{"paper":{"title":"LeanBET: Formally-verified surface area calculations in Lean","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A fully executable BET surface area pipeline has been formally verified in Lean with proofs over the reals and floating-point execution that matches a reference implementation.","cross_cats":["cs.MS","physics.chem-ph"],"primary_cat":"cs.LO","authors_text":"Colin T. Jones, Ejike D. Ugwuanyi, John Velkey, Tyler R. Josephson","submitted_at":"2026-05-15T16:48:52Z","abstract_excerpt":"The Brunauer--Emmett--Teller (BET) method is a standard tool for estimating surface areas from adsorption isotherms, yet practical implementations involve multiple algorithmic steps whose correctness is rarely made explicit. In this work, we present a fully executable and formally verified BET analysis pipeline implemented in the Lean~4 theorem prover.\n  Our formalization covers the complete BET Surface Identification (BETSI)-style workflow, including window enumeration, monotonicity checks, knee selection, and linear regression. We carry out computations in floating-point arithmetic and devel"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the regression coefficients returned by the algorithm agree with their specification-level definitions and minimize the least-squares error under the stated assumptions. We also prove that the window enumeration is sound and complete, and that the admissibility checks and knee-based selection satisfy their formal specifications.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The floating-point implementation is assumed to be a faithful enough approximation of the real-number proofs for the numerical results to be trusted in practice; the paper does not supply a formal proof of the floating-point semantics themselves.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"LeanBET supplies a fully executable, formally verified BET analysis pipeline in Lean 4 whose regression coefficients and window selections match their real-number specifications and agree with the BETSI reference to machine precision on 18 of 19 isotherms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A fully executable BET surface area pipeline has been formally verified in Lean with proofs over the reals and floating-point execution that matches a reference implementation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"727eb5940adde4f385a4f7a5766ab8a3dcfbc2bec46f54358597cb0de21025ee"},"source":{"id":"2605.16169","kind":"arxiv","version":1},"verdict":{"id":"292ff496-3ad8-4513-af4d-2dcd7cf0e2d7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:36:32.727924Z","strongest_claim":"We show that the regression coefficients returned by the algorithm agree with their specification-level definitions and minimize the least-squares error under the stated assumptions. We also prove that the window enumeration is sound and complete, and that the admissibility checks and knee-based selection satisfy their formal specifications.","one_line_summary":"LeanBET supplies a fully executable, formally verified BET analysis pipeline in Lean 4 whose regression coefficients and window selections match their real-number specifications and agree with the BETSI reference to machine precision on 18 of 19 isotherms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The floating-point implementation is assumed to be a faithful enough approximation of the real-number proofs for the numerical results to be trusted in practice; the paper does not supply a formal proof of the floating-point semantics themselves.","pith_extraction_headline":"A fully executable BET surface area pipeline has been formally verified in Lean with proofs over the reals and floating-point execution that matches a reference implementation."},"integrity":{"clean":false,"summary":{"advisory":0,"critical":1,"by_detector":{"doi_compliance":{"total":1,"advisory":0,"critical":1,"informational":0}},"informational":0},"endpoint":"/pith/2605.16169/integrity.json","findings":[{"note":"Identifier '10.1351/pac199466081739/html' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","detector":"doi_compliance","severity":"critical","ref_index":6,"audited_at":"2026-05-19T18:51:27.554398Z","detected_doi":"10.1351/pac199466081739/html","finding_type":"unresolvable_identifier","verdict_class":"cross_source","detected_arxiv_id":null}],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.912553Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:51:27.554398Z","status":"completed","version":"1.0.0","findings_count":1},{"name":"cited_work_retraction","ran_at":"2026-05-19T17:52:14.895275Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:31.031575Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T17:31:46.191614Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.430065Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"31b036a769ab216b82bb15f127b3359b693b5de35b8830d473b7eabed3d48b82"},"references":{"count":21,"sample":[{"doi":"10.1021/ja01269a023","year":1938,"title":"Stephen Brunauer, P. H. Emmett, and Edward Teller. Adsorption of Gases in Multimolecular Layers. Journal of the American Chemical Society, 60(2):309–319, February 1938. URL:https://pubs.a cs.org/doi/a","work_id":"a7ac02a1-7bf3-4b90-808a-8a0cd62d31ed","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.micromeso.20","year":2011,"title":"Van Erp and Johan A","work_id":"79c1f617-66af-4c41-b187-47f1623ed340","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1002/adma.202201502","year":2022,"title":"Johannes W. M. Osterrieth, James Rampersad, David Madden, Nakul Rampal, Luka Skoric, Bethany Connolly, Mark D. Allendorf, Vitalie Stavila, Jonathan L. Snider, Rob Ameloot, João Marreiros, Conchi Ania,","work_id":"81c4ce27-94e7-4646-ac76-f1280a08b875","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1002/smtd.201800173","year":2018,"title":"Macdonald, Vladimir Martis, and Ivan P","work_id":"6f3de6aa-2b27-4da9-a2fa-6a914716542f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.ces.2010.02.023","year":2010,"title":"D.D. Do, H.D. Do, and D. Nicholson. A computer appraisal of BET theory, BET surface area and the calculation of surface excess for gas adsorption on a graphite surface.Chemical Engineering Science, 65","work_id":"f13b03a5-06fe-43a1-af7b-a90f8e7c5dd3","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":21,"snapshot_sha256":"9db9379b8e70f1dbda727e689cfd15aa275956ddf080824d9e8d0027a3f50569","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"54e2062dc17f455418fa5dd6e2a36357427e4883d97848e9443ee8351757b665"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}