{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GTXAKJWY2UWYEWZRHP2QSJCPZ2","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":"5ed74d92bf96f534b82b5a4bd80fe3f50548d9fc3cd8a940b206954a41f982f9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-24T18:48:02Z","title_canon_sha256":"5b0b7ce144852e624aaaf96dfc899b5779d1fb8567dce1715c821f225954bcbc"},"schema_version":"1.0","source":{"id":"1008.4108","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4108","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4108v2","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4108","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"GTXAKJWY2UWY","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GTXAKJWY2UWYEWZR","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GTXAKJWY","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:cfe7cd62506b0c31fd321477a7bfa8c446ada426ac0c27bf1de58737f708d864","target":"graph","created_at":"2026-05-18T04:34:18Z","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":"In this paper, we obtain explicit formulas for the Hilbert series and Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring.","authors_text":"Jiayuan Lin, Maorong Ge, Yulan Wang","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-24T18:48:02Z","title":"Hilbert series and Hilbert depth of squarefree Veronese ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4108","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:da01af5feffc57446d8495f5575f97836b8941370c189859c25248f7cfc3f58f","target":"record","created_at":"2026-05-18T04:34:18Z","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":"5ed74d92bf96f534b82b5a4bd80fe3f50548d9fc3cd8a940b206954a41f982f9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-24T18:48:02Z","title_canon_sha256":"5b0b7ce144852e624aaaf96dfc899b5779d1fb8567dce1715c821f225954bcbc"},"schema_version":"1.0","source":{"id":"1008.4108","kind":"arxiv","version":2}},"canonical_sha256":"34ee0526d8d52d825b313bf509244fceabb15e8884d75d96459fe221ab861528","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34ee0526d8d52d825b313bf509244fceabb15e8884d75d96459fe221ab861528","first_computed_at":"2026-05-18T04:34:18.145035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:18.145035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/mblx0fdm2FaMCBXUni+P4hiaUvCjpv533cICc5pqbUdBQYsxEWdisD+tZkHPq4mrK4nEh9AKa30gB3PobrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:18.145510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4108","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da01af5feffc57446d8495f5575f97836b8941370c189859c25248f7cfc3f58f","sha256:cfe7cd62506b0c31fd321477a7bfa8c446ada426ac0c27bf1de58737f708d864"],"state_sha256":"84f1bba3f6d8a49130d656e77b321a8afe2cf296f5075b2e8de2b99f9d6b2d92"}