{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OR4KVAXFSLH5EZ5HNJOOS7E2L6","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":"8803e824a1d59628f5f4405aa56c0b595bf05376aa40e66391847cc23baeb3a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-16T00:04:43Z","title_canon_sha256":"82166ab09a78095043b1075120642a0b943be56c946a7453f8cf3a17c68b6f7e"},"schema_version":"1.0","source":{"id":"1703.05431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05431","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05431v1","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05431","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"OR4KVAXFSLH5","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OR4KVAXFSLH5EZ5H","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OR4KVAXF","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:4f56971eb346f810041a2d13ceda47df336a1bc1a250746c33c61abaac40f191","target":"graph","created_at":"2026-05-18T00:48:34Z","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 define branching systems for finitely aligned higher-rank graphs. From these we construct concrete representations of higher-rank graph C*-algebras on Hilbert spaces. We prove a generalized Cuntz-Krieger uniqueness theorem for periodic single-vertex 2-graphs. We use this result to give a sufficient condition under which representations of periodic single-vertex 2-graph C*-algebras arising from branching systems are faithful.","authors_text":"Daniel Gon\\c{c}alves, Danilo Royer, Hui Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-16T00:04:43Z","title":"Branching Systems for Higher-Rank Graph C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05431","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":"sha256:2f5c58a9f92c4437c95b3078a8b92cbd738ecd5b87e1853590058ce86d2e00b8","target":"record","created_at":"2026-05-18T00:48:34Z","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":"8803e824a1d59628f5f4405aa56c0b595bf05376aa40e66391847cc23baeb3a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-16T00:04:43Z","title_canon_sha256":"82166ab09a78095043b1075120642a0b943be56c946a7453f8cf3a17c68b6f7e"},"schema_version":"1.0","source":{"id":"1703.05431","kind":"arxiv","version":1}},"canonical_sha256":"7478aa82e592cfd267a76a5ce97c9a5fae39b36ebed2876c8c494095aae0a3f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7478aa82e592cfd267a76a5ce97c9a5fae39b36ebed2876c8c494095aae0a3f7","first_computed_at":"2026-05-18T00:48:34.301401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:34.301401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MkjehwYstxaoXdKY/EKvkmuUuB6vMU8fwQdkWPz3kMBTf9zQ0Psg496OYAEFAroSPBefcrmbO7O3ycLoKvzwBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:34.301882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f5c58a9f92c4437c95b3078a8b92cbd738ecd5b87e1853590058ce86d2e00b8","sha256:4f56971eb346f810041a2d13ceda47df336a1bc1a250746c33c61abaac40f191"],"state_sha256":"31421bb71f083e22b007ac31539ec32180f3503525140b738c29fd76ea8b888f"}