{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OR4KVAXFSLH5EZ5HNJOOS7E2L6","short_pith_number":"pith:OR4KVAXF","schema_version":"1.0","canonical_sha256":"7478aa82e592cfd267a76a5ce97c9a5fae39b36ebed2876c8c494095aae0a3f7","source":{"kind":"arxiv","id":"1703.05431","version":1},"attestation_state":"computed","paper":{"title":"Branching Systems for Higher-Rank Graph C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Daniel Gon\\c{c}alves, Danilo Royer, Hui Li","submitted_at":"2017-03-16T00:04:43Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.05431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-16T00:04:43Z","cross_cats_sorted":[],"title_canon_sha256":"82166ab09a78095043b1075120642a0b943be56c946a7453f8cf3a17c68b6f7e","abstract_canon_sha256":"8803e824a1d59628f5f4405aa56c0b595bf05376aa40e66391847cc23baeb3a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:34.301882Z","signature_b64":"MkjehwYstxaoXdKY/EKvkmuUuB6vMU8fwQdkWPz3kMBTf9zQ0Psg496OYAEFAroSPBefcrmbO7O3ycLoKvzwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7478aa82e592cfd267a76a5ce97c9a5fae39b36ebed2876c8c494095aae0a3f7","last_reissued_at":"2026-05-18T00:48:34.301401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:34.301401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Branching Systems for Higher-Rank Graph C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Daniel Gon\\c{c}alves, Danilo Royer, Hui Li","submitted_at":"2017-03-16T00:04:43Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05431","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.05431","created_at":"2026-05-18T00:48:34.301469+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.05431v1","created_at":"2026-05-18T00:48:34.301469+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05431","created_at":"2026-05-18T00:48:34.301469+00:00"},{"alias_kind":"pith_short_12","alias_value":"OR4KVAXFSLH5","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OR4KVAXFSLH5EZ5H","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OR4KVAXF","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OR4KVAXFSLH5EZ5HNJOOS7E2L6","json":"https://pith.science/pith/OR4KVAXFSLH5EZ5HNJOOS7E2L6.json","graph_json":"https://pith.science/api/pith-number/OR4KVAXFSLH5EZ5HNJOOS7E2L6/graph.json","events_json":"https://pith.science/api/pith-number/OR4KVAXFSLH5EZ5HNJOOS7E2L6/events.json","paper":"https://pith.science/paper/OR4KVAXF"},"agent_actions":{"view_html":"https://pith.science/pith/OR4KVAXFSLH5EZ5HNJOOS7E2L6","download_json":"https://pith.science/pith/OR4KVAXFSLH5EZ5HNJOOS7E2L6.json","view_paper":"https://pith.science/paper/OR4KVAXF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.05431&json=true","fetch_graph":"https://pith.science/api/pith-number/OR4KVAXFSLH5EZ5HNJOOS7E2L6/graph.json","fetch_events":"https://pith.science/api/pith-number/OR4KVAXFSLH5EZ5HNJOOS7E2L6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OR4KVAXFSLH5EZ5HNJOOS7E2L6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OR4KVAXFSLH5EZ5HNJOOS7E2L6/action/storage_attestation","attest_author":"https://pith.science/pith/OR4KVAXFSLH5EZ5HNJOOS7E2L6/action/author_attestation","sign_citation":"https://pith.science/pith/OR4KVAXFSLH5EZ5HNJOOS7E2L6/action/citation_signature","submit_replication":"https://pith.science/pith/OR4KVAXFSLH5EZ5HNJOOS7E2L6/action/replication_record"}},"created_at":"2026-05-18T00:48:34.301469+00:00","updated_at":"2026-05-18T00:48:34.301469+00:00"}