{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KEQZFHTFOJDRFBYHDNIPZIOHSI","short_pith_number":"pith:KEQZFHTF","schema_version":"1.0","canonical_sha256":"5121929e6572471287071b50fca1c79238748aa50fbdc60b265d008074bc77a9","source":{"kind":"arxiv","id":"1401.0234","version":3},"attestation_state":"computed","paper":{"title":"The Frobenius Complexity of a Local Ring of Prime Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Florian Enescu, Yongwei Yao","submitted_at":"2014-01-01T00:13:49Z","abstract_excerpt":"We introduce a new invariant for local rings of prime characteristic, called Frobenius complexity, that measures the abundance of Frobenius actions on the injective hull of the residue field of a local ring. We present an important case where the Frobenius complexity is finite, and prove that complete, normal rings of dimension two or less have Frobenius complexity less than or equal to zero. Moreover, we compute the Frobenius complexity for the determinantal ring obtained by modding out the $2 \\times 2$ minors of a $2 \\times 3$ matrix of indeterminates, showing that this number can be positiv"},"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":"1401.0234","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-01-01T00:13:49Z","cross_cats_sorted":[],"title_canon_sha256":"461e1fe91c511e72933f88a4a8f313d2f73216774a131c81a77dfdebf1976728","abstract_canon_sha256":"b97f46c4cd9f8222f2721a9a539ac2db86c729d775e5c3ac25647ff02d896a4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.041367Z","signature_b64":"jXoSGPil3VkccQCMGkQFsdc7Rzw7GmUqoHShQc2v50q/arWZgMysh5bxqbC7Xx+ceavUy262ca7nfOHE5U2NCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5121929e6572471287071b50fca1c79238748aa50fbdc60b265d008074bc77a9","last_reissued_at":"2026-05-18T02:25:19.041015Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.041015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Frobenius Complexity of a Local Ring of Prime Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Florian Enescu, Yongwei Yao","submitted_at":"2014-01-01T00:13:49Z","abstract_excerpt":"We introduce a new invariant for local rings of prime characteristic, called Frobenius complexity, that measures the abundance of Frobenius actions on the injective hull of the residue field of a local ring. We present an important case where the Frobenius complexity is finite, and prove that complete, normal rings of dimension two or less have Frobenius complexity less than or equal to zero. Moreover, we compute the Frobenius complexity for the determinantal ring obtained by modding out the $2 \\times 2$ minors of a $2 \\times 3$ matrix of indeterminates, showing that this number can be positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0234","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":"1401.0234","created_at":"2026-05-18T02:25:19.041069+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.0234v3","created_at":"2026-05-18T02:25:19.041069+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0234","created_at":"2026-05-18T02:25:19.041069+00:00"},{"alias_kind":"pith_short_12","alias_value":"KEQZFHTFOJDR","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KEQZFHTFOJDRFBYH","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KEQZFHTF","created_at":"2026-05-18T12:28:35.611951+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/KEQZFHTFOJDRFBYHDNIPZIOHSI","json":"https://pith.science/pith/KEQZFHTFOJDRFBYHDNIPZIOHSI.json","graph_json":"https://pith.science/api/pith-number/KEQZFHTFOJDRFBYHDNIPZIOHSI/graph.json","events_json":"https://pith.science/api/pith-number/KEQZFHTFOJDRFBYHDNIPZIOHSI/events.json","paper":"https://pith.science/paper/KEQZFHTF"},"agent_actions":{"view_html":"https://pith.science/pith/KEQZFHTFOJDRFBYHDNIPZIOHSI","download_json":"https://pith.science/pith/KEQZFHTFOJDRFBYHDNIPZIOHSI.json","view_paper":"https://pith.science/paper/KEQZFHTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.0234&json=true","fetch_graph":"https://pith.science/api/pith-number/KEQZFHTFOJDRFBYHDNIPZIOHSI/graph.json","fetch_events":"https://pith.science/api/pith-number/KEQZFHTFOJDRFBYHDNIPZIOHSI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KEQZFHTFOJDRFBYHDNIPZIOHSI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KEQZFHTFOJDRFBYHDNIPZIOHSI/action/storage_attestation","attest_author":"https://pith.science/pith/KEQZFHTFOJDRFBYHDNIPZIOHSI/action/author_attestation","sign_citation":"https://pith.science/pith/KEQZFHTFOJDRFBYHDNIPZIOHSI/action/citation_signature","submit_replication":"https://pith.science/pith/KEQZFHTFOJDRFBYHDNIPZIOHSI/action/replication_record"}},"created_at":"2026-05-18T02:25:19.041069+00:00","updated_at":"2026-05-18T02:25:19.041069+00:00"}