{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GFWJSCMF52CYQLEZSXVHEN7USG","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":"cfe5f8f6fb88c89874fc99451f53cb17fa6bc935780f93871abee215002336d0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-06-08T02:21:05Z","title_canon_sha256":"6e7795bf3292e3c668e26044d721e9727ddf898c57429655b8a620f87c730028"},"schema_version":"1.0","source":{"id":"1106.1484","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1484","created_at":"2026-05-18T03:25:35Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1484v3","created_at":"2026-05-18T03:25:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1484","created_at":"2026-05-18T03:25:35Z"},{"alias_kind":"pith_short_12","alias_value":"GFWJSCMF52CY","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GFWJSCMF52CYQLEZ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GFWJSCMF","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:e65691129fa33feb99e94d99ef55d18bc026d01c0fbc82220d160a84f1fc64bb","target":"graph","created_at":"2026-05-18T03:25:35Z","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":"We introduce the notion of the action of a group on a labeled graph and the quotient object, also a labeled graph. We define a skew product labeled graph and use it to prove a version of the Gross-Tucker theorem for labeled graphs. We then apply these results to the $C^*$-algebra associated to a labeled graph and provide some applications in nonabelian duality.","authors_text":"David Pask, Paulette Willis, Teresa Bates","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-06-08T02:21:05Z","title":"Group actions on labeled graphs and their C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1484","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":"sha256:73cd23a7559e6e662ef4e392f4aa13f7b16b6b09f7c3aded47d8b00a61a74f77","target":"record","created_at":"2026-05-18T03:25:35Z","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":"cfe5f8f6fb88c89874fc99451f53cb17fa6bc935780f93871abee215002336d0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-06-08T02:21:05Z","title_canon_sha256":"6e7795bf3292e3c668e26044d721e9727ddf898c57429655b8a620f87c730028"},"schema_version":"1.0","source":{"id":"1106.1484","kind":"arxiv","version":3}},"canonical_sha256":"316c990985ee85882c9995ea7237f4918fcb38192f71e594d3ffe1d2c7b3cb20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"316c990985ee85882c9995ea7237f4918fcb38192f71e594d3ffe1d2c7b3cb20","first_computed_at":"2026-05-18T03:25:35.304042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:35.304042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EInPSGD/YThCJmoanz9qzKTKu00eYuEPoxzuW2cWlzDX9MicM9+knAFEZ1giYSLFdhPN9ZWy4/1X1mkZvoaYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:35.304651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1484","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73cd23a7559e6e662ef4e392f4aa13f7b16b6b09f7c3aded47d8b00a61a74f77","sha256:e65691129fa33feb99e94d99ef55d18bc026d01c0fbc82220d160a84f1fc64bb"],"state_sha256":"2e6b2377945c2c1b5196228f54f2d772747c29195658717e9dfb67c6d757eb3d"}