{"id":"https://openalex.org/W7213247633","doi":"https://doi.org/10.48550/arxiv.2609.13607","title":"Stratification and realization of singularity data on the Loch Ness monster","display_name":"Stratification and realization of singularity data on the Loch Ness monster","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7213247633","doi":"https://doi.org/10.48550/arxiv.2609.13607"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13607","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13607","pdf_url":"https://arxiv.org/pdf/2609.13607","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.13607","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030505400","display_name":"Nate Fisher","orcid":"https://orcid.org/0000-0002-6816-9190","observed_orcids":["https://orcid.org/0000-0002-6816-9190"]},"institutions":[{"id":"https://openalex.org/I118020396","display_name":"Swarthmore College","ror":"https://ror.org/012dg8a96","country_code":"US","type":"education","lineage":["https://openalex.org/I118020396"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fisher, Nate","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS AND STATISTICS , SWARTHMORE COLLEGE , SWARTHMORE , PA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS AND STATISTICS , SWARTHMORE COLLEGE , SWARTHMORE , PA , USA","institution_ids":["https://openalex.org/I118020396"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011655608","display_name":"Camilo Ram\u00edrez Maluendas","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maluendas, Camilo Ram\u00edrez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.8734999895095825,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.8734999895095825,"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"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.07530000060796738,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.01209999993443489,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/loch-ness-monster","display_name":"Loch Ness Monster","score":0.9380000233650208},{"id":"https://openalex.org/keywords/strata","display_name":"strata","score":0.6269999742507935},{"id":"https://openalex.org/keywords/realization-problem","display_name":"realization problem","score":0.6019999980926514},{"id":"https://openalex.org/keywords/conical-singularities","display_name":"conical singularities","score":0.6430000066757202}],"concepts":[{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.8547000288963318},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6254000067710876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6169999837875366},{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.5066999793052673},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46059998869895935},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.45410001277923584},{"id":"https://openalex.org/C2778626061","wikidata":"https://www.wikidata.org/wiki/Q6902671","display_name":"Monster","level":2,"score":0.4196999967098236},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C207769094","wikidata":"https://www.wikidata.org/wiki/Q4245771","display_name":"Singularity theory","level":3,"score":0.3546999990940094},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.3476000130176544},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33980000019073486},{"id":"https://openalex.org/C71383303","wikidata":"https://www.wikidata.org/wiki/Q1876526","display_name":"Essential singularity","level":3,"score":0.33160001039505005},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.31769999861717224},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28349998593330383},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C143904861","wikidata":"https://www.wikidata.org/wiki/Q2297037","display_name":"Isolated singularity","level":3,"score":0.26809999346733093},{"id":"https://openalex.org/C102565666","wikidata":"https://www.wikidata.org/wiki/Q1378301","display_name":"Universal set","level":3,"score":0.2671000063419342}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13607","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13607","pdf_url":"https://arxiv.org/pdf/2609.13607","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.13607","doi":"https://doi.org/10.48550/arxiv.2609.13607","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13607","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"pmh:oai:arXiv.org:2609.13607","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13607","pdf_url":"https://arxiv.org/pdf/2609.13607","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306113","display_name":"U.S. Department of State","ror":"https://ror.org/03vvynj75"},{"id":"https://openalex.org/F4320321458","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68"},{"id":"https://openalex.org/F4320328425","display_name":"Fulbright Colombia","ror":"https://ror.org/01q2k1s41"},{"id":"https://openalex.org/F4320335258","display_name":"Universidad Nacional de Colombia, Sede Manizales","ror":"https://ror.org/059yx9a68"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213247633.pdf","grobid_xml":"https://content.openalex.org/works/W7213247633.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1937231211"],"related_works":["https://openalex.org/W2541653676","https://openalex.org/W2964304512","https://openalex.org/W2261767410","https://openalex.org/W6891871889","https://openalex.org/W7169509737","https://openalex.org/W2605919589","https://openalex.org/W2314806117","https://openalex.org/W2164987234","https://openalex.org/W6969399239","https://openalex.org/W7096023200"],"abstract_inverted_index":{"The":[0],"classical":[1],"theory":[2,54],"of":[3,12,19,22,30,34,41,77,81,90,93,103,141,184,187,196,209],"compact":[4],"translation":[5,32,57,68,129,169,189,212],"surfaces":[6,33,58,213],"is":[7,126,151,164],"organized":[8],"through":[9],"the":[10,17,20,23,28,75,88,91,100,104,108,115,132,152,161,172,185,203,223],"stratification":[11,53],"moduli":[13],"spaces":[14],"according":[15],"to":[16],"orders":[18],"zeros":[21],"associated":[24],"Abelian":[25],"differentials.":[26],"In":[27,47],"setting":[29],"tame":[31,56,67,128,168,188,211],"infinite":[35],"topological":[36],"type,":[37],"no":[38,127],"analogous":[39],"notion":[40],"strata":[42,186,208],"has":[43],"been":[44],"systematically":[45],"developed.":[46],"this":[48,98,150,192],"article,":[49],"we":[50,70,179],"introduce":[51],"a":[52,72,138,167,177,181,216],"for":[55,111,207],"based":[59],"on":[60,114,131,171,191],"their":[61,197],"singularity":[62,101,112,156,198,220],"data.":[63,199],"To":[64],"each":[65,82],"non-compact":[66,210],"surface,":[69],"associate":[71],"sequence":[73,99],"recording":[74],"cardinalities":[76],"finite-angle":[78],"cone":[79,84,143],"singularities":[80],"possible":[83],"angle":[85,144],"together":[86],"with":[87],"cardinality":[89],"set":[92],"infinite-angle":[94],"singularities.":[95,145],"We":[96,106,146],"call":[97],"data":[102,113,157,221],"surface.":[105],"study":[107],"realization":[109,205],"problem":[110],"Loch":[116,133,173],"Ness":[117,134,174],"monster.":[118,175],"Our":[119],"first":[120,204],"main":[121],"result":[122,163],"shows":[123],"that":[124,149],"there":[125],"structure":[130,170],"monster":[135],"having":[136],"only":[137,153],"finite":[139,142],"number":[140],"then":[147],"prove":[148],"obstruction:":[154],"every":[155],"not":[158],"excluded":[159],"by":[160,166],"previous":[162],"realized":[165],"As":[176],"consequence,":[178],"obtain":[180],"complete":[182],"characterization":[183],"structures":[190],"surface":[193],"in":[194],"terms":[195],"These":[200],"results":[201],"provide":[202],"theorem":[206],"and":[214,222],"reveal":[215],"strong":[217],"interaction":[218],"between":[219],"ends":[224],"space.":[225]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}