{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NTLFL5SMNUG5XA5HF2VPC7PIJQ","short_pith_number":"pith:NTLFL5SM","canonical_record":{"source":{"id":"1706.03808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-12T18:50:33Z","cross_cats_sorted":[],"title_canon_sha256":"9f2816ccdf6eb2a0a1060e834f78f456431e3d0ba0cb9471e13f46e68b5f8cca","abstract_canon_sha256":"69199b7606936690ba4ec8807301410e2e4df97992e348d6d58e5b47413aed20"},"schema_version":"1.0"},"canonical_sha256":"6cd655f64c6d0ddb83a72eaaf17de84c347fc773aa22eefdbc15c3d14a3ddd0f","source":{"kind":"arxiv","id":"1706.03808","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03808","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03808v1","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03808","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"pith_short_12","alias_value":"NTLFL5SMNUG5","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NTLFL5SMNUG5XA5H","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NTLFL5SM","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NTLFL5SMNUG5XA5HF2VPC7PIJQ","target":"record","payload":{"canonical_record":{"source":{"id":"1706.03808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-12T18:50:33Z","cross_cats_sorted":[],"title_canon_sha256":"9f2816ccdf6eb2a0a1060e834f78f456431e3d0ba0cb9471e13f46e68b5f8cca","abstract_canon_sha256":"69199b7606936690ba4ec8807301410e2e4df97992e348d6d58e5b47413aed20"},"schema_version":"1.0"},"canonical_sha256":"6cd655f64c6d0ddb83a72eaaf17de84c347fc773aa22eefdbc15c3d14a3ddd0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:28.321199Z","signature_b64":"Jbc3tEBpjlblKKHvAlzX/q0KNDNR0/9QdngEM41N40/6nq33C9r+PUG3/Womv27V5/SwxLwoq41xJmfIjwTDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cd655f64c6d0ddb83a72eaaf17de84c347fc773aa22eefdbc15c3d14a3ddd0f","last_reissued_at":"2026-05-18T00:42:28.320636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:28.320636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.03808","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVa1dSUR/idcx8tPHQFKXGlB1eNaUuejw6QGjCCENRJPu2PELGBLMckzMcl9AHcQ45E8ltDZ7U9pPTRZu7HSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:35:46.499574Z"},"content_sha256":"20d360391707d5fdab66e77e23b069e9ed06f33f89dc543fbc25454436c479fb","schema_version":"1.0","event_id":"sha256:20d360391707d5fdab66e77e23b069e9ed06f33f89dc543fbc25454436c479fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NTLFL5SMNUG5XA5HF2VPC7PIJQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shorter signed circuit covers of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edita M\\'a\\v{c}ajov\\'a, Edita Rollov\\'a, Robert Lukot'ka, Tom\\'a\\v{s} Kaiser","submitted_at":"2017-06-12T18:50:33Z","abstract_excerpt":"A signed circuit is a minimal signed graph (with respect to inclusion) that admits a nowhere-zero flow. We show that each flow-admissible signed graph on $m$ edges can be covered by signed circuits of total length at most $(3+2/3)\\cdot m$, improving a recent result of Cheng et al. [manuscript, 2015]. To obtain this improvement we prove several results on signed circuit covers of trees of Eulerian graphs, which are connected signed graphs such that removing all bridges results in a collection of Eulerian graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03808","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGG4eE9/EE5w/tPe3Rt47adAHrNqDdBwUm2qzuEm9WL9ZQRmb2SgBf/FnRMXF/fkPqp4Ippeow4VweBjoAJ2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:35:46.500026Z"},"content_sha256":"29d11302505088e1cd6e0f7ff6200cfe7cac3ba6c240c8005e0096563fd5ee13","schema_version":"1.0","event_id":"sha256:29d11302505088e1cd6e0f7ff6200cfe7cac3ba6c240c8005e0096563fd5ee13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NTLFL5SMNUG5XA5HF2VPC7PIJQ/bundle.json","state_url":"https://pith.science/pith/NTLFL5SMNUG5XA5HF2VPC7PIJQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NTLFL5SMNUG5XA5HF2VPC7PIJQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T20:35:46Z","links":{"resolver":"https://pith.science/pith/NTLFL5SMNUG5XA5HF2VPC7PIJQ","bundle":"https://pith.science/pith/NTLFL5SMNUG5XA5HF2VPC7PIJQ/bundle.json","state":"https://pith.science/pith/NTLFL5SMNUG5XA5HF2VPC7PIJQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NTLFL5SMNUG5XA5HF2VPC7PIJQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NTLFL5SMNUG5XA5HF2VPC7PIJQ","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":"69199b7606936690ba4ec8807301410e2e4df97992e348d6d58e5b47413aed20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-12T18:50:33Z","title_canon_sha256":"9f2816ccdf6eb2a0a1060e834f78f456431e3d0ba0cb9471e13f46e68b5f8cca"},"schema_version":"1.0","source":{"id":"1706.03808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03808","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03808v1","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03808","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"pith_short_12","alias_value":"NTLFL5SMNUG5","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NTLFL5SMNUG5XA5H","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NTLFL5SM","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:29d11302505088e1cd6e0f7ff6200cfe7cac3ba6c240c8005e0096563fd5ee13","target":"graph","created_at":"2026-05-18T00:42:28Z","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":"A signed circuit is a minimal signed graph (with respect to inclusion) that admits a nowhere-zero flow. We show that each flow-admissible signed graph on $m$ edges can be covered by signed circuits of total length at most $(3+2/3)\\cdot m$, improving a recent result of Cheng et al. [manuscript, 2015]. To obtain this improvement we prove several results on signed circuit covers of trees of Eulerian graphs, which are connected signed graphs such that removing all bridges results in a collection of Eulerian graphs.","authors_text":"Edita M\\'a\\v{c}ajov\\'a, Edita Rollov\\'a, Robert Lukot'ka, Tom\\'a\\v{s} Kaiser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-12T18:50:33Z","title":"Shorter signed circuit covers of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03808","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":"sha256:20d360391707d5fdab66e77e23b069e9ed06f33f89dc543fbc25454436c479fb","target":"record","created_at":"2026-05-18T00:42:28Z","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":"69199b7606936690ba4ec8807301410e2e4df97992e348d6d58e5b47413aed20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-12T18:50:33Z","title_canon_sha256":"9f2816ccdf6eb2a0a1060e834f78f456431e3d0ba0cb9471e13f46e68b5f8cca"},"schema_version":"1.0","source":{"id":"1706.03808","kind":"arxiv","version":1}},"canonical_sha256":"6cd655f64c6d0ddb83a72eaaf17de84c347fc773aa22eefdbc15c3d14a3ddd0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cd655f64c6d0ddb83a72eaaf17de84c347fc773aa22eefdbc15c3d14a3ddd0f","first_computed_at":"2026-05-18T00:42:28.320636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:28.320636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jbc3tEBpjlblKKHvAlzX/q0KNDNR0/9QdngEM41N40/6nq33C9r+PUG3/Womv27V5/SwxLwoq41xJmfIjwTDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:28.321199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20d360391707d5fdab66e77e23b069e9ed06f33f89dc543fbc25454436c479fb","sha256:29d11302505088e1cd6e0f7ff6200cfe7cac3ba6c240c8005e0096563fd5ee13"],"state_sha256":"8e591097f527a2862612d97664ba4f2a468a2586b77d9e9e8185ff11f877a30b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kdv+JO8TBn/3OjWv3O0VrZUu2WfLcvpoquZt/IXRDrHdup8jdWpNiW/YCPixCBJG0BQeLzs/P5Kidd2IAOHGDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:35:46.502412Z","bundle_sha256":"11b49e425eb0fa5dafe153d7ffd4a641d0409d7cebcba62e1eb6ac12813aec25"}}