{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:4U2FXLPHYGXCBFK2ZA64JVUQBI","short_pith_number":"pith:4U2FXLPH","schema_version":"1.0","canonical_sha256":"e5345bade7c1ae20955ac83dc4d6900a2cee4bac07f788a3d35419b99e290c40","source":{"kind":"arxiv","id":"0912.0216","version":3},"attestation_state":"computed","paper":{"title":"The lower semicontinuity of the Frobenius splitting numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Florian Enescu, Yongwei Yao","submitted_at":"2009-12-01T17:59:40Z","abstract_excerpt":"We show that, under mild conditions, the (normalized) Frobenius splitting numbers of a local ring of prime characteristic are lower semicontinuous."},"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":"0912.0216","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-12-01T17:59:40Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"98775e1aaa0b90f56c1d377f87da439638460b1a482e554747105d9dd1199ba3","abstract_canon_sha256":"38d151160dd5edba1c7a20879b7877b3fe732d9bee356aec0ce46dc3cf42e46f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:01.921300Z","signature_b64":"m70aSdcQk3GL66EVsKFqWS1LwgeWRRzhr5LL1Igh/N1mmTvysDNyUGU6EJhHsareEE/P645LqVswdcDDgXAiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5345bade7c1ae20955ac83dc4d6900a2cee4bac07f788a3d35419b99e290c40","last_reissued_at":"2026-05-18T04:42:01.920929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:01.920929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The lower semicontinuity of the Frobenius splitting numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Florian Enescu, Yongwei Yao","submitted_at":"2009-12-01T17:59:40Z","abstract_excerpt":"We show that, under mild conditions, the (normalized) Frobenius splitting numbers of a local ring of prime characteristic are lower semicontinuous."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0216","kind":"arxiv","version":3},"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":"0912.0216","created_at":"2026-05-18T04:42:01.920990+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.0216v3","created_at":"2026-05-18T04:42:01.920990+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0216","created_at":"2026-05-18T04:42:01.920990+00:00"},{"alias_kind":"pith_short_12","alias_value":"4U2FXLPHYGXC","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"4U2FXLPHYGXCBFK2","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"4U2FXLPH","created_at":"2026-05-18T12:25:58.837520+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/4U2FXLPHYGXCBFK2ZA64JVUQBI","json":"https://pith.science/pith/4U2FXLPHYGXCBFK2ZA64JVUQBI.json","graph_json":"https://pith.science/api/pith-number/4U2FXLPHYGXCBFK2ZA64JVUQBI/graph.json","events_json":"https://pith.science/api/pith-number/4U2FXLPHYGXCBFK2ZA64JVUQBI/events.json","paper":"https://pith.science/paper/4U2FXLPH"},"agent_actions":{"view_html":"https://pith.science/pith/4U2FXLPHYGXCBFK2ZA64JVUQBI","download_json":"https://pith.science/pith/4U2FXLPHYGXCBFK2ZA64JVUQBI.json","view_paper":"https://pith.science/paper/4U2FXLPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.0216&json=true","fetch_graph":"https://pith.science/api/pith-number/4U2FXLPHYGXCBFK2ZA64JVUQBI/graph.json","fetch_events":"https://pith.science/api/pith-number/4U2FXLPHYGXCBFK2ZA64JVUQBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4U2FXLPHYGXCBFK2ZA64JVUQBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4U2FXLPHYGXCBFK2ZA64JVUQBI/action/storage_attestation","attest_author":"https://pith.science/pith/4U2FXLPHYGXCBFK2ZA64JVUQBI/action/author_attestation","sign_citation":"https://pith.science/pith/4U2FXLPHYGXCBFK2ZA64JVUQBI/action/citation_signature","submit_replication":"https://pith.science/pith/4U2FXLPHYGXCBFK2ZA64JVUQBI/action/replication_record"}},"created_at":"2026-05-18T04:42:01.920990+00:00","updated_at":"2026-05-18T04:42:01.920990+00:00"}