{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RNW677EXZXBJMJ26V7X57VXS7L","short_pith_number":"pith:RNW677EX","schema_version":"1.0","canonical_sha256":"8b6deffc97cdc296275eafefdfd6f2faccd2565338e5e469eb831ff9500b0835","source":{"kind":"arxiv","id":"1808.10119","version":1},"attestation_state":"computed","paper":{"title":"A combinatorial property of flows on a cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zhuo Diao","submitted_at":"2018-08-30T04:52:55Z","abstract_excerpt":"In this paper, we prove a combinatorial property of flows on a cycle. $C(V,E)$ is an undirected cycle with two commodities: $\\{s_{1},t_{1}\\}, \\{s_{2},t_{2}\\}$;$r_1>0,r_2>0, \\mathbf r=(r_i)_{i=1,2}$ and $f,f'$ are both feasible flows for $(C,(s_i,t_i)_{i=1,2},\\mathbf r)$. Then $\\exists i\\in\\{1,2\\}, p\\in P_i, f(p)>0, \\forall e\\in p, f(e)\\geq f'(e)$ ; Here for each $i\\in\\{1,2\\}$, let $P_i$ be the set of $s_i$-$t_i$ paths in $C$ and $P=\\cup_{i=1,2}P_i$. This means given a two-commodity instance on a cycle, any two distinct network flow $f$ and $f'$, compared with $f'$, $f$ can't decrease every pat"},"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":"1808.10119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-30T04:52:55Z","cross_cats_sorted":[],"title_canon_sha256":"cfedb181d33e80a374eed336f7824762c8d3e48c294de5e5f955a02445db8efc","abstract_canon_sha256":"d57c018ab1fc383e7a32d146c1ecdea7d8cc63b2539a3fbc42b281ee642841b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:49.763246Z","signature_b64":"IQG3dKYx3SNgjnQcRQA4axfBV5RRgQl4Oyc5CgG7envsLRvnoFPcnlXoShYMmFcZVHx0qUyhY6wGeIKYi2wFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b6deffc97cdc296275eafefdfd6f2faccd2565338e5e469eb831ff9500b0835","last_reissued_at":"2026-05-18T00:06:49.762598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:49.762598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A combinatorial property of flows on a cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zhuo Diao","submitted_at":"2018-08-30T04:52:55Z","abstract_excerpt":"In this paper, we prove a combinatorial property of flows on a cycle. $C(V,E)$ is an undirected cycle with two commodities: $\\{s_{1},t_{1}\\}, \\{s_{2},t_{2}\\}$;$r_1>0,r_2>0, \\mathbf r=(r_i)_{i=1,2}$ and $f,f'$ are both feasible flows for $(C,(s_i,t_i)_{i=1,2},\\mathbf r)$. Then $\\exists i\\in\\{1,2\\}, p\\in P_i, f(p)>0, \\forall e\\in p, f(e)\\geq f'(e)$ ; Here for each $i\\in\\{1,2\\}$, let $P_i$ be the set of $s_i$-$t_i$ paths in $C$ and $P=\\cup_{i=1,2}P_i$. This means given a two-commodity instance on a cycle, any two distinct network flow $f$ and $f'$, compared with $f'$, $f$ can't decrease every pat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10119","kind":"arxiv","version":1},"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":"1808.10119","created_at":"2026-05-18T00:06:49.762706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.10119v1","created_at":"2026-05-18T00:06:49.762706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10119","created_at":"2026-05-18T00:06:49.762706+00:00"},{"alias_kind":"pith_short_12","alias_value":"RNW677EXZXBJ","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RNW677EXZXBJMJ26","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RNW677EX","created_at":"2026-05-18T12:32:50.500415+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/RNW677EXZXBJMJ26V7X57VXS7L","json":"https://pith.science/pith/RNW677EXZXBJMJ26V7X57VXS7L.json","graph_json":"https://pith.science/api/pith-number/RNW677EXZXBJMJ26V7X57VXS7L/graph.json","events_json":"https://pith.science/api/pith-number/RNW677EXZXBJMJ26V7X57VXS7L/events.json","paper":"https://pith.science/paper/RNW677EX"},"agent_actions":{"view_html":"https://pith.science/pith/RNW677EXZXBJMJ26V7X57VXS7L","download_json":"https://pith.science/pith/RNW677EXZXBJMJ26V7X57VXS7L.json","view_paper":"https://pith.science/paper/RNW677EX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.10119&json=true","fetch_graph":"https://pith.science/api/pith-number/RNW677EXZXBJMJ26V7X57VXS7L/graph.json","fetch_events":"https://pith.science/api/pith-number/RNW677EXZXBJMJ26V7X57VXS7L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RNW677EXZXBJMJ26V7X57VXS7L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RNW677EXZXBJMJ26V7X57VXS7L/action/storage_attestation","attest_author":"https://pith.science/pith/RNW677EXZXBJMJ26V7X57VXS7L/action/author_attestation","sign_citation":"https://pith.science/pith/RNW677EXZXBJMJ26V7X57VXS7L/action/citation_signature","submit_replication":"https://pith.science/pith/RNW677EXZXBJMJ26V7X57VXS7L/action/replication_record"}},"created_at":"2026-05-18T00:06:49.762706+00:00","updated_at":"2026-05-18T00:06:49.762706+00:00"}