{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q3SUYW5GVVNFZ3ZJEJZIKNSEZ4","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":"248dc955f960fc3914e4b0c179e7cc7a6503846d216c4046a8989be4f871b43a","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-24T18:42:49Z","title_canon_sha256":"74d90c1a23149c43092a3716a4185bebeb0b9cabbeb75d9f748744c569ef4f7b"},"schema_version":"1.0","source":{"id":"1305.5823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5823","created_at":"2026-05-18T03:24:54Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5823v1","created_at":"2026-05-18T03:24:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5823","created_at":"2026-05-18T03:24:54Z"},{"alias_kind":"pith_short_12","alias_value":"Q3SUYW5GVVNF","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q3SUYW5GVVNFZ3ZJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q3SUYW5G","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:7d11c7c748af811b4af887016e8b064de15e1a45613d8a33bed1227bfd6f1085","target":"graph","created_at":"2026-05-18T03:24:54Z","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":"Minimum cuts have been closely related to shortest paths in planar graphs via planar duality - so long as the graphs are undirected. Even maximum flows are closely related to shortest paths for the same reason - so long as the source and the sink are on a common face. In this paper, we give a correspondence between maximum flows and shortest paths via duality in directed planar graphs with no constraints on the source and sink. We believe this a promising avenue for developing algorithms that are more practical than the current asymptotically best algorithms for maximum st-flow.","authors_text":"Anna Harutyunyan, Glencora Borradaile","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-24T18:42:49Z","title":"Maximum st-flow in directed planar graphs via shortest paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5823","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:ad5807a22db8181077cccbda09079a01732b3589309466be5b2f9216edc87321","target":"record","created_at":"2026-05-18T03:24:54Z","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":"248dc955f960fc3914e4b0c179e7cc7a6503846d216c4046a8989be4f871b43a","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-24T18:42:49Z","title_canon_sha256":"74d90c1a23149c43092a3716a4185bebeb0b9cabbeb75d9f748744c569ef4f7b"},"schema_version":"1.0","source":{"id":"1305.5823","kind":"arxiv","version":1}},"canonical_sha256":"86e54c5ba6ad5a5cef292272853644cf0e5e5cfc2707342054c3ce40df8fd28d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86e54c5ba6ad5a5cef292272853644cf0e5e5cfc2707342054c3ce40df8fd28d","first_computed_at":"2026-05-18T03:24:54.714338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:54.714338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZqwWzSoqiWxSVQa04/xHAuEBfacKwGPjhxYl/J2sE3YuxB3NSQsVdRGNCJBQqW9o7ejOxCAfBZ8JgMEZ+u1iCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:54.715109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad5807a22db8181077cccbda09079a01732b3589309466be5b2f9216edc87321","sha256:7d11c7c748af811b4af887016e8b064de15e1a45613d8a33bed1227bfd6f1085"],"state_sha256":"cbcb4efcd952e5c1ac8359a6340ba91d92a3af6200f7989992cef28c79745f7b"}