{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DRM2IZSHJICRHDTQHOXNGX7WN5","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":"746ad2625e9b58d7fd004d082a56dcc02ae8eba60c5b0edddb58e3d0082f38e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-11T08:29:28Z","title_canon_sha256":"e38dcb311d430efa825ace1d8edcf47ff9f7e3d18aab6ec843c790109a81310c"},"schema_version":"1.0","source":{"id":"1110.2300","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2300","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2300v1","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2300","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"DRM2IZSHJICR","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DRM2IZSHJICRHDTQ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DRM2IZSH","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:2386e5c134f28775947dae387ce6951336edd5d4bfcd544a49f30b9ffcb73ff1","target":"graph","created_at":"2026-05-18T04:11:17Z","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":"It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial ideal.","authors_text":"Giancarlo Rinaldo, J\\\"urgen Herzog, Shamila Bayati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-11T08:29:28Z","title":"On the stable set of associated prime ideals of a monomial ideal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2300","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":"sha256:1887a69c1cc4fbef45b0df44b268eeced9b680d2e589eed26513be17739a3c77","target":"record","created_at":"2026-05-18T04:11:17Z","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":"746ad2625e9b58d7fd004d082a56dcc02ae8eba60c5b0edddb58e3d0082f38e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-11T08:29:28Z","title_canon_sha256":"e38dcb311d430efa825ace1d8edcf47ff9f7e3d18aab6ec843c790109a81310c"},"schema_version":"1.0","source":{"id":"1110.2300","kind":"arxiv","version":1}},"canonical_sha256":"1c59a466474a05138e703baed35ff66f40ee6f220089ccc2012bab1fbd2a77d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c59a466474a05138e703baed35ff66f40ee6f220089ccc2012bab1fbd2a77d8","first_computed_at":"2026-05-18T04:11:17.065747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:17.065747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4WgkgviJ7zTCFLS2jsoOu3LM+ooLTXY6Pm+MklHbpaEqGlYjDsOiUNcZ+0OJ7ejGmjAvrTky2tD8LWmUfqfQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:17.066416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2300","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1887a69c1cc4fbef45b0df44b268eeced9b680d2e589eed26513be17739a3c77","sha256:2386e5c134f28775947dae387ce6951336edd5d4bfcd544a49f30b9ffcb73ff1"],"state_sha256":"2acebc4692cf0457d823b2ed54a41801814e7083844c5d9f98d43d64e6a8868e"}