{"id":"https://openalex.org/W7159653888","doi":"https://doi.org/10.48550/arxiv.2604.28103","title":"Bounded, Commuting, Discrete-trace Preserving Projections","display_name":"Bounded, Commuting, Discrete-trace Preserving Projections","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7159653888","doi":"https://doi.org/10.48550/arxiv.2604.28103"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-05608667v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05608667","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.28103","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061539614","display_name":"Alexandre Ern","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ern, Alexandre","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036599010","display_name":"Johnny Guzm\u00e1n","orcid":"https://orcid.org/0000-0002-6769-2393"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guzm\u00e1n, Johnny","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134961214","display_name":"Pratyush Potu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Potu, Pratyush","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.4749999940395355,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.4749999940395355,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.032999999821186066,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.03220000118017197,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/piecewise","display_name":"Piecewise","score":0.7721999883651733},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6047000288963318},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5123000144958496},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.4900999963283539},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.47380000352859497},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.45969998836517334},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.44780001044273376}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7878000140190125},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7721999883651733},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6047000288963318},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5123000144958496},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.4900999963283539},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.47380000352859497},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.45969998836517334},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.44780001044273376},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.367000013589859},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.34950000047683716},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3230000138282776},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31700000166893005},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2971999943256378},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.29670000076293945},{"id":"https://openalex.org/C2780719617","wikidata":"https://www.wikidata.org/wiki/Q1030752","display_name":"Salient","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2563000023365021},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2524999976158142}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:HAL:hal-05608667v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05608667","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2604.28103","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.28103","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.28103","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.28103","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,102],"construct":[1],"bounded,":[2,110],"commuting":[3],"projections":[4,17,36,83],"for":[5],"the":[6,12,16,19,24,31,43,48,51,55,60,72,77,82,99,108,115,129],"three-dimensional":[7],"de":[8],"Rham":[9],"complex":[10],"with":[11],"additional":[13],"property":[14],"that":[15],"preserve":[18],"trace":[20,33],"of":[21,50,62,69,107,117,120,134],"functions/fields":[22,90],"if":[23],"latter":[25],"is":[26,94],"a":[27,66,95],"piecewise":[28,96,121,135],"polynomial":[29,97,122,136],"in":[30,42,65,98],"appropriate":[32,100],"space.":[34,101],"The":[35],"are":[37,84],"locally":[38,86],"defined":[39],"and":[40,74,124],"stable":[41,118],"graph":[44,52],"norm.":[45],"More":[46],"precisely,":[47],"part":[49],"norm":[53],"involving":[54],"exterior":[56,92],"derivative":[57,64,93],"only":[58],"involves":[59],"oscillation":[61],"this":[63],"narrow":[67],"strip":[68],"elements":[70],"touching":[71],"boundary":[73],"weighted":[75],"by":[76],"local":[78],"mesh":[79],"size.":[80],"Moreover,":[81],"$L^2$-stable":[85],"when":[87],"acting":[88],"on":[89,128],"whose":[91],"present":[103,109],"two":[104],"salient":[105],"applications":[106],"commuting,":[111],"discrete-trace":[112],"preserving":[113],"projections:":[114],"construction":[116],"liftings":[119],"data":[123],"an":[125],"optimality":[126],"result":[127],"discrete":[130],"versus":[131],"continuous":[132],"extension":[133],"data.":[137]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-02T00:00:00"}