{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UPNB6QZZKENVMBWWKH5WWVNKO4","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":"5e46e5bf8ff496d4b41680e6fec8eab459b242a4faa4993d5570146cd265ad4e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-04-24T01:33:12Z","title_canon_sha256":"445bd47ffa7f9ead1e973cfb3db6823933421345c10257e800cc33d7ef43d41c"},"schema_version":"1.0","source":{"id":"1204.5247","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5247","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5247v2","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5247","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"pith_short_12","alias_value":"UPNB6QZZKENV","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UPNB6QZZKENVMBWW","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UPNB6QZZ","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:b6ea775785ca796bc8c2b8451ad5ee610f852daa1ef0c100dfd358ad2585abaf","target":"graph","created_at":"2026-05-18T03:33:14Z","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":"This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also presented.","authors_text":"Fabrizio Zanello, Juan Migliore, Uwe Nagel","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-04-24T01:33:12Z","title":"Pure O-sequences: known results, applications, and open problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5247","kind":"arxiv","version":2},"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":"sha256:2fa51c1238431d06444ab5822b2e61e327160e71ba54e52deb90bd75499a6900","target":"record","created_at":"2026-05-18T03:33:14Z","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":"5e46e5bf8ff496d4b41680e6fec8eab459b242a4faa4993d5570146cd265ad4e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-04-24T01:33:12Z","title_canon_sha256":"445bd47ffa7f9ead1e973cfb3db6823933421345c10257e800cc33d7ef43d41c"},"schema_version":"1.0","source":{"id":"1204.5247","kind":"arxiv","version":2}},"canonical_sha256":"a3da1f4339511b5606d651fb6b55aa77260db0ae840981db5a82ca54330ef577","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3da1f4339511b5606d651fb6b55aa77260db0ae840981db5a82ca54330ef577","first_computed_at":"2026-05-18T03:33:14.165976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:14.165976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"959cJ80SO7kUJW5A656rXggtjPuk8YcYBnh2IX5xQQo0LpcTNC+1NmzqwsykxzYXOP6KWnMR44K1ar8kjJ8kCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:14.166739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5247","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fa51c1238431d06444ab5822b2e61e327160e71ba54e52deb90bd75499a6900","sha256:b6ea775785ca796bc8c2b8451ad5ee610f852daa1ef0c100dfd358ad2585abaf"],"state_sha256":"25d1674a0ec8e187b58308b41a91d9ec0097fd54c9111dc4c292d7af8d41564b"}