{"id":"https://openalex.org/W7225637684","doi":"https://doi.org/10.5281/zenodo.24093999","title":"A single fixed-endpoint M\u00f6bius input for the Goldbach reduction","display_name":"A single fixed-endpoint M\u00f6bius input for the Goldbach reduction","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225637684","doi":"https://doi.org/10.5281/zenodo.24093999"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24093999","doi":"https://doi.org/10.5281/zenodo.24093999","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24093999","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.24093999","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005309350","display_name":"Masayuki Aoki","orcid":"https://orcid.org/0000-0001-5746-332X","observed_orcids":["https://orcid.org/0000-0001-5746-332X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"AOKI, Masayuki","raw_affiliation_strings":["Independent researcher"],"raw_orcid":"https://orcid.org/0000-0001-5746-332X","affiliations":[{"raw_affiliation_string":"Independent researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5005309350"],"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":1.0,"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":1.0,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/goldbach-conjecture","display_name":"Goldbach conjecture","score":0.9739999771118164},{"id":"https://openalex.org/keywords/mobius-function","display_name":"M\u00f6bius function","score":0.7699999809265137},{"id":"https://openalex.org/keywords/bombieri-vinogradov-theorem","display_name":"Bombieri-Vinogradov theorem","score":0.9049999713897705},{"id":"https://openalex.org/keywords/prime-pairs","display_name":"prime pairs","score":0.6019999980926514},{"id":"https://openalex.org/keywords/even-integers","display_name":"even integers","score":0.3709999918937683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8909000158309937},{"id":"https://openalex.org/C143732363","wikidata":"https://www.wikidata.org/wiki/Q485520","display_name":"Goldbach's conjecture","level":3,"score":0.7419000267982483},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5852000117301941},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.5587999820709229},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4634000062942505},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.4544000029563904},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.43790000677108765},{"id":"https://openalex.org/C188139237","wikidata":"https://www.wikidata.org/wiki/Q50706","display_name":"Square-free integer","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C2778217198","wikidata":"https://www.wikidata.org/wiki/Q556977","display_name":"Cutoff","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C50742451","wikidata":"https://www.wikidata.org/wiki/Q1530388","display_name":"Equidistributed sequence","level":2,"score":0.3659000098705292},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.35690000653266907},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.3221000134944916},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.2802000045776367},{"id":"https://openalex.org/C7720571","wikidata":"https://www.wikidata.org/wiki/Q1136880","display_name":"Power of two","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2630999982357025},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C130594498","wikidata":"https://www.wikidata.org/wiki/Q2028293","display_name":"Iterated logarithm","level":3,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24093999","doi":"https://doi.org/10.5281/zenodo.24093999","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24093999","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.24094000","doi":"https://doi.org/10.5281/zenodo.24094000","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24094000","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.24093999","doi":"https://doi.org/10.5281/zenodo.24093999","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24093999","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/W7225405802","https://openalex.org/W7221530533","https://openalex.org/W7216087521","https://openalex.org/W7215082955","https://openalex.org/W7220380864","https://openalex.org/W7214663972","https://openalex.org/W6912159283","https://openalex.org/W7214668372","https://openalex.org/W7215032976","https://openalex.org/W7223210878"],"abstract_inverted_index":{"A":[0],"fixed-endpoint,":[1],"fixed-residue":[2],"Bombieri\u2013Vinogradov-type":[3],"estimate":[4,124,166],"for":[5,49,174,221],"\u039b(n)\u03bc(N\u2212n)":[6],"over":[7],"squarefree":[8],"moduli":[9],"up":[10],"to":[11,40],"\u221aN":[12],"(log":[13,18],"N)^12,":[14],"with":[15],"unweighted":[16,93],"saving":[17,48],"N)^(\u22123),":[19],"implies":[20],"\u226b":[21],"N/(log":[22],"N)^3":[23],"unordered":[24],"Goldbach":[25,217,233],"prime":[26],"pairs.":[27],"Ordinary":[28],"Bombieri\u2013Vinogradov":[29],"supplies":[30],"the":[31,50,88,106,121,131,153,193,231],"untwisted":[32],"input.":[33],"Full":[34],"divisor":[35],"cancellation":[36,104],"switches":[37],"complementary":[38],"sums":[39,43],"ordinary":[41,150],"small-divisor":[42],"and":[44,53,67,92,156,160,167,177,188],"gives":[45],"arbitrary":[46],"logarithmic":[47,89],"signed":[51,103,147],"\u03bc":[52,54,108],"log":[55,109],"discrepancies":[56],"at":[57,73,137,200],"fixed":[58,96,182],"power":[59,75],"cutoffs":[60],"above":[61],"\u221aN.":[62],"The":[63,102,219],"cancellation,":[64],"residual":[65],"relation,":[66],"a":[68,74,142,161,214],"fixed-endpoint":[69,113],"absolute-value":[70],"sufficient":[71,148],"condition":[72],"cutoff":[76,91],"occur":[77],"in":[78,111,115,209],"Lee's":[79],"manuscript":[80],"(September":[81],"2026).":[82,241],"This":[83,212],"independently":[84],"prepared":[85],"note":[86],"specifies":[87],"square-root":[90],"saving;":[94],"every":[95,222],"exponent":[97],"greater":[98],"than":[99],"11":[100,238],"suffices.":[101],"bypasses":[105],"separate":[107],"input":[110,133,220],"Cantarini's":[112,197],"formulation":[114],"this":[116],"range.":[117],"Huang\u2013Li":[118],"already":[119],"derive":[120],"logarithmically":[122],"weighted":[123],"from":[125],"their":[126],"endpoint-uniform":[127],"twisted":[128],"hypothesis;":[129],"here":[130],"remaining":[132],"is":[134,235],"required":[135],"only":[136],"one":[138],"endpoint.":[139],"We":[140],"give":[141],"direct":[143],"remainder":[144],"identity,":[145],"weaker":[146],"conditions,":[149],"evaluations":[151],"of":[152,196],"moving":[154],"tail":[155],"corrected":[157],"triangular":[158],"error,":[159],"general":[162],"ordinary-level":[163],"formulation.":[164],"Davenport's":[165],"Parseval":[168],"yield":[169],"an":[170,228],"unconditional":[171],"mean-square":[172],"bound":[173],"both":[175],"weights":[176],"all":[178],"coprime":[179],"moduli.":[180],"For":[181],"0":[183],"<":[184,186],"\u03b8":[185],"1":[187],"A,":[189],"H":[190],">":[191],"0,":[192],"two":[194],"bounds":[195],"Conjecture":[198],"6":[199],"level":[201],"N^\u03b8":[202],"hold":[203],"simultaneously":[204],"outside":[205],"O(X/(log":[206],"X)^H)":[207],"totals":[208],"[X,":[210],"2X].":[211],"recovers":[213],"classical":[215],"almost-all":[216],"consequence.":[218],"sufficiently":[223],"large":[224],"even":[225],"N":[226],"remains":[227],"assumption,":[229],"so":[230],"pointwise":[232],"conclusion":[234],"conditional.":[236],"Revision":[237],"(5":[239],"November":[240],"Comments":[242],"are":[243],"welcome.":[244]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}