{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OTMFPBSZRYZGWPMZYLC45Y23J6","short_pith_number":"pith:OTMFPBSZ","schema_version":"1.0","canonical_sha256":"74d85786598e326b3d99c2c5cee35b4f936bf76b8b8c89740912094707573494","source":{"kind":"arxiv","id":"1404.1851","version":2},"attestation_state":"computed","paper":{"title":"Extremal permutations in routing cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gexin Yu, Junhua He, Louis A. Valentin, Xiaoyan Yin","submitted_at":"2014-04-07T17:11:29Z","abstract_excerpt":"Let $G$ be a graph on $n$ vertices, labeled $v_1,\\ldots,v_n$ and $\\pi$ be a permutation on $[n]:=\\{1,2,\\cdots, n\\}$. Suppose that each pebble $p_i$ is placed at vertex $v_{\\pi(i)}$ and has destination $v_i$. During each step, a disjoint set of edges is selected and the pebbles on each edge are swapped. Let $rt(G, \\pi)$, the routing number for $\\pi$, be the minimum number of steps necessary for the pebbles to reach their destinations.\n  Li, Lu, and Yang prove that $rt(C_n, \\pi)\\le n-1$ for any permutation on $n$-cycle $C_n$ and conjecture that for $n \\geq 5$, if $rt(C_n, \\pi) = n-1$, then $\\pi "},"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":"1404.1851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-07T17:11:29Z","cross_cats_sorted":[],"title_canon_sha256":"662d5510fb1ff30b8fa74a448996d4c9f145f68a4e7d44a5c4165926d96210ec","abstract_canon_sha256":"abf56cf829cd0485f54fcde502c1a0df599a58c166d72f50dc2d83d67c7ac6df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:41.260286Z","signature_b64":"4Slg9zxPid0cxUff4JMO+/hIRF45DYHKv8nXLrDRLSspGFGmddTJ8bG6Ao5dvBQtAjnJd8XT9yanU4vuwZVwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74d85786598e326b3d99c2c5cee35b4f936bf76b8b8c89740912094707573494","last_reissued_at":"2026-05-18T01:06:41.259706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:41.259706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal permutations in routing cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gexin Yu, Junhua He, Louis A. Valentin, Xiaoyan Yin","submitted_at":"2014-04-07T17:11:29Z","abstract_excerpt":"Let $G$ be a graph on $n$ vertices, labeled $v_1,\\ldots,v_n$ and $\\pi$ be a permutation on $[n]:=\\{1,2,\\cdots, n\\}$. Suppose that each pebble $p_i$ is placed at vertex $v_{\\pi(i)}$ and has destination $v_i$. During each step, a disjoint set of edges is selected and the pebbles on each edge are swapped. Let $rt(G, \\pi)$, the routing number for $\\pi$, be the minimum number of steps necessary for the pebbles to reach their destinations.\n  Li, Lu, and Yang prove that $rt(C_n, \\pi)\\le n-1$ for any permutation on $n$-cycle $C_n$ and conjecture that for $n \\geq 5$, if $rt(C_n, \\pi) = n-1$, then $\\pi "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1851","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":"1404.1851","created_at":"2026-05-18T01:06:41.259814+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.1851v2","created_at":"2026-05-18T01:06:41.259814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1851","created_at":"2026-05-18T01:06:41.259814+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTMFPBSZRYZG","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTMFPBSZRYZGWPMZ","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTMFPBSZ","created_at":"2026-05-18T12:28:43.426989+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/OTMFPBSZRYZGWPMZYLC45Y23J6","json":"https://pith.science/pith/OTMFPBSZRYZGWPMZYLC45Y23J6.json","graph_json":"https://pith.science/api/pith-number/OTMFPBSZRYZGWPMZYLC45Y23J6/graph.json","events_json":"https://pith.science/api/pith-number/OTMFPBSZRYZGWPMZYLC45Y23J6/events.json","paper":"https://pith.science/paper/OTMFPBSZ"},"agent_actions":{"view_html":"https://pith.science/pith/OTMFPBSZRYZGWPMZYLC45Y23J6","download_json":"https://pith.science/pith/OTMFPBSZRYZGWPMZYLC45Y23J6.json","view_paper":"https://pith.science/paper/OTMFPBSZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.1851&json=true","fetch_graph":"https://pith.science/api/pith-number/OTMFPBSZRYZGWPMZYLC45Y23J6/graph.json","fetch_events":"https://pith.science/api/pith-number/OTMFPBSZRYZGWPMZYLC45Y23J6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTMFPBSZRYZGWPMZYLC45Y23J6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTMFPBSZRYZGWPMZYLC45Y23J6/action/storage_attestation","attest_author":"https://pith.science/pith/OTMFPBSZRYZGWPMZYLC45Y23J6/action/author_attestation","sign_citation":"https://pith.science/pith/OTMFPBSZRYZGWPMZYLC45Y23J6/action/citation_signature","submit_replication":"https://pith.science/pith/OTMFPBSZRYZGWPMZYLC45Y23J6/action/replication_record"}},"created_at":"2026-05-18T01:06:41.259814+00:00","updated_at":"2026-05-18T01:06:41.259814+00:00"}