{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3MYPVUI7STXDKFCCV7TSQW4RPI","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":"941bc98e49a0d65f4a11d0e47deb121469dd7db3e8b94a705f92297eb704d6d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-04-04T02:01:43Z","title_canon_sha256":"8aaca6f1915637e02016bf5c9c0734da02469763d245ea98647ef5cc88bd9187"},"schema_version":"1.0","source":{"id":"1904.02305","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02305","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02305v1","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02305","created_at":"2026-05-17T23:49:23Z"},{"alias_kind":"pith_short_12","alias_value":"3MYPVUI7STXD","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3MYPVUI7STXDKFCC","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3MYPVUI7","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:0f82beb8387263da2426c218cdd214599f22aa604fc9448f8339ac03eb11ddae","target":"graph","created_at":"2026-05-17T23:49:23Z","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 provide some exact formulas for the regularity of powers of edge ideals of vertex-weighted oriented cycles and vertex-weighted unicyclic graphs. These formulas are functions of the weight of vertices and the number of edges. We also give some examples to show that these formulas are related to direction selection and the weight of vertices.","authors_text":"Guangjun Zhu, Hong Wang, Jiaqi Zhang, Li Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-04-04T02:01:43Z","title":"Regularity of powers of edge ideals of vertex-weighted oriented unicyclic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02305","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":"sha256:512909f3ee9c811b5992823726c3a154ebe32144784ea0b28f2b767cfde6c295","target":"record","created_at":"2026-05-17T23:49:23Z","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":"941bc98e49a0d65f4a11d0e47deb121469dd7db3e8b94a705f92297eb704d6d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-04-04T02:01:43Z","title_canon_sha256":"8aaca6f1915637e02016bf5c9c0734da02469763d245ea98647ef5cc88bd9187"},"schema_version":"1.0","source":{"id":"1904.02305","kind":"arxiv","version":1}},"canonical_sha256":"db30fad11f94ee351442afe7285b917a0147b6265700647f168f7286cd47be86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db30fad11f94ee351442afe7285b917a0147b6265700647f168f7286cd47be86","first_computed_at":"2026-05-17T23:49:23.978809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:23.978809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TDgnvt1TX9IuvjLKY7nB+IPFFBjeGPjAKNxYC/zYLTuXai9PrnCKwHMnfSkGLX63AjYYAPBuFMVT+ju7kLGTAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:23.979302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02305","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:512909f3ee9c811b5992823726c3a154ebe32144784ea0b28f2b767cfde6c295","sha256:0f82beb8387263da2426c218cdd214599f22aa604fc9448f8339ac03eb11ddae"],"state_sha256":"8e786b206c897ab1383823d77c1284f8ac0932e29dbacae8e4762deb37409f2c"}