{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:EXVM5KYZRSHVEZE6O3FYKM5IRO","short_pith_number":"pith:EXVM5KYZ","schema_version":"1.0","canonical_sha256":"25eaceab198c8f52649e76cb8533a88baa2f748bf7f8a59716867254c1adceee","source":{"kind":"arxiv","id":"1112.2423","version":1},"attestation_state":"computed","paper":{"title":"F-purity versus log canonicity for polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Daniel J. Hern\\'andez","submitted_at":"2011-12-12T02:27:57Z","abstract_excerpt":"In this article, we consider the conjectured relationship between F-purity and log canonicity for polynomials over the complex numbers. We associate to a collection M of n monomials a rational polytope P contained in [0,1]^n. Using P and the Newton polyhedron associated to M, we define a non-degeneracy condition under which log canonicity and dense F-pure type are equivalent for all linear combinations of the monomials in M. We also show that log canonicity corresponds to F-purity for very general polynomials. Our methods rely on showing that the F-pure and log canonical threshold agree for in"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.2423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-12T02:27:57Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"04ffad91665fa2d880f8c24e97d192de3a7faf52cda3b768f3d9896a72fb7337","abstract_canon_sha256":"a8b10a7ecb1176d0456c7129e6b150f8f06df504587810fc072cddb5235dd058"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:34.459079Z","signature_b64":"HhtUgUnsZ/TnWESyxfXrr/WIXyQtkuYfIdpgxLe4ZNegocNP0Fd7BixeIZDZBXZMIUT1MKiCW1w0yQJSICX2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25eaceab198c8f52649e76cb8533a88baa2f748bf7f8a59716867254c1adceee","last_reissued_at":"2026-05-18T04:06:34.458361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:34.458361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"F-purity versus log canonicity for polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Daniel J. Hern\\'andez","submitted_at":"2011-12-12T02:27:57Z","abstract_excerpt":"In this article, we consider the conjectured relationship between F-purity and log canonicity for polynomials over the complex numbers. We associate to a collection M of n monomials a rational polytope P contained in [0,1]^n. Using P and the Newton polyhedron associated to M, we define a non-degeneracy condition under which log canonicity and dense F-pure type are equivalent for all linear combinations of the monomials in M. We also show that log canonicity corresponds to F-purity for very general polynomials. Our methods rely on showing that the F-pure and log canonical threshold agree for in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2423","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.2423","created_at":"2026-05-18T04:06:34.458483+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.2423v1","created_at":"2026-05-18T04:06:34.458483+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2423","created_at":"2026-05-18T04:06:34.458483+00:00"},{"alias_kind":"pith_short_12","alias_value":"EXVM5KYZRSHV","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"EXVM5KYZRSHVEZE6","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"EXVM5KYZ","created_at":"2026-05-18T12:26:28.662955+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EXVM5KYZRSHVEZE6O3FYKM5IRO","json":"https://pith.science/pith/EXVM5KYZRSHVEZE6O3FYKM5IRO.json","graph_json":"https://pith.science/api/pith-number/EXVM5KYZRSHVEZE6O3FYKM5IRO/graph.json","events_json":"https://pith.science/api/pith-number/EXVM5KYZRSHVEZE6O3FYKM5IRO/events.json","paper":"https://pith.science/paper/EXVM5KYZ"},"agent_actions":{"view_html":"https://pith.science/pith/EXVM5KYZRSHVEZE6O3FYKM5IRO","download_json":"https://pith.science/pith/EXVM5KYZRSHVEZE6O3FYKM5IRO.json","view_paper":"https://pith.science/paper/EXVM5KYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.2423&json=true","fetch_graph":"https://pith.science/api/pith-number/EXVM5KYZRSHVEZE6O3FYKM5IRO/graph.json","fetch_events":"https://pith.science/api/pith-number/EXVM5KYZRSHVEZE6O3FYKM5IRO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EXVM5KYZRSHVEZE6O3FYKM5IRO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EXVM5KYZRSHVEZE6O3FYKM5IRO/action/storage_attestation","attest_author":"https://pith.science/pith/EXVM5KYZRSHVEZE6O3FYKM5IRO/action/author_attestation","sign_citation":"https://pith.science/pith/EXVM5KYZRSHVEZE6O3FYKM5IRO/action/citation_signature","submit_replication":"https://pith.science/pith/EXVM5KYZRSHVEZE6O3FYKM5IRO/action/replication_record"}},"created_at":"2026-05-18T04:06:34.458483+00:00","updated_at":"2026-05-18T04:06:34.458483+00:00"}