{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RX23BHDYGB7G2CW6SCXZTOOB33","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":"2666ac11ce99d2d27c5613326109f0bfd3b4b065eaa1f992cafe0072ccc3b82f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-01T06:56:24Z","title_canon_sha256":"9ff30a2e58e5538ec8488a0207aae7b5905ad9eab49c40d2799eba02513f9890"},"schema_version":"1.0","source":{"id":"1903.00178","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00178","created_at":"2026-07-05T02:13:01Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00178v2","created_at":"2026-07-05T02:13:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00178","created_at":"2026-07-05T02:13:01Z"},{"alias_kind":"pith_short_12","alias_value":"RX23BHDYGB7G","created_at":"2026-07-05T02:13:01Z"},{"alias_kind":"pith_short_16","alias_value":"RX23BHDYGB7G2CW6","created_at":"2026-07-05T02:13:01Z"},{"alias_kind":"pith_short_8","alias_value":"RX23BHDY","created_at":"2026-07-05T02:13:01Z"}],"graph_snapshots":[{"event_id":"sha256:42498b6200cd0390a5aa8104b888a8fa0685137fef7efa091eace32402258ec8","target":"graph","created_at":"2026-07-05T02:13:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.00178/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we compute the regularity and Hilbert series of symbolic powers of the cover ideal of a graph $G$ when $G$ is either a crown graph or a complete multipartite graph. We also compute the multiplicity of symbolic powers of cover ideals in terms of the number of edges.","authors_text":"Arvind Kumar, Rajib Sarkar, Rajiv Kumar, S. Selvaraja","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-01T06:56:24Z","title":"Symbolic powers of certain cover ideals of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00178","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":"sha256:598ee28144f0d01119000b215c8ee1a1c725ec6ee8f706f9f61f1e728a61ef0e","target":"record","created_at":"2026-07-05T02:13:01Z","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":"2666ac11ce99d2d27c5613326109f0bfd3b4b065eaa1f992cafe0072ccc3b82f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-01T06:56:24Z","title_canon_sha256":"9ff30a2e58e5538ec8488a0207aae7b5905ad9eab49c40d2799eba02513f9890"},"schema_version":"1.0","source":{"id":"1903.00178","kind":"arxiv","version":2}},"canonical_sha256":"8df5b09c78307e6d0ade90af99b9c1dee9a41ab9cd46226794a83a9b4c43779c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8df5b09c78307e6d0ade90af99b9c1dee9a41ab9cd46226794a83a9b4c43779c","first_computed_at":"2026-07-05T02:13:01.458751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:13:01.458751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bVwca1WGcjelzIGau+rq1ALdfFhI3klsqHUJeuVS/ULD/gUHS5WZ3zX2kyhxi8LKE8HsFMOgGhLgHMm6l7zODA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:13:01.459152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00178","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:598ee28144f0d01119000b215c8ee1a1c725ec6ee8f706f9f61f1e728a61ef0e","sha256:42498b6200cd0390a5aa8104b888a8fa0685137fef7efa091eace32402258ec8"],"state_sha256":"80b92afef7484c495159f8112ce18b4f7d4d7695bbd23fc6fa7627b275b71299"}