{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IABAPWKIJ24CRC5PFUO4QAJ2DH","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":"30b01e2e4d797973fcc9592dfe63bed2497fd045862c17428b8479cab3fa9851","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-19T16:28:35Z","title_canon_sha256":"90afff8f461c25e09681a6fee3228af518e21d65ed41c6fae0ebe404fb35d7c6"},"schema_version":"1.0","source":{"id":"1803.07020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07020","created_at":"2026-05-18T00:20:40Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07020v1","created_at":"2026-05-18T00:20:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07020","created_at":"2026-05-18T00:20:40Z"},{"alias_kind":"pith_short_12","alias_value":"IABAPWKIJ24C","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IABAPWKIJ24CRC5P","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IABAPWKI","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:8606a9d361f3dc2bb84cb80aa4e74c131dfc0fe7d9f5f7a3d2458c9f690c7088","target":"graph","created_at":"2026-05-18T00:20:40Z","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 consider a planar graph $G$ in which the edges have nonnegative integer lengths such that the length of every cycle of $G$ is even, and three faces are distinguished, called holes in $G$. It is known that there exists a packing of cuts and (2,3)-metrics with nonnegative integer weights in $G$ which realizes the distances within each hole. We develop a strongly polynomial purely combinatorial algorithm to find such a packing.","authors_text":"Alexander V. Karzanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-19T16:28:35Z","title":"An efficient algorithm for packing cuts and (2,3)-metrics in a planar graph with three holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07020","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":"sha256:52045cb269ff42bb114853b9da4dc3302ee046386b3c63eb4e2919f2af2b430d","target":"record","created_at":"2026-05-18T00:20:40Z","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":"30b01e2e4d797973fcc9592dfe63bed2497fd045862c17428b8479cab3fa9851","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-19T16:28:35Z","title_canon_sha256":"90afff8f461c25e09681a6fee3228af518e21d65ed41c6fae0ebe404fb35d7c6"},"schema_version":"1.0","source":{"id":"1803.07020","kind":"arxiv","version":1}},"canonical_sha256":"400207d9484eb8288baf2d1dc8013a19e082cc0c1530cc52347f4d4854dffcc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"400207d9484eb8288baf2d1dc8013a19e082cc0c1530cc52347f4d4854dffcc0","first_computed_at":"2026-05-18T00:20:40.574798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:40.574798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CebhuygDZMAEPOXXn9dEQoE5lIpMOZr9EPlMTkn2oXL9zBYqtJidecuu4P32oloAY1Im57W586fNOhPRrC8+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:40.575625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52045cb269ff42bb114853b9da4dc3302ee046386b3c63eb4e2919f2af2b430d","sha256:8606a9d361f3dc2bb84cb80aa4e74c131dfc0fe7d9f5f7a3d2458c9f690c7088"],"state_sha256":"2f005debb83951100b695c8f234255cd2fadadb11760cab7dfc4baed02588d29"}