{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MQ3VKPIVUITKAPCBAZP4WGDIAB","short_pith_number":"pith:MQ3VKPIV","schema_version":"1.0","canonical_sha256":"6437553d15a226a03c41065fcb1868004fe8df3bc9fb653f2f46e931f3f8e617","source":{"kind":"arxiv","id":"1603.00325","version":3},"attestation_state":"computed","paper":{"title":"The Diameters of Network-flow Polytopes satisfy the Hirsch Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"E. Finhold, J. A. De Loera, S. Borgwardt","submitted_at":"2016-03-01T15:39:38Z","abstract_excerpt":"We solve a problem in the combinatorics of polyhedra motivated by the network simplex method. We show that the Hirsch conjecture holds for the diameter of the graphs of all network-flow polytopes, in particular the diameter of a network-flow polytope for a network with $n$ nodes and $m$ arcs is never more than $m+n-1$. A key step to prove this is to show the same result for classical transportation polytopes."},"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":"1603.00325","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-01T15:39:38Z","cross_cats_sorted":[],"title_canon_sha256":"4672953d5e80f6cdd11140f706313e843bce6b7561fcc310ccf3d74a6509f7e7","abstract_canon_sha256":"3e5ef57e8527c8f71d28ed2f1ee88019a5b61c2cd81415fc33566d7e7bafc2a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:09.185143Z","signature_b64":"RU66Xyw3kDf7prOF+SObZz5mQwEbm+E5mLeBH3lbc2+CvjeyZd3vZ/OGbatrbcrot45SJPWx8tiJ1X+4Vy9iAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6437553d15a226a03c41065fcb1868004fe8df3bc9fb653f2f46e931f3f8e617","last_reissued_at":"2026-05-18T01:04:09.184555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:09.184555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Diameters of Network-flow Polytopes satisfy the Hirsch Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"E. Finhold, J. A. De Loera, S. Borgwardt","submitted_at":"2016-03-01T15:39:38Z","abstract_excerpt":"We solve a problem in the combinatorics of polyhedra motivated by the network simplex method. We show that the Hirsch conjecture holds for the diameter of the graphs of all network-flow polytopes, in particular the diameter of a network-flow polytope for a network with $n$ nodes and $m$ arcs is never more than $m+n-1$. A key step to prove this is to show the same result for classical transportation polytopes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00325","kind":"arxiv","version":3},"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":"1603.00325","created_at":"2026-05-18T01:04:09.184665+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.00325v3","created_at":"2026-05-18T01:04:09.184665+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00325","created_at":"2026-05-18T01:04:09.184665+00:00"},{"alias_kind":"pith_short_12","alias_value":"MQ3VKPIVUITK","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MQ3VKPIVUITKAPCB","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MQ3VKPIV","created_at":"2026-05-18T12:30:32.724797+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/MQ3VKPIVUITKAPCBAZP4WGDIAB","json":"https://pith.science/pith/MQ3VKPIVUITKAPCBAZP4WGDIAB.json","graph_json":"https://pith.science/api/pith-number/MQ3VKPIVUITKAPCBAZP4WGDIAB/graph.json","events_json":"https://pith.science/api/pith-number/MQ3VKPIVUITKAPCBAZP4WGDIAB/events.json","paper":"https://pith.science/paper/MQ3VKPIV"},"agent_actions":{"view_html":"https://pith.science/pith/MQ3VKPIVUITKAPCBAZP4WGDIAB","download_json":"https://pith.science/pith/MQ3VKPIVUITKAPCBAZP4WGDIAB.json","view_paper":"https://pith.science/paper/MQ3VKPIV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.00325&json=true","fetch_graph":"https://pith.science/api/pith-number/MQ3VKPIVUITKAPCBAZP4WGDIAB/graph.json","fetch_events":"https://pith.science/api/pith-number/MQ3VKPIVUITKAPCBAZP4WGDIAB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MQ3VKPIVUITKAPCBAZP4WGDIAB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MQ3VKPIVUITKAPCBAZP4WGDIAB/action/storage_attestation","attest_author":"https://pith.science/pith/MQ3VKPIVUITKAPCBAZP4WGDIAB/action/author_attestation","sign_citation":"https://pith.science/pith/MQ3VKPIVUITKAPCBAZP4WGDIAB/action/citation_signature","submit_replication":"https://pith.science/pith/MQ3VKPIVUITKAPCBAZP4WGDIAB/action/replication_record"}},"created_at":"2026-05-18T01:04:09.184665+00:00","updated_at":"2026-05-18T01:04:09.184665+00:00"}