{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZV4645VSAE5LP6WNGGHBRCNM5Y","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":"5e104c03cefeff44878da00fc06f9d54edd058e20ba7048859b75a919404eea6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-07T14:37:39Z","title_canon_sha256":"b204c009d0b9ff7253197ce7dc429d0168cd0f795c2a56d302c4f6b3d2e9b737"},"schema_version":"1.0","source":{"id":"1512.02068","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02068","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02068v2","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02068","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZV4645VSAE5L","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZV4645VSAE5LP6WN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZV4645VS","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:e14d82445694ba4a08d0f0c8e3b86ab71ecd538922da60a8cc87402126523b3a","target":"graph","created_at":"2026-05-18T00:59:26Z","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 give an $O(n \\log \\log n)$ time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest $O(n\\log^3 n)$ solution. Interestingly, while in undirected planar graphs both min-cut and min $st$-cut have $O(n \\log \\log n)$ solutions, in directed planar graphs our result makes min-cut faster than min $st$-cut, which currently requires $O(n \\log n)$.","authors_text":"Cyril Nikolaev, Oren Weimann, Shay Mozes, Yahav Nussbaum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-07T14:37:39Z","title":"Minimum Cut of Directed Planar Graphs in O(nloglogn) Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02068","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:feacaa80f9739311e09064bb04fa546d183076be981609094ba50abffb4db8ea","target":"record","created_at":"2026-05-18T00:59:26Z","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":"5e104c03cefeff44878da00fc06f9d54edd058e20ba7048859b75a919404eea6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-07T14:37:39Z","title_canon_sha256":"b204c009d0b9ff7253197ce7dc429d0168cd0f795c2a56d302c4f6b3d2e9b737"},"schema_version":"1.0","source":{"id":"1512.02068","kind":"arxiv","version":2}},"canonical_sha256":"cd79ee76b2013ab7facd318e1889acee0ac22ffa8a7facf80a58fd5addf01e9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd79ee76b2013ab7facd318e1889acee0ac22ffa8a7facf80a58fd5addf01e9c","first_computed_at":"2026-05-18T00:59:26.249810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:26.249810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mvASVPJVh0zDRLoKraFF+QsmNMyZRYZkuWclErgvdZEuExoG00px33JeYGUgKJJdse4OlKYVOrQKr0iBgGB6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:26.250446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02068","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:feacaa80f9739311e09064bb04fa546d183076be981609094ba50abffb4db8ea","sha256:e14d82445694ba4a08d0f0c8e3b86ab71ecd538922da60a8cc87402126523b3a"],"state_sha256":"967f0dcc57a1c5b0cba92b5cb52533d59a6619ce6cd229e2afee2e3119d49af9"}