{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FWRZUGYJBYRKJRT6KAYB6FSNQG","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":"03d6fa07c0bef738893e9c388604935572e85ba31df4890ae690fa23cc270222","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-27T20:40:43Z","title_canon_sha256":"b07e5370ed06c714cc5cfd966ae0b2a2f643ba44a98c1cb8c45fa1ae59112715"},"schema_version":"1.0","source":{"id":"1410.7423","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7423","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7423v2","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7423","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"FWRZUGYJBYRK","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FWRZUGYJBYRKJRT6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FWRZUGYJ","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:204f95774596b217ac39476f3520906b21521de0ebd1f5eacdf327a4caf7f860","target":"graph","created_at":"2026-05-18T00:15:10Z","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":"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,","authors_text":"Ahmad Abdi, Bertrand Guenin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-27T20:40:43Z","title":"Packing odd $T$-joins with at most two terminals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7423","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":"sha256:794bf6e48660bffdffa0f23688c93f955fb67372840c7d111c488fed83cb599c","target":"record","created_at":"2026-05-18T00:15:10Z","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":"03d6fa07c0bef738893e9c388604935572e85ba31df4890ae690fa23cc270222","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-27T20:40:43Z","title_canon_sha256":"b07e5370ed06c714cc5cfd966ae0b2a2f643ba44a98c1cb8c45fa1ae59112715"},"schema_version":"1.0","source":{"id":"1410.7423","kind":"arxiv","version":2}},"canonical_sha256":"2da39a1b090e22a4c67e50301f164d81b01f24414c8475b309063375d690c6f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2da39a1b090e22a4c67e50301f164d81b01f24414c8475b309063375d690c6f8","first_computed_at":"2026-05-18T00:15:10.919729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:10.919729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fQ7+K0U/+zvkLyp1vilKJ1T1sr5HZKUVRsaA/YUCetGePV56fWqt/tt9MvD3gjHPEQiBkXAmdgppxDKb6ABnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:10.920438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7423","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:794bf6e48660bffdffa0f23688c93f955fb67372840c7d111c488fed83cb599c","sha256:204f95774596b217ac39476f3520906b21521de0ebd1f5eacdf327a4caf7f860"],"state_sha256":"59e98030d870bb1fa99e0c55b5672af0d66f6804a620854e685871e79b22a4fd"}