{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FWRZUGYJBYRKJRT6KAYB6FSNQG","short_pith_number":"pith:FWRZUGYJ","schema_version":"1.0","canonical_sha256":"2da39a1b090e22a4c67e50301f164d81b01f24414c8475b309063375d690c6f8","source":{"kind":"arxiv","id":"1410.7423","version":2},"attestation_state":"computed","paper":{"title":"Packing odd $T$-joins with at most two terminals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ahmad Abdi, Bertrand Guenin","submitted_at":"2014-10-27T20:40:43Z","abstract_excerpt":"Take a graph $G$, an edge subset $\\Sigma\\subseteq E(G)$, and a set of terminals $T\\subseteq V(G)$ where $|T|$ is even. The triple $(G,\\Sigma,T)$ is called a signed graft. A $T$-join is odd if it contains an odd number of edges from $\\Sigma$. Let $\\nu$ be the maximum number of edge-disjoint odd $T$-joins. A signature is a set of the form $\\Sigma\\triangle \\delta(U)$ where $U\\subseteq V(G)$ and $|U\\cap T)$ is even. Let $\\tau$ be the minimum cardinality a $T$-cut or a signature can achieve. Then $\\nu\\leq \\tau$ and we say that $(G,\\Sigma,T)$ packs if equality holds here.\n  We prove that $(G,\\Sigma,"},"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":"1410.7423","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-27T20:40:43Z","cross_cats_sorted":[],"title_canon_sha256":"b07e5370ed06c714cc5cfd966ae0b2a2f643ba44a98c1cb8c45fa1ae59112715","abstract_canon_sha256":"03d6fa07c0bef738893e9c388604935572e85ba31df4890ae690fa23cc270222"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:10.920438Z","signature_b64":"fQ7+K0U/+zvkLyp1vilKJ1T1sr5HZKUVRsaA/YUCetGePV56fWqt/tt9MvD3gjHPEQiBkXAmdgppxDKb6ABnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2da39a1b090e22a4c67e50301f164d81b01f24414c8475b309063375d690c6f8","last_reissued_at":"2026-05-18T00:15:10.919729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:10.919729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Packing odd $T$-joins with at most two terminals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ahmad Abdi, Bertrand Guenin","submitted_at":"2014-10-27T20:40:43Z","abstract_excerpt":"Take a graph $G$, an edge subset $\\Sigma\\subseteq E(G)$, and a set of terminals $T\\subseteq V(G)$ where $|T|$ is even. The triple $(G,\\Sigma,T)$ is called a signed graft. A $T$-join is odd if it contains an odd number of edges from $\\Sigma$. Let $\\nu$ be the maximum number of edge-disjoint odd $T$-joins. A signature is a set of the form $\\Sigma\\triangle \\delta(U)$ where $U\\subseteq V(G)$ and $|U\\cap T)$ is even. Let $\\tau$ be the minimum cardinality a $T$-cut or a signature can achieve. Then $\\nu\\leq \\tau$ and we say that $(G,\\Sigma,T)$ packs if equality holds here.\n  We prove that $(G,\\Sigma,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7423","kind":"arxiv","version":2},"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":"1410.7423","created_at":"2026-05-18T00:15:10.919832+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.7423v2","created_at":"2026-05-18T00:15:10.919832+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7423","created_at":"2026-05-18T00:15:10.919832+00:00"},{"alias_kind":"pith_short_12","alias_value":"FWRZUGYJBYRK","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FWRZUGYJBYRKJRT6","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FWRZUGYJ","created_at":"2026-05-18T12:28:28.263976+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/FWRZUGYJBYRKJRT6KAYB6FSNQG","json":"https://pith.science/pith/FWRZUGYJBYRKJRT6KAYB6FSNQG.json","graph_json":"https://pith.science/api/pith-number/FWRZUGYJBYRKJRT6KAYB6FSNQG/graph.json","events_json":"https://pith.science/api/pith-number/FWRZUGYJBYRKJRT6KAYB6FSNQG/events.json","paper":"https://pith.science/paper/FWRZUGYJ"},"agent_actions":{"view_html":"https://pith.science/pith/FWRZUGYJBYRKJRT6KAYB6FSNQG","download_json":"https://pith.science/pith/FWRZUGYJBYRKJRT6KAYB6FSNQG.json","view_paper":"https://pith.science/paper/FWRZUGYJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.7423&json=true","fetch_graph":"https://pith.science/api/pith-number/FWRZUGYJBYRKJRT6KAYB6FSNQG/graph.json","fetch_events":"https://pith.science/api/pith-number/FWRZUGYJBYRKJRT6KAYB6FSNQG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FWRZUGYJBYRKJRT6KAYB6FSNQG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FWRZUGYJBYRKJRT6KAYB6FSNQG/action/storage_attestation","attest_author":"https://pith.science/pith/FWRZUGYJBYRKJRT6KAYB6FSNQG/action/author_attestation","sign_citation":"https://pith.science/pith/FWRZUGYJBYRKJRT6KAYB6FSNQG/action/citation_signature","submit_replication":"https://pith.science/pith/FWRZUGYJBYRKJRT6KAYB6FSNQG/action/replication_record"}},"created_at":"2026-05-18T00:15:10.919832+00:00","updated_at":"2026-05-18T00:15:10.919832+00:00"}