],"covariant":[160],"collapse":[161],"criterion":[162],"temporal":[164],"entanglement.":[165],"IV":[167],"Matter":[169],"Sediment":[171],"Standing":[173],"Waves.":[174],"Spatial":[175],"localization":[176,202],"Helmholtz":[178],"modes":[179],"spectrally":[181],"fixed":[182],"wavenumbers;":[183],"Gibbs-Boltzmann":[185],"sediment":[186],"law":[187],"(Chladni":[188],"figures,":[189],"optical":[190],"lattices,":[191],"cosmic":[192],"structures);":[193],"three":[194],"shapes":[196],"discriminator":[200],"mechanisms":[203],"testable":[204],"by":[205,218],"DESI/Euclid.":[206],"Four":[207],"falsifiable":[208],"predictions:":[209],"(1)":[210],"nonlinear":[211],"delay":[213],"TeV":[215],"photons":[216],"modulated":[217],"(1+z)^-0.15;":[219],"(2)":[220],"vacuum":[221],"transparency":[222],"at":[223,230],"Planck":[224],"energies;":[225],"(3)":[226],"holographic":[227],"phase":[228],"noise":[229],"T_C,vac":[231],"10^-30":[233],"K;":[234],"(4)":[235],"deviations":[236],"near":[241],"critical":[242],"tension.":[243]},"counts_by_year":[],"updated_date":"2026-10-19T09:35:57.686232","created_date":"2026-10-19T00:00:00"}
