{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5EAYII7OF5GOROHFTCJHRCSXQT","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":"eb5c582e49dec28904ca1ff6599ba520bd6f47bc8dcce272fbf8b4e51d5fef84","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-11-05T03:34:45Z","title_canon_sha256":"d7bfc2351033c422159726459ee4537c759c0b9a2fcdc030512ef51be7d1d7f6"},"schema_version":"1.0","source":{"id":"1211.0752","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0752","created_at":"2026-05-18T03:40:35Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0752v2","created_at":"2026-05-18T03:40:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0752","created_at":"2026-05-18T03:40:35Z"},{"alias_kind":"pith_short_12","alias_value":"5EAYII7OF5GO","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5EAYII7OF5GOROHF","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5EAYII7O","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:a44a616b05746de6e212d133ab712e728dabc59f421b1c30331a8fbaf6253951","target":"graph","created_at":"2026-05-18T03:40:35Z","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":"I extend the methods in \"Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs, with Paul Christiano, Jonathan Kelner, Daniel Spielman, and Shang-Hua Teng\" to directed graphs with a variation of the framework in the paper, which lead to an algorithm that approximately solves the directed max flow problem in nearly-linear time.","authors_text":"Cheng Wang","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-11-05T03:34:45Z","title":"Faster Approximation of Max Flow for Directed Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0752","kind":"arxiv","version":2},"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:b0a102f145b3cffc2ad2f2b1a68ad488a6cba82e413e1315c78ad9bb6baf03ff","target":"record","created_at":"2026-05-18T03:40:35Z","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":"eb5c582e49dec28904ca1ff6599ba520bd6f47bc8dcce272fbf8b4e51d5fef84","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-11-05T03:34:45Z","title_canon_sha256":"d7bfc2351033c422159726459ee4537c759c0b9a2fcdc030512ef51be7d1d7f6"},"schema_version":"1.0","source":{"id":"1211.0752","kind":"arxiv","version":2}},"canonical_sha256":"e9018423ee2f4ce8b8e59892788a5784fed3a3b3bd7ef5a0a7cc7b9db394c896","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9018423ee2f4ce8b8e59892788a5784fed3a3b3bd7ef5a0a7cc7b9db394c896","first_computed_at":"2026-05-18T03:40:35.682419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:35.682419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"73e0D+RPIEto2m4qjMNgnCdPfXmQgwFPCWW+huzsNMAF6AXMwpoTptxfej0K1ZMkaCLhmyuM4D8hA4D7+nTpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:35.685907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0752","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0a102f145b3cffc2ad2f2b1a68ad488a6cba82e413e1315c78ad9bb6baf03ff","sha256:a44a616b05746de6e212d133ab712e728dabc59f421b1c30331a8fbaf6253951"],"state_sha256":"80b45833ccbf1f7d44eca2ef547fe2d8652808f60b1a20e6957d9b37302d08f4"}