{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MPUUTT7JTQ5THH6R5UEKIZSMBT","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":"a71b0f923464c8bb08f20717acafe48fd32ce4f4f90007aa52745992969d4745","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-23T08:52:13Z","title_canon_sha256":"9b1f28f0580a5b0e6cc446fe3fc433bb26909ff9efb144c276d027813665ef4e"},"schema_version":"1.0","source":{"id":"1503.06556","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06556","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06556v4","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06556","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"MPUUTT7JTQ5T","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MPUUTT7JTQ5THH6R","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MPUUTT7J","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:494b6f968956571b62732d4b607488a2cd74209b2b6dd083149464ef66ddb390","target":"graph","created_at":"2026-05-18T00:20:49Z","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 graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular coverings in which this homomorphism is prescribed by an action of a semiregular subgroup $\\Gamma$ of $\\textrm{Aut}(G)$; so $H \\cong G / \\Gamma$. In this paper, we study the behaviour of regular graph covering with respect to 1-cuts and 2-cuts in $G$.\n  We describe reductions which produce a series of graphs $G = G_0,\\dots,G_r$ such that $G_{i+1}$ is created from $G_i$ by replacing certain inclusion minimal subgraphs with colored edges. The process ends with a primitive graph $","authors_text":"Jan Kratochv\\'il, Ji\\v{r}\\'i Fiala, Pavel Klav\\'ik, Roman Nedela","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-23T08:52:13Z","title":"3-connected Reduction for Regular Graph Covers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06556","kind":"arxiv","version":4},"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":"sha256:4cfe25b2412562df44ad73c823ebaf621e3c7740229bcb57d9be7b070514a93b","target":"record","created_at":"2026-05-18T00:20:49Z","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":"a71b0f923464c8bb08f20717acafe48fd32ce4f4f90007aa52745992969d4745","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-23T08:52:13Z","title_canon_sha256":"9b1f28f0580a5b0e6cc446fe3fc433bb26909ff9efb144c276d027813665ef4e"},"schema_version":"1.0","source":{"id":"1503.06556","kind":"arxiv","version":4}},"canonical_sha256":"63e949cfe99c3b339fd1ed08a4664c0ce5c2d1487a4c72515a8bca591aabfd00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63e949cfe99c3b339fd1ed08a4664c0ce5c2d1487a4c72515a8bca591aabfd00","first_computed_at":"2026-05-18T00:20:49.534236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:49.534236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y44SfXW+S/EnRCIFL+JFWhzHKgxULpIzY7cHWZwxktf90JoP8r85qmLvZR7S5EqjCj2c10SV8VjcMJLRYEhnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:49.534887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06556","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cfe25b2412562df44ad73c823ebaf621e3c7740229bcb57d9be7b070514a93b","sha256:494b6f968956571b62732d4b607488a2cd74209b2b6dd083149464ef66ddb390"],"state_sha256":"f3fac60e6055cfc68229af1ab5cc5693c301466f3a1748116170d12c66538ca2"}