{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WMJXHWQMS5G7MWRYQX2YQDS5JY","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":"3b485ee1583d247fdaf37c4214eca7c3bb2e01d1754d46feaf6cafe819df6e7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-18T11:27:46Z","title_canon_sha256":"db1ac6d76bb9c9152b7377d84adf67ed367c2508988b8bca8533a6ad3a7bca21"},"schema_version":"1.0","source":{"id":"1304.5089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5089","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5089v1","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5089","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"WMJXHWQMS5G7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WMJXHWQMS5G7MWRY","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WMJXHWQM","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:b0df65bb0340d85a2a46526cf7bface9f21ced7f8ae09752980fe323269a9244","target":"graph","created_at":"2026-05-18T03:27:41Z","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 characterize Cohen-Macaulay and Gorenstein rings obtained from certain types of convex body semigroups. Algorithmic methods to check if a polygonal or circle semigroup is Cohen-Macaulay/Gorenstein are given. We also provide some families of Cohen-Macaulay and Gorenstein rings.","authors_text":"A. Vigneron-Tenorio, J. I. Garc\\'ia-Garc\\'ia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-18T11:27:46Z","title":"Computing families of Cohen-Macaulay and Gorenstein rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5089","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":"sha256:4e713373d0673269e449a5de3e022ee35d955d16ae1e80083fc8836e2194451f","target":"record","created_at":"2026-05-18T03:27:41Z","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":"3b485ee1583d247fdaf37c4214eca7c3bb2e01d1754d46feaf6cafe819df6e7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-04-18T11:27:46Z","title_canon_sha256":"db1ac6d76bb9c9152b7377d84adf67ed367c2508988b8bca8533a6ad3a7bca21"},"schema_version":"1.0","source":{"id":"1304.5089","kind":"arxiv","version":1}},"canonical_sha256":"b31373da0c974df65a3885f5880e5d4e1e594223d49915e5847cff655bf94404","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b31373da0c974df65a3885f5880e5d4e1e594223d49915e5847cff655bf94404","first_computed_at":"2026-05-18T03:27:41.813593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:41.813593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3H5wfD02FEr9350SjgTiVuQc9lu9Sr2Mp4wGRaL6mj9DU+ciiepTQcX9xJ2r5LAh5oXLGfFTJhot+QMo5/kVBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:41.814199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e713373d0673269e449a5de3e022ee35d955d16ae1e80083fc8836e2194451f","sha256:b0df65bb0340d85a2a46526cf7bface9f21ced7f8ae09752980fe323269a9244"],"state_sha256":"8563315b258466208772784f4be99b95010474b7ab6a981d86794cf1fd7ad20a"}