{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y7MT377KLMUOB5ISX4EY377WTZ","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":"bf7500a8b7d0f5e11868083abda2b2a376d08788164a086c663d03a95586ac00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-14T02:15:48Z","title_canon_sha256":"9460d8cf8f619aa08c6113af57d8b376ebc7b438831f387c3d00b5b1f0dc8bfe"},"schema_version":"1.0","source":{"id":"1211.3179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3179","created_at":"2026-05-18T03:40:50Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3179v1","created_at":"2026-05-18T03:40:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3179","created_at":"2026-05-18T03:40:50Z"},{"alias_kind":"pith_short_12","alias_value":"Y7MT377KLMUO","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y7MT377KLMUOB5IS","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y7MT377K","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:6f0575e86cafb7d8ed117ff89c0b8d311140c0c16affd07941c5de904f7e00d1","target":"graph","created_at":"2026-05-18T03:40:50Z","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":"This paper proves that for any positive integer $k$, every essentially $(2k+1)$-unbalanced $(12k-1)$-edge connected signed graph has circular flow number at most $2+\\frac 1k$.","authors_text":"Xuding Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-14T02:15:48Z","title":"Circular flow number of highly edge connected signed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3179","kind":"arxiv","version":1},"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:be23a6cd5dc530888da69e846a5c6d716f113982ba24326b4a37418ce247d8d5","target":"record","created_at":"2026-05-18T03:40:50Z","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":"bf7500a8b7d0f5e11868083abda2b2a376d08788164a086c663d03a95586ac00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-14T02:15:48Z","title_canon_sha256":"9460d8cf8f619aa08c6113af57d8b376ebc7b438831f387c3d00b5b1f0dc8bfe"},"schema_version":"1.0","source":{"id":"1211.3179","kind":"arxiv","version":1}},"canonical_sha256":"c7d93dffea5b28e0f512bf098dfff69e672d61a5b0c6fd4d6786d3a5664d453c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7d93dffea5b28e0f512bf098dfff69e672d61a5b0c6fd4d6786d3a5664d453c","first_computed_at":"2026-05-18T03:40:50.665039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:50.665039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K2yG8Ns3Oxxev0zeivLaV4fYg6/b4yFo/yxqWZNrvENDbucBvyTLEx8teGP60gFwj58LYS4trI8EPsZjUdOFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:50.665660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be23a6cd5dc530888da69e846a5c6d716f113982ba24326b4a37418ce247d8d5","sha256:6f0575e86cafb7d8ed117ff89c0b8d311140c0c16affd07941c5de904f7e00d1"],"state_sha256":"3181816ce73b5299970592ce10a804f3a17832f9a736ec29da4855af98831a37"}