{"id":"https://openalex.org/W7225393307","doi":"https://doi.org/10.5281/zenodo.24020896","title":"Formal Verification of the Frequency Torus Model: Constructive Proof of Quantum Eversion in Lean 4","display_name":"Formal Verification of the Frequency Torus Model: Constructive Proof of Quantum Eversion in Lean 4","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225393307","doi":"https://doi.org/10.5281/zenodo.24020896"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24020896","doi":"https://doi.org/10.5281/zenodo.24020896","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24020896","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","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24020896","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158975371","display_name":"Saltykov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Saltykov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5158975371"],"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.271699994802475,"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":0.271699994802475,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.11900000274181366,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.09780000150203705,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/formal-verification","display_name":"formal verification","score":0.6380000114440918},{"id":"https://openalex.org/keywords/lean-4","display_name":"Lean 4","score":0.984000027179718},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"constructive proof","score":0.8040000200271606},{"id":"https://openalex.org/keywords/4pi-periodicity","display_name":"4\u03c0 periodicity","score":0.9319999814033508},{"id":"https://openalex.org/keywords/fermion-spin","display_name":"fermion spin","score":0.8119999766349792},{"id":"https://openalex.org/keywords/spinor-representation","display_name":"spinor representation","score":0.6859999895095825},{"id":"https://openalex.org/keywords/resonant-medium","display_name":"resonant media","score":0.7950000166893005}],"concepts":[{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.49079999327659607},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4404999911785126},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.42289999127388},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.42179998755455017},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.413100004196167},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38769999146461487},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.3862999975681305},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3653999865055084},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.31299999356269836},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28049999475479126},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C43506125","wikidata":"https://www.wikidata.org/wiki/Q604907","display_name":"Spinor","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.2567000091075897},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.25619998574256897},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24020896","doi":"https://doi.org/10.5281/zenodo.24020896","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24020896","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"},{"id":"doi:10.5281/zenodo.24020897","doi":"https://doi.org/10.5281/zenodo.24020897","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24020897","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"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24020896","doi":"https://doi.org/10.5281/zenodo.24020896","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24020896","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":[],"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/W7223068533","https://openalex.org/W7213587953","https://openalex.org/W7204658964","https://openalex.org/W7168292463","https://openalex.org/W7172382960","https://openalex.org/W7204732919","https://openalex.org/W7172399669","https://openalex.org/W7154984375","https://openalex.org/W7172441193","https://openalex.org/W7221054617"],"abstract_inverted_index":{"The":[0,67],"paper":[1],"presents":[2],"a":[3,8],"rigorous":[4],"mathematical":[5,92],"specification":[6],"and":[7,61,87],"complete":[9],"formal":[10],"proof":[11],"of":[12,57,64,89],"quantum":[13,31,49],"eversion":[14],"within":[15],"the":[16,22,29,43,55,58,62,74,84,90],"frequency":[17,45],"torus":[18],"model,":[19],"implemented":[20],"in":[21],"computer":[23],"logic":[24],"language":[25],"Lean":[26,75],"4.":[27],"Unlike":[28],"classical":[30],"mechanics":[32],"approach,":[33],"where":[34],"fermion":[35],"spin":[36],"is":[37],"postulated":[38],"through":[39],"continuous":[40],"spinor":[41],"representations,":[42],"proposed":[44],"mathematics":[46],"derives":[47],"discrete":[48],"properties":[50],"(4\u03c0":[51],"periodicity)":[52],"naturally":[53],"from":[54],"geometry":[56],"resonant":[59],"medium":[60],"requirement":[63],"twist":[65],"continuity.":[66],"code":[68],"has":[69],"been":[70],"fully":[71],"verified":[72],"by":[73],"4":[76],"compiler":[77],"without":[78],"any":[79],"logical":[80],"placeholders":[81],"(sorry),":[82],"confirming":[83],"internal":[85],"consistency":[86],"rigor":[88],"developed":[91],"framework.":[93]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}
