{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TNDYYSX5KDYKNISLHOJDQ7IO4D","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":"eeba4f4ca0e93c72a60ef2f1a4484d6f4f95b4697915482995bcb0cbfb0bf5dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-03T10:44:37Z","title_canon_sha256":"d0b2155184cb2e23f69491f6ecbb8bce8eb039096da3e6d9a904e7de3dd58102"},"schema_version":"1.0","source":{"id":"1112.0642","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0642","created_at":"2026-05-18T02:21:28Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0642v2","created_at":"2026-05-18T02:21:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0642","created_at":"2026-05-18T02:21:28Z"},{"alias_kind":"pith_short_12","alias_value":"TNDYYSX5KDYK","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNDYYSX5KDYKNISL","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNDYYSX5","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:295ede7f6c6e1653d33d8294180947d686dacd7810b2d45b39bd8a990eaa7c06","target":"graph","created_at":"2026-05-18T02:21:28Z","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":"An indecomposable flow $f$ on a signed graph $\\Sigma$ is a nontrivial integral flow that cannot be decomposed into $f=f_1+f_2$, where $f_1,f_2$ are nontrivial integral flows having the same sign (both $\\geq 0$ or both $\\leq 0$) at each edge of $\\Sigma$. This paper is to classify indecomposable flows into characteristic vectors of circuits and Eulerian cycle-trees --- a class of signed graphs having a kind of tree structure in which all cycles can be viewed as vertices of a tree. Moreover, each indecomposable flow other than circuit characteristic vectors can be further decomposed into a sum of","authors_text":"Beifang Chen, Jue Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-03T10:44:37Z","title":"Classification of Indecomposable Flows of Signed Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0642","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:d867b3a1edd0c36dc13e1f0950dadf6438bafa7b9ce942d6a7d5373671eb0d59","target":"record","created_at":"2026-05-18T02:21:28Z","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":"eeba4f4ca0e93c72a60ef2f1a4484d6f4f95b4697915482995bcb0cbfb0bf5dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-03T10:44:37Z","title_canon_sha256":"d0b2155184cb2e23f69491f6ecbb8bce8eb039096da3e6d9a904e7de3dd58102"},"schema_version":"1.0","source":{"id":"1112.0642","kind":"arxiv","version":2}},"canonical_sha256":"9b478c4afd50f0a6a24b3b92387d0ee0fde4d005ce5f48d535690b3a77861112","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b478c4afd50f0a6a24b3b92387d0ee0fde4d005ce5f48d535690b3a77861112","first_computed_at":"2026-05-18T02:21:28.097391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:28.097391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TqvE1pOXi1A9Xxhn4XELmoGylY46Jp6ncxRyMHWUT1NblPca5CF9CHJ1qNJOSSmR2wgDZm6Wu0/B2RKUbWluCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:28.098034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0642","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d867b3a1edd0c36dc13e1f0950dadf6438bafa7b9ce942d6a7d5373671eb0d59","sha256:295ede7f6c6e1653d33d8294180947d686dacd7810b2d45b39bd8a990eaa7c06"],"state_sha256":"78ab28139adb2e852a814a1b14135d529bc1025fe27537fe17f634c265f01cff"}