{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PN3PA4J23KBPB2DRH4UMUDEJZ4","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":"874f6733d5fdfec32c1b0d24d7e6bc1331960831c40852839c9c28938ac3fdcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-03-30T01:09:47Z","title_canon_sha256":"dd551d85b816658ef15b75c79c67e09f35adf56195316f826e7e9418c157b852"},"schema_version":"1.0","source":{"id":"1603.09009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09009","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09009v1","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09009","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"PN3PA4J23KBP","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PN3PA4J23KBPB2DR","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PN3PA4J2","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:6fbec00e3f82da020aff4595bf82cfc9ebfa2c46e076b5e493f9d2bce55c396c","target":"graph","created_at":"2026-05-18T01:18:04Z","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 the notion of balance for directed graphs: a weighted directed graph is $\\alpha$-balanced if for every cut $S \\subseteq V$, the total weight of edges going from $S$ to $V\\setminus S$ is within factor $\\alpha$ of the total weight of edges going from $V\\setminus S$ to $S$. Several important families of graphs are nearly balanced, in particular, Eulerian graphs (with $\\alpha = 1$) and residual graphs of $(1+\\epsilon)$-approximate undirected maximum flows (with $\\alpha=O(1/\\epsilon)$).\n  We use the notion of balance to give a more fine-grained understanding of several well-studied rou","authors_text":"Aaron Sidford, Alina Ene, Gary Miller, Jakub Pachocki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-03-30T01:09:47Z","title":"Routing under Balance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09009","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":"sha256:448f9ac1645adb647071a9fadc7b60d65c1525ff4f2b04b70e1310ca96f5ef65","target":"record","created_at":"2026-05-18T01:18:04Z","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":"874f6733d5fdfec32c1b0d24d7e6bc1331960831c40852839c9c28938ac3fdcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-03-30T01:09:47Z","title_canon_sha256":"dd551d85b816658ef15b75c79c67e09f35adf56195316f826e7e9418c157b852"},"schema_version":"1.0","source":{"id":"1603.09009","kind":"arxiv","version":1}},"canonical_sha256":"7b76f0713ada82f0e8713f28ca0c89cf3b78e5fd079e4b76c45a993e1fba76a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b76f0713ada82f0e8713f28ca0c89cf3b78e5fd079e4b76c45a993e1fba76a3","first_computed_at":"2026-05-18T01:18:04.024472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:04.024472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gFzCC2m1NwMQA8RnkeJDs4xj4EC8uQjNyziXpg08Mk1Rw8cGnHgunNLRFY4jpzhkRKrM+WsUEUVJXAHzNsqeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:04.025284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.09009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:448f9ac1645adb647071a9fadc7b60d65c1525ff4f2b04b70e1310ca96f5ef65","sha256:6fbec00e3f82da020aff4595bf82cfc9ebfa2c46e076b5e493f9d2bce55c396c"],"state_sha256":"dde8660a0a866bdb425cde22cf633c46cea2eab319ad0b8ccc6f450a8a1b5cab"}