{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7CBYLNIV6HHMPZ6SEPEILUZI4G","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":"044aca5296bb114b8268e18ffc7aa64e929078d32b1cd552333233b8f2ddb633","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T06:26:03Z","title_canon_sha256":"11c04ec947370a7df7c753ba279ede78762c7aefa55106d0addab1f5cecb2634"},"schema_version":"1.0","source":{"id":"1902.10351","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10351","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10351v1","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10351","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"7CBYLNIV6HHM","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7CBYLNIV6HHMPZ6S","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7CBYLNIV","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:fbb3dee012678da816074325bd047b7e5d024835da26bd41bb4f624f1a2a5b7d","target":"graph","created_at":"2026-05-17T23:52:31Z","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":"A constructive method is provided that outputs a directed graph which is named a broken crown graph, containing $5n-9$ vertices and $k$ Hamiltonian cycles for any choice of integers $n \\geq k \\geq 4$. The construction is not designed to be minimal in any sense, but rather to ensure that the graphs produced remain non-trivial instances of the Hamiltonian cycle problem even when $k$ is chosen to be much smaller than $n$.","authors_text":"Michael Haythorpe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T06:26:03Z","title":"Constructing Arbitrarily Large Graphs with a Specified Number of Hamiltonian Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10351","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":"sha256:58aa0174b646d0c65f15a312db6de8b271d255455243e4b9a608a1bffed83fb2","target":"record","created_at":"2026-05-17T23:52:31Z","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":"044aca5296bb114b8268e18ffc7aa64e929078d32b1cd552333233b8f2ddb633","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T06:26:03Z","title_canon_sha256":"11c04ec947370a7df7c753ba279ede78762c7aefa55106d0addab1f5cecb2634"},"schema_version":"1.0","source":{"id":"1902.10351","kind":"arxiv","version":1}},"canonical_sha256":"f88385b515f1cec7e7d223c885d328e1bb0be890e68f4de902f42e341c2671c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f88385b515f1cec7e7d223c885d328e1bb0be890e68f4de902f42e341c2671c7","first_computed_at":"2026-05-17T23:52:31.101242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:31.101242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vFBz1wo0cKe/DkCFucovZyuZKEJh/NwRw3hHrhV/ZbDsqKGpnyiZnc34mSs3E2MTdetpQsNG/IXPbKZnU+CPAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:31.101684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10351","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58aa0174b646d0c65f15a312db6de8b271d255455243e4b9a608a1bffed83fb2","sha256:fbb3dee012678da816074325bd047b7e5d024835da26bd41bb4f624f1a2a5b7d"],"state_sha256":"7b7f598aaab365d891c1391548b7f20d53fd57ab2d6e86b3ed37aa62d548ee7c"}