{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:D7GWOC7NFINP54XFDB6LMRRBSC","short_pith_number":"pith:D7GWOC7N","schema_version":"1.0","canonical_sha256":"1fcd670bed2a1afef2e5187cb64621908695e2e8a27127c9b21d72d0fdd84d05","source":{"kind":"arxiv","id":"1407.5268","version":1},"attestation_state":"computed","paper":{"title":"Characteristic flows on signed graphs and short circuit covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edita Macajova, Martin Skoviera","submitted_at":"2014-07-20T10:49:49Z","abstract_excerpt":"We generalise to signed graphs a classical result of Tutte [Canad. J. Math. 8 (1956), 13--28] stating that every integer flow can be expressed as a sum of characteristic flows of circuits. In our generalisation, the r\\^ole of circuits is taken over by signed circuits of a signed graph which occur in two types -- either balanced circuits or pairs of disjoint unbalanced circuits connected with a path intersecting them only at its ends. As an application of this result we show that a signed graph $G$ admitting a nowhere-zero $k$-flow has a covering with signed circuits of total length at most $2("},"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":"1407.5268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-20T10:49:49Z","cross_cats_sorted":[],"title_canon_sha256":"39767a0c5e2e7150724cecc1503bde06c12554069502858cfc165ba99b78e451","abstract_canon_sha256":"cd176ee147d755fa9a5c54794450061476ff5c3461edb1a80eb520f335adf98b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:14.467762Z","signature_b64":"XbbIIlCDyAjohnO6mL7eTCBj8LIzGtZ8KSE+axFMvi8mlen7F+Y86N+QMFdK/YKHm7mjmsyJB50tIG8W7bHHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fcd670bed2a1afef2e5187cb64621908695e2e8a27127c9b21d72d0fdd84d05","last_reissued_at":"2026-05-18T02:47:14.467157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:14.467157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characteristic flows on signed graphs and short circuit covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edita Macajova, Martin Skoviera","submitted_at":"2014-07-20T10:49:49Z","abstract_excerpt":"We generalise to signed graphs a classical result of Tutte [Canad. J. Math. 8 (1956), 13--28] stating that every integer flow can be expressed as a sum of characteristic flows of circuits. In our generalisation, the r\\^ole of circuits is taken over by signed circuits of a signed graph which occur in two types -- either balanced circuits or pairs of disjoint unbalanced circuits connected with a path intersecting them only at its ends. As an application of this result we show that a signed graph $G$ admitting a nowhere-zero $k$-flow has a covering with signed circuits of total length at most $2("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5268","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":"1407.5268","created_at":"2026-05-18T02:47:14.467253+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.5268v1","created_at":"2026-05-18T02:47:14.467253+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5268","created_at":"2026-05-18T02:47:14.467253+00:00"},{"alias_kind":"pith_short_12","alias_value":"D7GWOC7NFINP","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"D7GWOC7NFINP54XF","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"D7GWOC7N","created_at":"2026-05-18T12:28:25.294606+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/D7GWOC7NFINP54XFDB6LMRRBSC","json":"https://pith.science/pith/D7GWOC7NFINP54XFDB6LMRRBSC.json","graph_json":"https://pith.science/api/pith-number/D7GWOC7NFINP54XFDB6LMRRBSC/graph.json","events_json":"https://pith.science/api/pith-number/D7GWOC7NFINP54XFDB6LMRRBSC/events.json","paper":"https://pith.science/paper/D7GWOC7N"},"agent_actions":{"view_html":"https://pith.science/pith/D7GWOC7NFINP54XFDB6LMRRBSC","download_json":"https://pith.science/pith/D7GWOC7NFINP54XFDB6LMRRBSC.json","view_paper":"https://pith.science/paper/D7GWOC7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.5268&json=true","fetch_graph":"https://pith.science/api/pith-number/D7GWOC7NFINP54XFDB6LMRRBSC/graph.json","fetch_events":"https://pith.science/api/pith-number/D7GWOC7NFINP54XFDB6LMRRBSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D7GWOC7NFINP54XFDB6LMRRBSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D7GWOC7NFINP54XFDB6LMRRBSC/action/storage_attestation","attest_author":"https://pith.science/pith/D7GWOC7NFINP54XFDB6LMRRBSC/action/author_attestation","sign_citation":"https://pith.science/pith/D7GWOC7NFINP54XFDB6LMRRBSC/action/citation_signature","submit_replication":"https://pith.science/pith/D7GWOC7NFINP54XFDB6LMRRBSC/action/replication_record"}},"created_at":"2026-05-18T02:47:14.467253+00:00","updated_at":"2026-05-18T02:47:14.467253+00:00"}