{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LUTTTK77ZDEYEDV7FGJP2LVS7Q","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":"fb879d8716292276e6815aaa5eb2a91c398dfd0874affcc90a5a9218704fad89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-14T14:04:22Z","title_canon_sha256":"128568ca615a9b3e783b47f7fe4ae9632cb39d00a6c169930e0b5512019f3963"},"schema_version":"1.0","source":{"id":"1301.2977","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2977","created_at":"2026-07-05T01:08:19Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2977v3","created_at":"2026-07-05T01:08:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2977","created_at":"2026-07-05T01:08:19Z"},{"alias_kind":"pith_short_12","alias_value":"LUTTTK77ZDEY","created_at":"2026-07-05T01:08:19Z"},{"alias_kind":"pith_short_16","alias_value":"LUTTTK77ZDEYEDV7","created_at":"2026-07-05T01:08:19Z"},{"alias_kind":"pith_short_8","alias_value":"LUTTTK77","created_at":"2026-07-05T01:08:19Z"}],"graph_snapshots":[{"event_id":"sha256:37b259aa3380d9f4d2fbce003bce2211a176d73f70189222a604c790b3634d3b","target":"graph","created_at":"2026-07-05T01:08:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1301.2977/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above kernel can be identified with a naturally defined voltage graph critical group. For double covers, the voltage graph is a signed graph, and the theory takes a particularly pleasant form, leading also to a theory of double covers of signed graphs.","authors_text":"Dennis Tseng, Victor Reiner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-14T14:04:22Z","title":"Critical groups of covering, voltage, and signed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2977","kind":"arxiv","version":3},"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":"sha256:992e8d7f9edcc1a89bc8ee1944ae2d0d4535efa010e7401e6cd0edc15c176e18","target":"record","created_at":"2026-07-05T01:08:19Z","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":"fb879d8716292276e6815aaa5eb2a91c398dfd0874affcc90a5a9218704fad89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-14T14:04:22Z","title_canon_sha256":"128568ca615a9b3e783b47f7fe4ae9632cb39d00a6c169930e0b5512019f3963"},"schema_version":"1.0","source":{"id":"1301.2977","kind":"arxiv","version":3}},"canonical_sha256":"5d2739abffc8c9820ebf2992fd2eb2fc038df432f5a78ff73c2fbf1a92a4a3fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d2739abffc8c9820ebf2992fd2eb2fc038df432f5a78ff73c2fbf1a92a4a3fc","first_computed_at":"2026-07-05T01:08:19.826306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:08:19.826306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ao+q7u40AmTktKOx/X7B7xt5QuGl9YBZT5pNY16u+ozhq7/6qk+i7s7rk16VA4ZX/tlQvWcH12NUuiJQHpxYCw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:08:19.826719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2977","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:992e8d7f9edcc1a89bc8ee1944ae2d0d4535efa010e7401e6cd0edc15c176e18","sha256:37b259aa3380d9f4d2fbce003bce2211a176d73f70189222a604c790b3634d3b"],"state_sha256":"514f7d58d9357a9c97155db3ae5c1f4deb2f4728fce931f6916ee927edf4f165"}