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If $\\mathcal{C}$ has no parallel classes, we call such a system unparalleled.\n  We show that there exists an unparalleled $2t$-cycle system of order $v \\equiv 0 \\pmod{2t}$ if and only if $v>2t>2$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.07082","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-23T22:56:20Z","cross_cats_sorted":[],"title_canon_sha256":"e4727cdae8f134b4449830fe951f4e928dc22e7ef93b43587180925055bf9940","abstract_canon_sha256":"ffaa02f16cb740db61e16584cd19b056562dc0b034116423aa9b58ba88156d01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:59.569258Z","signature_b64":"wyBh+CNNJL4cZjB0RI3kJbRA4Zt7WxSgkwVt3OE1ZCjNMHV81mVrMASeXUgoOB98cQE3udNcoroFH1Go9FpwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd802b554df0462e3d446765f3b5788fd77ecffce86f895ea581ba1a89d8e8e9","last_reissued_at":"2026-05-18T01:17:59.568499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:59.568499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence of unparalleled even cycle systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eric Mendelsohn, Peter Danziger, Tommaso Traetta","submitted_at":"2015-10-23T22:56:20Z","abstract_excerpt":"A $2t$-cycle system of order $v$ is a set $\\mathcal{C}$ of cycles whose edges partition the edge-set of $K_v-I$ (i.e., the complete graph minus the $1$-factor $I$). 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If $\\mathcal{C}$ has no parallel classes, we call such a system unparalleled.\n  We show that there exists an unparalleled $2t$-cycle system of order $v \\equiv 0 \\pmod{2t}$ if and only if $v>2t>2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07082","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.07082","created_at":"2026-05-18T01:17:59.568635+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.07082v2","created_at":"2026-05-18T01:17:59.568635+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07082","created_at":"2026-05-18T01:17:59.568635+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZWACWVKN6BDC","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZWACWVKN6BDC4PKE","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZWACWVKN","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZWACWVKN6BDC4PKEM5S7HNLYR7","json":"https://pith.science/pith/ZWACWVKN6BDC4PKEM5S7HNLYR7.json","graph_json":"https://pith.science/api/pith-number/ZWACWVKN6BDC4PKEM5S7HNLYR7/graph.json","events_json":"https://pith.science/api/pith-number/ZWACWVKN6BDC4PKEM5S7HNLYR7/events.json","paper":"https://pith.science/paper/ZWACWVKN"},"agent_actions":{"view_html":"https://pith.science/pith/ZWACWVKN6BDC4PKEM5S7HNLYR7","download_json":"https://pith.science/pith/ZWACWVKN6BDC4PKEM5S7HNLYR7.json","view_paper":"https://pith.science/paper/ZWACWVKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.07082&json=true","fetch_graph":"https://pith.science/api/pith-number/ZWACWVKN6BDC4PKEM5S7HNLYR7/graph.json","fetch_events":"https://pith.science/api/pith-number/ZWACWVKN6BDC4PKEM5S7HNLYR7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZWACWVKN6BDC4PKEM5S7HNLYR7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZWACWVKN6BDC4PKEM5S7HNLYR7/action/storage_attestation","attest_author":"https://pith.science/pith/ZWACWVKN6BDC4PKEM5S7HNLYR7/action/author_attestation","sign_citation":"https://pith.science/pith/ZWACWVKN6BDC4PKEM5S7HNLYR7/action/citation_signature","submit_replication":"https://pith.science/pith/ZWACWVKN6BDC4PKEM5S7HNLYR7/action/replication_record"}},"created_at":"2026-05-18T01:17:59.568635+00:00","updated_at":"2026-05-18T01:17:59.568635+00:00"}