{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6U5YWDJW33YRDQDKXMIBYJMFEB","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":"2cb3b5d835c72405a7b92e8e3de68507ea0d0826116abf88196da55c27fb54de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-22T03:10:19Z","title_canon_sha256":"ef38463d5ef8b4ceca1a0162e36b5722a9c6bbcac52807d79ef518720fcfca9f"},"schema_version":"1.0","source":{"id":"1705.07545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07545","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07545v1","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07545","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"6U5YWDJW33YR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6U5YWDJW33YRDQDK","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6U5YWDJW","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:9c220864877d1032db77acd382f93d8290bf722ed09691ce0b99a1e44fcad726","target":"graph","created_at":"2026-05-18T00:44:05Z","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":"Let $G$ be an $n$-vertex graph obtained by adding chords to a cycle of length $n$. Markstr\\\"{o}m asked for the maximum number of edges in $G$ if there are no two cycles in $G$ with the same length. A simple counting argument shows that such a graph can have at most $n + \\sqrt{2n} +1 $ edges. Using difference sets in $\\mathbb{Z}_n$, we show that for infinitely many $n$, there is an $n$-vertex Hamiltonian graph with $n + \\sqrt{n - 3/4} - 3/2$ edges and no repeated cycle length.","authors_text":"Craig Timmons, Joey Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-22T03:10:19Z","title":"A note on the number of edges in a Hamiltonian graph with no repeated cycle length"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07545","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":"sha256:0d2b7c87d77631e1f2f0983f1d08cc8596707eb3b5f6095fa9d957ed902ff354","target":"record","created_at":"2026-05-18T00:44:05Z","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":"2cb3b5d835c72405a7b92e8e3de68507ea0d0826116abf88196da55c27fb54de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-22T03:10:19Z","title_canon_sha256":"ef38463d5ef8b4ceca1a0162e36b5722a9c6bbcac52807d79ef518720fcfca9f"},"schema_version":"1.0","source":{"id":"1705.07545","kind":"arxiv","version":1}},"canonical_sha256":"f53b8b0d36def111c06abb101c2585204fa214f0798e16431f551da14ac0e081","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f53b8b0d36def111c06abb101c2585204fa214f0798e16431f551da14ac0e081","first_computed_at":"2026-05-18T00:44:05.248393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:05.248393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c5Tyj8noX7/v4+zmHIsfnzdkAa/rXmc/fbqhZlxsgf/cfn4esgWavPIozAiNEym126sJ8N3kdCK4vct7e0pGAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:05.249004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d2b7c87d77631e1f2f0983f1d08cc8596707eb3b5f6095fa9d957ed902ff354","sha256:9c220864877d1032db77acd382f93d8290bf722ed09691ce0b99a1e44fcad726"],"state_sha256":"6228c011b9eb1e5080095bd4bd11487f0722bb0a2a8a83dff67274f8eed2fdc3"}