{"id":"https://openalex.org/W7225005791","doi":"https://doi.org/10.5281/zenodo.23841912","title":"PRIME NUMBERS AS STATES OF TRANSDUCTION","display_name":"PRIME NUMBERS AS STATES OF TRANSDUCTION","publication_year":2026,"publication_date":"2026-10-31","ids":{"openalex":"https://openalex.org/W7225005791","doi":"https://doi.org/10.5281/zenodo.23841912"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23841912","doi":"https://doi.org/10.5281/zenodo.23841912","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23841912","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.23841912","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151219749","display_name":"Cl\u00e1udio Vicente da Silva","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Vicente da Silva, Cl\u00e1udio","raw_affiliation_strings":["pesquisador independente"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"pesquisador independente","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5151219749"],"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/T11166","display_name":"Analytic Number Theory Research","score":0.9965999722480774,"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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9965999722480774,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.0010999999940395355,"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/prime-numbers","display_name":"prime numbers","score":1.0},{"id":"https://openalex.org/keywords/transduction","display_name":"transduction","score":0.8690000176429749},{"id":"https://openalex.org/keywords/multiplicative-relations","display_name":"multiplicative relations","score":0.7739999890327454},{"id":"https://openalex.org/keywords/composite-numbers","display_name":"composite numbers","score":0.7789999842643738},{"id":"https://openalex.org/keywords/integer-factorization","display_name":"integer factorization","score":0.8669999837875366},{"id":"https://openalex.org/keywords/residue-classes","display_name":"residue classes","score":0.6869999766349792},{"id":"https://openalex.org/keywords/prime-gaps","display_name":"prime gaps","score":0.9679999947547913},{"id":"https://openalex.org/keywords/quadratic-forms","display_name":"quadratic forms","score":0.8199999928474426},{"id":"https://openalex.org/keywords/structural-invariants","display_name":"structural invariants","score":0.6959999799728394},{"id":"https://openalex.org/keywords/algorithmic-number-theory","display_name":"computational number theory","score":0.7039999961853027}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7469000220298767},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7437000274658203},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5759000182151794},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.4999000132083893},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.49799999594688416},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4966000020503998},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4869000017642975},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.4828000068664551},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4560999870300293},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.4528000056743622},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.43779999017715454},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3912999927997589},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.3686000108718872},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.36500000953674316},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.359499990940094},{"id":"https://openalex.org/C71480937","wikidata":"https://www.wikidata.org/wiki/Q3086516","display_name":"Residue number system","level":2,"score":0.3582000136375427},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C15152581","wikidata":"https://www.wikidata.org/wiki/Q7833966","display_name":"Transduction (biophysics)","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C116335209","wikidata":"https://www.wikidata.org/wiki/Q240651","display_name":"Prime element","level":3,"score":0.30079999566078186},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C157351203","wikidata":"https://www.wikidata.org/wiki/Q216906","display_name":"Multiplicative inverse","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.26919999718666077},{"id":"https://openalex.org/C134765980","wikidata":"https://www.wikidata.org/wiki/Q879126","display_name":"Bitwise operation","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C14367171","wikidata":"https://www.wikidata.org/wiki/Q173523","display_name":"Geometric progression","level":2,"score":0.25540000200271606}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23841912","doi":"https://doi.org/10.5281/zenodo.23841912","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23841912","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.23841913","doi":"https://doi.org/10.5281/zenodo.23841913","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23841913","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.23841912","doi":"https://doi.org/10.5281/zenodo.23841912","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23841912","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7212388059","https://openalex.org/W7212361586","https://openalex.org/W7202282950","https://openalex.org/W7203648981","https://openalex.org/W7085513760","https://openalex.org/W7170155640","https://openalex.org/W6911922541","https://openalex.org/W7221435357","https://openalex.org/W7084205440","https://openalex.org/W6912103505"],"abstract_inverted_index":{"PRIME":[0],"NUMBERS":[1],"AS":[2],"STATES":[3],"OF":[4],"TRANSDUCTION":[5],"The":[6,59,94,113,195,231,258],"Primitive":[7],"Architecture,":[8],"the":[9,13,30,54,62,67,77,87,97,107,117,151,165,239,247],"Arithmetic":[10,118,209,287],"Funnel":[11],"and":[12,23,74,85,106,142,158,170,193,208,228,268,279],"Generation":[14],"of":[15,32,56,79,90,109,205,242,249],"Multiplicative":[16,289],"Relations":[17],"This":[18,174],"work":[19,259],"presents":[20],"a":[21,120,159,179,243,253,272],"structural":[22,132],"computational":[24,196,229,269],"approach":[25,175],"to":[26,163,235],"prime":[27,41,92,136,240,277],"numbers":[28,42,51,84,278],"through":[29,127,150,200,251],"concept":[31],"transduction":[33,181],"states.":[34],"It":[35],"proposes":[36],"an":[37],"architecture":[38,122,212,270],"in":[39,271],"which":[40,252],"are":[43],"treated":[44],"as":[45,66],"primitive":[46,100],"arithmetic":[47,88,111,172,262],"states,":[48,101],"while":[49],"composite":[50,83],"emerge":[52],"from":[53],"composition":[55,78],"multiplicative":[57,72,102,219,254,281],"relations.":[58],"study":[60],"establishes":[61],"operator":[63,161],"[T_p(n)=p\\cdot":[64],"n]":[65],"fundamental":[68],"mechanism":[69],"for":[70,123,215,275],"generating":[71],"sequences":[73],"examines":[75],"how":[76],"these":[80],"operators":[81],"produces":[82],"preserves":[86],"structure":[89],"their":[91,280],"factors.":[93],"framework":[95,274],"develops":[96],"relationship":[98,166],"between":[99,167],"operators,":[103],"relational":[104,266],"structures,":[105],"formation":[108],"new":[110],"configurations.":[112],"research":[114],"also":[115,246],"introduces":[116],"Funnel,":[119],"layered":[121],"organizing":[124],"prime-number":[125],"analysis":[126],"discrete":[128,171],"geometry,":[129],"modular":[130],"filters,":[131],"invariants,":[133],"residue":[134],"classes,":[135],"gaps,":[137],"quadratic":[138],"forms,":[139],"local":[140],"information,":[141],"p-adic":[143],"liftings.":[144],"A":[145],"geometric":[146,264],"component":[147],"is":[148,176,198,233,256],"developed":[149],"UNO":[152,293],"spiral":[153],"model,":[154],"incorporating":[155],"directional":[156],"states":[157],"transductive":[160],"designed":[162,234],"represent":[164],"continuous":[168],"movement":[169],"structures.":[173,282],"integrated":[177],"into":[178],"broader":[180],"sequence":[182,248],"involving":[183],"latency,":[184],"structure,":[185],"generation,":[186],"state,":[187],"refinement,":[188],"memory,":[189,224],"coverage,":[190,226],"branching,":[191],"recovery,":[192,227],"audit.":[194],"dimension":[197],"organized":[199],"SCEPTA":[201],"\u2014":[202],"Computational":[203,296],"System":[204],"Prime":[206,284],"States":[207],"Transduction.":[210],"Its":[211],"specifies":[213],"modules":[214],"prime-state":[216],"identification,":[217],"registration,":[218],"operations,":[220],"composition,":[221],"property":[222],"analysis,":[223],"interval":[225],"auditing.":[230],"system":[232],"record":[236],"not":[237],"only":[238],"factorization":[241],"number":[244],"but":[245],"operations":[250],"result":[255],"generated.":[257],"brings":[260],"together":[261],"identities,":[263],"representation,":[265],"organization,":[267],"unified":[273],"investigating":[276],"Keywords:":[283],"Numbers;":[285],"Transduction;":[286],"Funnel;":[288],"Relations;":[290],"Prime-State":[291],"Architecture;":[292],"Spiral;":[294],"SCEPTA;":[295],"Number":[297],"Theory;":[298],"Structural":[299],"Invariants;":[300],"Mathematical":[301],"Modeling.":[302]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-11-01T00:00:00"}