{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:IABAPWKIJ24CRC5PFUO4QAJ2DH","short_pith_number":"pith:IABAPWKI","schema_version":"1.0","canonical_sha256":"400207d9484eb8288baf2d1dc8013a19e082cc0c1530cc52347f4d4854dffcc0","source":{"kind":"arxiv","id":"1803.07020","version":1},"attestation_state":"computed","paper":{"title":"An efficient algorithm for packing cuts and (2,3)-metrics in a planar graph with three holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander V. Karzanov","submitted_at":"2018-03-19T16:28:35Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.07020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-19T16:28:35Z","cross_cats_sorted":[],"title_canon_sha256":"90afff8f461c25e09681a6fee3228af518e21d65ed41c6fae0ebe404fb35d7c6","abstract_canon_sha256":"30b01e2e4d797973fcc9592dfe63bed2497fd045862c17428b8479cab3fa9851"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:40.575625Z","signature_b64":"CebhuygDZMAEPOXXn9dEQoE5lIpMOZr9EPlMTkn2oXL9zBYqtJidecuu4P32oloAY1Im57W586fNOhPRrC8+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"400207d9484eb8288baf2d1dc8013a19e082cc0c1530cc52347f4d4854dffcc0","last_reissued_at":"2026-05-18T00:20:40.574798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:40.574798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An efficient algorithm for packing cuts and (2,3)-metrics in a planar graph with three holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander V. Karzanov","submitted_at":"2018-03-19T16:28:35Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07020","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.07020","created_at":"2026-05-18T00:20:40.574925+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.07020v1","created_at":"2026-05-18T00:20:40.574925+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07020","created_at":"2026-05-18T00:20:40.574925+00:00"},{"alias_kind":"pith_short_12","alias_value":"IABAPWKIJ24C","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"IABAPWKIJ24CRC5P","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"IABAPWKI","created_at":"2026-05-18T12:32:28.185984+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IABAPWKIJ24CRC5PFUO4QAJ2DH","json":"https://pith.science/pith/IABAPWKIJ24CRC5PFUO4QAJ2DH.json","graph_json":"https://pith.science/api/pith-number/IABAPWKIJ24CRC5PFUO4QAJ2DH/graph.json","events_json":"https://pith.science/api/pith-number/IABAPWKIJ24CRC5PFUO4QAJ2DH/events.json","paper":"https://pith.science/paper/IABAPWKI"},"agent_actions":{"view_html":"https://pith.science/pith/IABAPWKIJ24CRC5PFUO4QAJ2DH","download_json":"https://pith.science/pith/IABAPWKIJ24CRC5PFUO4QAJ2DH.json","view_paper":"https://pith.science/paper/IABAPWKI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.07020&json=true","fetch_graph":"https://pith.science/api/pith-number/IABAPWKIJ24CRC5PFUO4QAJ2DH/graph.json","fetch_events":"https://pith.science/api/pith-number/IABAPWKIJ24CRC5PFUO4QAJ2DH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IABAPWKIJ24CRC5PFUO4QAJ2DH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IABAPWKIJ24CRC5PFUO4QAJ2DH/action/storage_attestation","attest_author":"https://pith.science/pith/IABAPWKIJ24CRC5PFUO4QAJ2DH/action/author_attestation","sign_citation":"https://pith.science/pith/IABAPWKIJ24CRC5PFUO4QAJ2DH/action/citation_signature","submit_replication":"https://pith.science/pith/IABAPWKIJ24CRC5PFUO4QAJ2DH/action/replication_record"}},"created_at":"2026-05-18T00:20:40.574925+00:00","updated_at":"2026-05-18T00:20:40.574925+00:00"}