{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HT5T6YZWMRGQXNL32I73OLKSM5","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":"1ddde10a194495b5a9f9441a2db83b88c9e528ee85a7cc0a3c247a7dfb2d5915","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-10-14T13:54:38Z","title_canon_sha256":"c3695386a036c6fc32271a5bb206be7a4a9b5a1442a48dbf73bd8d20b57ef145"},"schema_version":"1.0","source":{"id":"1010.2921","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2921","created_at":"2026-05-18T04:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2921v2","created_at":"2026-05-18T04:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2921","created_at":"2026-05-18T04:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"HT5T6YZWMRGQ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HT5T6YZWMRGQXNL3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HT5T6YZW","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:63f3ba20b595b33ed865b13205d46fbff2e311e812870453eb69c947eed26675","target":"graph","created_at":"2026-05-18T04:39:07Z","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":"We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a system of linear equations in a Laplacian matrix, and thus may be approximately computed in nearly-linear time.\n  Using this approach, we develop the fastest known algorithm for computing approximately maximum s-t flows. For a graph having n vertices and m edges, our algorithm computes a (1-\\epsilon)-approximately maximum s-t flow in time \\tilde{O}(mn^{1/3} \\epsi","authors_text":"Aleksander Madry, Daniel A. Spielman, Jonathan A. Kelner, Paul Christiano, Shang-Hua Teng","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-10-14T13:54:38Z","title":"Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2921","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":"sha256:2d910ba000da7ef9ee7c9a240d4d699dcb361f5db3795f4b5fe4b91383ed0301","target":"record","created_at":"2026-05-18T04:39:07Z","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":"1ddde10a194495b5a9f9441a2db83b88c9e528ee85a7cc0a3c247a7dfb2d5915","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-10-14T13:54:38Z","title_canon_sha256":"c3695386a036c6fc32271a5bb206be7a4a9b5a1442a48dbf73bd8d20b57ef145"},"schema_version":"1.0","source":{"id":"1010.2921","kind":"arxiv","version":2}},"canonical_sha256":"3cfb3f6336644d0bb57bd23fb72d52677c4d8815f3813e6dd9fb42919fd610a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cfb3f6336644d0bb57bd23fb72d52677c4d8815f3813e6dd9fb42919fd610a2","first_computed_at":"2026-05-18T04:39:07.796253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:07.796253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rMaATWI5fRoXzSGYLz/3on+vgoCZS62nXhIzc+jFNJG68eU4nGY104Z/M3fxXc0VtKFBoX8OKy7ZvfosGjzJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:07.796860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2921","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d910ba000da7ef9ee7c9a240d4d699dcb361f5db3795f4b5fe4b91383ed0301","sha256:63f3ba20b595b33ed865b13205d46fbff2e311e812870453eb69c947eed26675"],"state_sha256":"3fa43fdbfcfc703937e27765d7dc97e743700c60edd4016a99493d5a705c3166"}