{"id":"https://openalex.org/W7225795706","doi":"https://doi.org/10.5281/zenodo.24128119","title":"Local Smoothability Without Global Smoothability: An Explicit Two-Chart Surface and Its Fourteen-Dimensional Formal Deformation Space","display_name":"Local Smoothability Without Global Smoothability: An Explicit Two-Chart Surface and Its Fourteen-Dimensional Formal Deformation Space","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225795706","doi":"https://doi.org/10.5281/zenodo.24128119"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24128119","doi":"https://doi.org/10.5281/zenodo.24128119","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24128119","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.24128119","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160631401","display_name":"Miyoboku Sage","orcid":"https://orcid.org/0009-0009-2632-8411","observed_orcids":["https://orcid.org/0009-0009-2632-8411"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sage, Miyoboku","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160631401"],"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9750999808311462,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9750999808311462,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.02280000038444996,"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/T12351","display_name":"Geometry and complex manifolds","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.647599995136261},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.555899977684021},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5078999996185303},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.43130001425743103},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4124000072479248},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4052000045776367},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4018999934196472},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.38350000977516174},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C2780391921","wikidata":"https://www.wikidata.org/wiki/Q1454193","display_name":"Free-form deformation","level":3,"score":0.2883000075817108},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.2863999903202057},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.26269999146461487},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2590000033378601},{"id":"https://openalex.org/C18109118","wikidata":"https://www.wikidata.org/wiki/Q5251702","display_name":"Deformation theory","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24128119","doi":"https://doi.org/10.5281/zenodo.24128119","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24128119","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.24128120","doi":"https://doi.org/10.5281/zenodo.24128120","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24128120","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.24128119","doi":"https://doi.org/10.5281/zenodo.24128119","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24128119","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":[],"abstract_inverted_index":{"We":[0,40],"construct":[1,55],"an":[2,35,56,190],"explicit":[3,57,175],"separated":[4],"nonnormal":[5],"surface":[6,28,177],"over":[7,34,61],"a":[8,62,84,95,120,161],"field":[9],"of":[10,124],"characteristic":[11],"zero":[12],"by":[13],"gluing":[14],"two":[15],"affine":[16,21],"semigroup":[17],"surfaces.":[18],"Although":[19],"both":[20,150],"charts":[22],"admit":[23],"flat":[24,31],"smoothings,":[25],"the":[26,42,91,100,125,131,174,180,185],"resulting":[27],"admits":[29],"no":[30],"finite-type":[32],"smoothing":[33],"equicharacteristic-zero":[36],"discrete":[37],"valuation":[38],"ring.":[39],"compute":[41],"complete":[43,85,132],"unrestricted":[44],"first-order":[45],"deformation":[46,89],"space,":[47],"establishing":[48],"that":[49],"it":[50],"has":[51],"dimension":[52],"fourteen,":[53],"and":[54,83,141,146,152,169],"formally":[58],"miniversal":[59],"family":[60,93],"smooth":[63],"fourteen-dimensional":[64],"formal":[65,92],"base.":[66],"The":[67,128,171],"construction":[68],"combines":[69],"multigraded":[70],"conormal":[71],"linear":[72],"algebra,":[73],"finite":[74],"free":[75],"algebra":[76],"constructions,":[77],"determinantal":[78],"presentations,":[79],"exact":[80,138],"overlap":[81],"identities,":[82],"Kodaira\u2013Spencer":[86],"calculation.":[87],"Every":[88],"in":[90,179],"carries":[94],"distinguished":[96],"section":[97,113],"along":[98],"which":[99],"relative":[101],"cotangent":[102],"module":[103],"requires":[104],"at":[105],"least":[106],"three":[107],"generators.":[108],"Formal":[109],"versality":[110],"transports":[111],"this":[112],"to":[114,122,165],"any":[115],"putative":[116],"DVR":[117],"smoothing,":[118],"yielding":[119],"contradiction":[121],"smoothness":[123],"generic":[126],"fiber.":[127],"manuscript":[129],"includes":[130],"mathematical":[133],"proof,":[134],"independent":[135,167],"verification":[136,168],"certificates,":[137],"computational":[139],"scripts":[140],"outputs,":[142],"detailed":[143],"experiment":[144],"ledgers,":[145],"historical":[147],"calculations":[148],"documenting":[149],"successful":[151],"unsuccessful":[153],"approaches.":[154],"All":[155],"supporting":[156],"materials":[157],"are":[158],"consolidated":[159],"into":[160],"single":[162],"self-contained":[163],"PDF":[164],"facilitate":[166],"reproducibility.":[170],"theorem":[172],"concerns":[173],"abstract":[176],"constructed":[178],"manuscript.":[181],"Its":[182],"identification":[183],"with":[184],"motivating":[186],"algebraic-cycle":[187],"geometry":[188],"remains":[189],"open":[191],"problem.":[192]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}