{"id":"https://openalex.org/W7214048341","doi":"https://doi.org/10.48550/arxiv.2609.24924","title":"Terminal Ambiguity Geometry for Finite-Dimensional Algebras","display_name":"Terminal Ambiguity Geometry for Finite-Dimensional Algebras","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214048341","doi":"https://doi.org/10.48550/arxiv.2609.24924"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.24924","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24924","pdf_url":"https://arxiv.org/pdf/2609.24924","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.24924","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123901433","display_name":"Joe Gildea","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I94876832","display_name":"Dundalk Institute of Technology","ror":"https://ror.org/01800zd49","country_code":"IE","type":"education","lineage":["https://openalex.org/I94876832"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Gildea, Joe","raw_affiliation_strings":["Department of Computing Science and Mathematics ,","School of Informatics and Creative Arts , Dundalk Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science and Mathematics ,","institution_ids":[]},{"raw_affiliation_string":"School of Informatics and Creative Arts , Dundalk Institute of Technology","institution_ids":["https://openalex.org/I94876832"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5123901433"],"corresponding_institution_ids":["https://openalex.org/I94876832"],"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.5853999853134155,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.5853999853134155,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.30320000648498535,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.033799998462200165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-dimensional-algebras","display_name":"finite-dimensional algebras","score":0.9570000171661377},{"id":"https://openalex.org/keywords/module-classification","display_name":"classification of modules","score":0.5519999861717224},{"id":"https://openalex.org/keywords/rigidity","display_name":"rigidity","score":0.5370000004768372},{"id":"https://openalex.org/keywords/non-uniqueness","display_name":"non-uniqueness","score":0.8949999809265137},{"id":"https://openalex.org/keywords/automorphisms","display_name":"automorphisms","score":0.5450000166893005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7534999847412109},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.7027000188827515},{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.5684000253677368},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.4683000147342682},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38440001010894775},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3790999948978424},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.3619999885559082},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34790000319480896},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.27869999408721924},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.2718999981880188}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.24924","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24924","pdf_url":"https://arxiv.org/pdf/2609.24924","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.2609.24924","doi":"https://doi.org/10.48550/arxiv.2609.24924","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.24924","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.24924","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24924","pdf_url":"https://arxiv.org/pdf/2609.24924","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214048341.pdf","grobid_xml":"https://content.openalex.org/works/W7214048341.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7109985917","https://openalex.org/W2009546732","https://openalex.org/W2076152711","https://openalex.org/W1983507128","https://openalex.org/W2952511232","https://openalex.org/W2060360924","https://openalex.org/W2026155640","https://openalex.org/W2118414194","https://openalex.org/W1597967112","https://openalex.org/W1608021137"],"abstract_inverted_index":{"Radical":[0],"truncation":[1],"forgets":[2,169],"information":[3,36,167,176],"about":[4],"a":[5,53],"module.":[6],"We":[7,42,112],"study":[8],"the":[9,29,62,80,93,97,100,120,128,132,154,162,166,171,181],"ambiguity":[10,45,58,77,129,163],"created":[11],"by":[12,61,71,148,165],"this":[13,49],"loss:":[14],"which":[15,174],"nonisomorphic":[16,109],"modules":[17],"remain":[18],"indistinguishable":[19],"after":[20],"all":[21],"proper":[22],"radical":[23,64,141,160],"truncations":[24],"have":[25],"been":[26],"fixed,":[27],"how":[28],"resulting":[30,182],"families":[31],"are":[32,146],"organized,":[33],"and":[34,66,89,103,116,139,170],"what":[35],"can":[37,177],"be":[38,178],"recovered":[39,179],"from":[40,180],"them.":[41],"introduce":[43],"terminal":[44,63,69,110,137,140],"geometry":[46,130],"to":[47,173],"make":[48],"residual":[50],"indeterminacy":[51],"into":[52],"geometric":[54],"object.":[55],"The":[56],"remaining":[57],"is":[59],"governed":[60],"layer,":[65,142],"we":[67],"classify":[68],"completions":[70],"Grassmannian":[72],"orbit":[73],"spaces,":[74],"with":[75],"projective":[76,122,150],"appearing":[78],"as":[79],"rank-one":[81,121],"case.":[82],"This":[83],"classification":[84],"gives":[85,104],"criteria":[86],"for":[87,119],"rigidity":[88],"nonuniqueness":[90],"and,":[91],"in":[92],"split":[94],"case,":[95],"determines":[96],"dimensions":[98],"of":[99,108,159],"completion":[101],"spaces":[102],"exact":[105],"finite-field":[106],"counts":[107],"completions.":[111],"also":[113],"establish":[114],"reconstruction":[115],"symmetry":[117],"results":[118],"geometry.":[123,183],"Under":[124],"suitable":[125],"rank":[126],"hypotheses,":[127],"recovers":[131],"corresponding":[133],"residue":[134],"division-algebra":[135],"data,":[136],"species,":[138],"while":[143],"its":[144],"automorphisms":[145],"described":[147],"classical":[149],"semilinear":[151],"groups.":[152],"Thus":[153],"paper":[155],"studies":[156],"both":[157],"sides":[158],"truncation:":[161],"produced":[164],"it":[168],"extent":[172],"that":[175]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-23T00:00:00"}
