{"paper":{"title":"On positivity of the limit F-signature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The limit of F-signatures for KLT singularities stays bounded away from zero in three dimensions for non-weakly exceptional cases and for smooth hypersurfaces of very low degree.","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Suchitra Pande, Yuchen Liu","submitted_at":"2026-05-15T21:06:09Z","abstract_excerpt":"We study a conjecture of Carvajal-Rojas, Schwede and Tucker which states that for a complex KLT singularity $(R, \\mathfrak{m})$, the F-signatures of the reductions of $R$ to characteristic $p \\gg 0$ remain bounded away from zero as $p \\to \\infty$. We prove that this conjecture holds for three-dimensional non-weakly exceptional singularities by an inductive argument. We also prove that the conjecture holds for smooth hypersurfaces of very low degree by constructing isotrivial normal toric degenerations. By considering the version of this conjecture for the Frobenius-alpha invariant, our techniq"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that this conjecture holds for three-dimensional non-weakly exceptional singularities by an inductive argument. We also prove that the conjecture holds for smooth hypersurfaces of very low degree by constructing isotrivial normal toric degenerations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The inductive argument for three-dimensional non-weakly exceptional singularities and the construction of isotrivial normal toric degenerations for low-degree hypersurfaces both rely on the existence of suitable birational models or degenerations whose F-signature behavior can be controlled uniformly in p; this modeling choice is invoked when the authors reduce the problem via K-stability-inspired techniques.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The authors establish the Carvajal-Rojas-Schwede-Tucker conjecture on positive limiting F-signature for two specific classes of complex KLT singularities using inductive arguments and toric degenerations inspired by K-stability.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The limit of F-signatures for KLT singularities stays bounded away from zero in three dimensions for non-weakly exceptional cases and for smooth hypersurfaces of very low degree.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b997703a50edab01989243a55963e1672880d4e8ff1e3566d44690ed317e5303"},"source":{"id":"2605.16636","kind":"arxiv","version":1},"verdict":{"id":"19534edb-a108-4dd1-b68d-abfe84e8c7ac","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:59:27.531448Z","strongest_claim":"We prove that this conjecture holds for three-dimensional non-weakly exceptional singularities by an inductive argument. We also prove that the conjecture holds for smooth hypersurfaces of very low degree by constructing isotrivial normal toric degenerations.","one_line_summary":"The authors establish the Carvajal-Rojas-Schwede-Tucker conjecture on positive limiting F-signature for two specific classes of complex KLT singularities using inductive arguments and toric degenerations inspired by K-stability.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The inductive argument for three-dimensional non-weakly exceptional singularities and the construction of isotrivial normal toric degenerations for low-degree hypersurfaces both rely on the existence of suitable birational models or degenerations whose F-signature behavior can be controlled uniformly in p; this modeling choice is invoked when the authors reduce the problem via K-stability-inspired techniques.","pith_extraction_headline":"The limit of F-signatures for KLT singularities stays bounded away from zero in three dimensions for non-weakly exceptional cases and for smooth hypersurfaces of very low degree."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16636/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T21:31:19.411007Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:12:02.402851Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:21:56.722360Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.578361Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"3604fd33a289f15affe326ce798eab93151714792171b87ae9789e5b797f0eb0"},"references":{"count":300,"sample":[{"doi":"10.1007/s00222-021-01046-0","year":2021,"title":"Zhuang, Ziquan , TITLE =. 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