{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DY5QG2CTVPUJ5RXAMF6MBEDKJI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"da16aa234381465ba9b037bf023ec52f4bdfa3f9a1bec17d93f662acd79688b3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-28T14:35:50Z","title_canon_sha256":"e5328157981031a28ea187ece06c3f5a3cd7b10933ac2a8b1f6110f3f2a2d127"},"schema_version":"1.0","source":{"id":"1106.5686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5686","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5686v1","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5686","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"DY5QG2CTVPUJ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DY5QG2CTVPUJ5RXA","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DY5QG2CT","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:7f161bd8cd5901a39e055238b8407819626feea1ff4ec710561c28ba7a2b07bb","target":"graph","created_at":"2026-05-18T04:19:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that the Frobenius algebra of the injective hull of a complete Stanley-Reisner ring as well as its Matlis dual notion of Cartier algebra can be only principally generated or infinitely generated. As a consequence we are able to show that the set of F-jumping numbers of generalized test ideals associated to complete Stanley-Reisner rings form a discrete set.","authors_text":"Alberto F. Boix, Josep Alvarez Montaner, Santiago Zarzuela","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-28T14:35:50Z","title":"Frobenius and Cartier algebras of Stanley-Reisner rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5686","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:772bf61c345140cff574d498eb818570b7529571c49fcdcffb9bcb5ede882044","target":"record","created_at":"2026-05-18T04:19:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"da16aa234381465ba9b037bf023ec52f4bdfa3f9a1bec17d93f662acd79688b3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-28T14:35:50Z","title_canon_sha256":"e5328157981031a28ea187ece06c3f5a3cd7b10933ac2a8b1f6110f3f2a2d127"},"schema_version":"1.0","source":{"id":"1106.5686","kind":"arxiv","version":1}},"canonical_sha256":"1e3b036853abe89ec6e0617cc0906a4a07f862bfeeb593a821cbe9b85d74a0af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e3b036853abe89ec6e0617cc0906a4a07f862bfeeb593a821cbe9b85d74a0af","first_computed_at":"2026-05-18T04:19:12.684457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:12.684457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Mz1P+obWP72KWJyKYWk26QqOJZEyz1WaI7NAafKyp2eNfp9CBChrG5AP4nRkCmgDdAW5SYLXi0Zsybbc9csCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:12.685089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:772bf61c345140cff574d498eb818570b7529571c49fcdcffb9bcb5ede882044","sha256:7f161bd8cd5901a39e055238b8407819626feea1ff4ec710561c28ba7a2b07bb"],"state_sha256":"2751b2d7a20f25c478745f2d6bcca9851c90f5f674851483495e4c1a02ec91c4"}