{"id":"https://openalex.org/W7161555577","doi":"https://doi.org/10.48550/arxiv.2605.16169","title":"LeanBET: Formally-verified surface area calculations in Lean","display_name":"LeanBET: Formally-verified surface area calculations in Lean","publication_year":2026,"publication_date":"2026-05-15","ids":{"openalex":"https://openalex.org/W7161555577","doi":"https://doi.org/10.48550/arxiv.2605.16169"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.16169","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.16169","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.16169","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136419110","display_name":"Ejike D. Ugwuanyi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ugwuanyi, Ejike D.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113541627","display_name":"Colin T. Jones","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jones, Colin T.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5119306154","display_name":"John Velkey","orcid":"https://orcid.org/0000-0001-5156-7451"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Velkey, John","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135462837","display_name":"Tyler R. Josephson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Josephson, Tyler R.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"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/T12012","display_name":"Diatoms and Algae Research","score":0.15209999680519104,"subfield":{"id":"https://openalex.org/subfields/2502","display_name":"Biomaterials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12012","display_name":"Diatoms and Algae Research","score":0.15209999680519104,"subfield":{"id":"https://openalex.org/subfields/2502","display_name":"Biomaterials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11986","display_name":"Scientific Computing and Data Management","score":0.1298000067472458,"subfield":{"id":"https://openalex.org/subfields/1802","display_name":"Information Systems and Management"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.10209999978542328,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.7929999828338623},{"id":"https://openalex.org/keywords/executable","display_name":"Executable","score":0.659500002861023},{"id":"https://openalex.org/keywords/python","display_name":"Python (programming language)","score":0.5253000259399414},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.519599974155426},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.45590001344680786},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4490000009536743},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.36719998717308044},{"id":"https://openalex.org/keywords/algebraic-expression","display_name":"Algebraic expression","score":0.34040001034736633},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.32670000195503235}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7929999828338623},{"id":"https://openalex.org/C160145156","wikidata":"https://www.wikidata.org/wiki/Q778586","display_name":"Executable","level":2,"score":0.659500002861023},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.5253000259399414},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.519599974155426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4918000102043152},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4578999876976013},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4490000009536743},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3896999955177307},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35370001196861267},{"id":"https://openalex.org/C18912844","wikidata":"https://www.wikidata.org/wiki/Q4724001","display_name":"Algebraic expression","level":3,"score":0.34040001034736633},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.335099995136261},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C177212765","wikidata":"https://www.wikidata.org/wiki/Q627335","display_name":"Workflow","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.29660001397132874},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C168065819","wikidata":"https://www.wikidata.org/wiki/Q845566","display_name":"Debugging","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.2556000053882599}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.16169","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.16169","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.16169","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.16169","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"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":{"The":[0],"Brunauer--Emmett--Teller":[1],"(BET)":[2],"method":[3,173],"is":[4,24,149],"a":[5,33,86,194,204],"standard":[6],"tool":[7],"for":[8,186,197],"estimating":[9],"surface":[10],"areas":[11],"from":[12],"adsorption":[13,176],"isotherms,":[14,191],"yet":[15],"practical":[16],"implementations":[17],"involve":[18],"multiple":[19],"algorithmic":[20],"steps":[21],"whose":[22],"correctness":[23,79],"rarely":[25],"made":[26],"explicit.":[27],"In":[28],"this":[29],"work,":[30],"we":[31,97],"present":[32],"fully":[34],"executable":[35,139],"and":[36,65,75,112,132,151,153,158,218],"formally":[37],"verified":[38],"BET":[39,53,129],"analysis":[40,140],"pipeline":[41],"implemented":[42],"in":[43,72,211],"the":[44,51,77,82,94,100,105,114,118,124,128,138,146,155,167,170,189,198],"Lean~4":[45],"theorem":[46],"prover.":[47],"Our":[48],"formalization":[49],"covers":[50],"complete":[52],"Surface":[54],"Identification":[55],"(BETSI)-style":[56],"workflow,":[57],"including":[58],"window":[59,147],"enumeration,":[60],"monotonicity":[61],"checks,":[62],"knee":[63],"selection,":[64],"linear":[66],"regression.":[67],"We":[68,121,142,165],"carry":[69],"out":[70],"computations":[71],"floating-point":[73],"arithmetic":[74],"develop":[76],"corresponding":[78],"proofs":[80],"over":[81],"real":[83],"numbers,":[84],"using":[85],"shared":[87],"polymorphic":[88],"implementation":[89,168],"that":[90,99,134,145,154,203],"supports":[91],"both.":[92],"On":[93],"proof":[95],"side,":[96],"show":[98],"regression":[101],"coefficients":[102],"returned":[103],"by":[104],"algorithm":[106],"agree":[107],"with":[108,192,221],"their":[109,162],"specification-level":[110],"definitions":[111],"minimize":[113],"least-squares":[115],"error":[116],"under":[117],"stated":[119],"assumptions.":[120],"also":[122],"formalize":[123],"algebraic":[125],"derivation":[126],"of":[127,188],"linearized":[130],"expression":[131],"connect":[133],"result":[135],"directly":[136],"to":[137,179,183],"pipeline.":[141],"further":[143],"prove":[144],"enumeration":[148],"sound":[150],"complete,":[152],"admissibility":[156],"checks":[157],"knee-based":[159],"selection":[160],"satisfy":[161],"formal":[163,215],"specifications.":[164],"evaluate":[166],"against":[169],"BETSI":[171],"reference":[172,225],"on":[174],"benchmark":[175],"isotherms.":[177],"Compared":[178],"BETSI,":[180],"LeanBET":[181],"agrees":[182],"machine":[184],"precision":[185],"18":[187],"19":[190],"only":[193],"0.03\\%":[195],"deviation":[196],"UiO-66":[199],"dataset.":[200],"This":[201],"demonstrates":[202],"scientific":[205],"computing":[206],"workflow":[207],"can":[208],"be":[209],"built":[210],"Lean,":[212],"yielding":[213],"both":[214],"verification":[216],"guarantees":[217],"numerical":[219],"agreement":[220],"an":[222],"established":[223],"Python":[224],"implementation.":[226]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-19T00:00:00"}
