{"paper":{"title":"Representability of the automorphism group of finitely generated vertex algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The automorphism group of finitely generated vertex algebras over noetherian rings is an affine group scheme.","cross_cats":["math.AG","math.RA"],"primary_cat":"math.QA","authors_text":"Arturo Pianzola, Robin Mader, Terry Gannon","submitted_at":"2026-05-15T04:32:38Z","abstract_excerpt":"We study the automorphism groups attached to a free algebra with multiple, possibly infinitely many, composition laws. As an application, we prove that the automorphism group of finitely generated vertex algebras over noetherian rings are affine group schemes."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the automorphism group of finitely generated vertex algebras over noetherian rings are affine group schemes.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The vertex algebra must be finitely generated and the base ring must be noetherian; the representability statement is stated to hold under these hypotheses and may fail without them.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Automorphism groups of finitely generated vertex algebras over noetherian rings are affine group schemes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The automorphism group of finitely generated vertex algebras over noetherian rings is an affine group scheme.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"83f7b9d1979961abdc10303f391a1856318138e38ffc65e9521fa2057ed98c3a"},"source":{"id":"2605.15605","kind":"arxiv","version":1},"verdict":{"id":"a10e7b83-3ee4-408c-b024-37d282f586b9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:33:49.203583Z","strongest_claim":"We prove that the automorphism group of finitely generated vertex algebras over noetherian rings are affine group schemes.","one_line_summary":"Automorphism groups of finitely generated vertex algebras over noetherian rings are affine group schemes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The vertex algebra must be finitely generated and the base ring must be noetherian; the representability statement is stated to hold under these hypotheses and may fail without them.","pith_extraction_headline":"The automorphism group of finitely generated vertex algebras over noetherian rings is an affine group scheme."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15605/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:34:34.892436Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:19.026150Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:41:27.421950Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:41:56.050999Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"0bb540ad10ff81fd5271100a87f212cd3a069082818b0ff359524af51deb0508"},"references":{"count":17,"sample":[{"doi":"","year":1963,"title":"Bass, Big projective modules are free , Illinois J","work_id":"81f8611d-4097-4386-9dea-f99631d73ac9","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1996,"title":"R. 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