{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:WUIIHQOGRBWOZEKU2LQORKE67P","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":"ff82d736870933ba0e1ed92f4671613b3ab16bd931f89d8de2f9583431fdc1b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-09-09T23:13:53Z","title_canon_sha256":"28d5602057eb43600a4e12979d283c6aac67275b6188290021fdf00cd3f3dfd6"},"schema_version":"1.0","source":{"id":"2209.04552","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.04552","created_at":"2026-07-05T04:56:02Z"},{"alias_kind":"arxiv_version","alias_value":"2209.04552v1","created_at":"2026-07-05T04:56:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.04552","created_at":"2026-07-05T04:56:02Z"},{"alias_kind":"pith_short_12","alias_value":"WUIIHQOGRBWO","created_at":"2026-07-05T04:56:02Z"},{"alias_kind":"pith_short_16","alias_value":"WUIIHQOGRBWOZEKU","created_at":"2026-07-05T04:56:02Z"},{"alias_kind":"pith_short_8","alias_value":"WUIIHQOG","created_at":"2026-07-05T04:56:02Z"}],"graph_snapshots":[{"event_id":"sha256:52621a5d54310bf84984d7335164acbc6204074c247761c272cd9b5e5c3b5f39","target":"graph","created_at":"2026-07-05T04:56:02Z","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/2209.04552/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we showcase the process of using an automated conjecturing program called \\emph{TxGraffiti} written and maintained by the second author. We begin by proving a conjecture formulated by \\emph{TxGraffiti} that for a claw-free graph $G$, the vertex cover number $\\beta(G)$ is greater than or equal to the zero forcing number $Z(G)$. Our proof of this result is constructive, and yields a polynomial time algorithm to find a zero forcing set with cardinality $\\beta(G)$. We also use the output of \\emph{TxGraffiti} to construct several infinite families of claw-free graphs for which $Z(G)=","authors_text":"Boris Brimkov, Houston Schuerger, Michael Young, Randy Davila","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-09-09T23:13:53Z","title":"Computer assisted discovery: Zero forcing vs vertex cover"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.04552","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":"sha256:675443c69258008162cec0d5fbf0a855c3d932a909597dc2d82249f4829d7511","target":"record","created_at":"2026-07-05T04:56:02Z","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":"ff82d736870933ba0e1ed92f4671613b3ab16bd931f89d8de2f9583431fdc1b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-09-09T23:13:53Z","title_canon_sha256":"28d5602057eb43600a4e12979d283c6aac67275b6188290021fdf00cd3f3dfd6"},"schema_version":"1.0","source":{"id":"2209.04552","kind":"arxiv","version":1}},"canonical_sha256":"b51083c1c6886cec9154d2e0e8a89efbd870bbf5db90598101ac2224ba52a817","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b51083c1c6886cec9154d2e0e8a89efbd870bbf5db90598101ac2224ba52a817","first_computed_at":"2026-07-05T04:56:02.869064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:56:02.869064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mts8ZeL4YnJaQc8g+QTXny617awWecyYU6T5oNEGHt6wUyljOrixjG4YTzIZT7FXjToSiXspdPSafEcNSbQfBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:56:02.869428Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.04552","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:675443c69258008162cec0d5fbf0a855c3d932a909597dc2d82249f4829d7511","sha256:52621a5d54310bf84984d7335164acbc6204074c247761c272cd9b5e5c3b5f39"],"state_sha256":"db0a59a4d0eaaca0ae9fca14577a14dcc1703e133e0ae8912aa58bfc59c8dd08"}