{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ENV6KIEWDWGOPM27D74WYQQ5LR","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":"38ad245c1832778daaab2ac949c224111967ac581c310db1343fc2e1d31d24d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-07T03:49:31Z","title_canon_sha256":"fffc1c7928db527191348de23da6162ef34febf758ca8a817ba88cf1bdcef2c9"},"schema_version":"1.0","source":{"id":"1812.02894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02894","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02894v1","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02894","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"pith_short_12","alias_value":"ENV6KIEWDWGO","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ENV6KIEWDWGOPM27","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ENV6KIEW","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:2ff859bf7a1df69127b78635d8359eb4deee16ca757a7520f8b963b662018d46","target":"graph","created_at":"2026-05-17T23:58:51Z","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":"The prism over a graph $G$ is the cartesian product $G \\Box K_2$. It is known that the property of having a Hamiltonian prism (prism-Hamiltonicity) is stronger than that of having a $2$-walk (spanning closed walk using every vertex at most twice) and weaker than that of having a Hamilton path. For a graph $G$, it is known that $\\alpha(G) \\leq 2 \\kappa(G)$, where $\\alpha(G)$ is the independence number and $\\kappa(G)$ is the connectivity, imples existence of a $2$-walk in $G$, and the bound is sharp. West asked for a bound on $\\alpha (G)$ in terms of $\\kappa (G)$ guaranteeing prism-Hamiltonicity","authors_text":"M. N. Ellingham, Pouria Salehi Nowbandegani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-07T03:49:31Z","title":"The Chv\\'atal-Erd\\H{o}s condition for prism-Hamiltonicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02894","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":"sha256:9dd0260e0a1ec8498c7bb1acd166b0fe156ea917037e839a215bfe902655a61d","target":"record","created_at":"2026-05-17T23:58:51Z","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":"38ad245c1832778daaab2ac949c224111967ac581c310db1343fc2e1d31d24d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-07T03:49:31Z","title_canon_sha256":"fffc1c7928db527191348de23da6162ef34febf758ca8a817ba88cf1bdcef2c9"},"schema_version":"1.0","source":{"id":"1812.02894","kind":"arxiv","version":1}},"canonical_sha256":"236be520961d8ce7b35f1ff96c421d5c672a562c3d72475d3375869409250b16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"236be520961d8ce7b35f1ff96c421d5c672a562c3d72475d3375869409250b16","first_computed_at":"2026-05-17T23:58:51.508957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:51.508957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rv7rWxSIk/unwoaA/abSFnnfxV8FJ7mOdeFEYmMFs3BFNg5otiWmVtoHgShnWCfp46+hTx9Ojgbc/KHbWssHBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:51.509462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dd0260e0a1ec8498c7bb1acd166b0fe156ea917037e839a215bfe902655a61d","sha256:2ff859bf7a1df69127b78635d8359eb4deee16ca757a7520f8b963b662018d46"],"state_sha256":"02ce8dc5dfbb261018586c18458ad1e0fc592d1dca92fb779a35829e47796c2a"}