{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Y2DPYVC5HBSDEGDXJ77OAQD6W4","short_pith_number":"pith:Y2DPYVC5","schema_version":"1.0","canonical_sha256":"c686fc545d38643218774ffee0407eb70333c9da003a936264f43351a9f9b23f","source":{"kind":"arxiv","id":"1908.07814","version":3},"attestation_state":"computed","paper":{"title":"Quasi-local Algebras and Asymptotic Expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.FA"],"primary_cat":"math.OA","authors_text":"J\\'an \\v{S}pakula, Jiawen Zhang, Kang Li, Piotr Nowak","submitted_at":"2019-08-21T12:36:49Z","abstract_excerpt":"In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being a sequence of asymptotic expanders is a coarse property under certain connectedness condition, and it implies non-uniformly local amenability. Moreover, we also analyse some $C^*$-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underl"},"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":"1908.07814","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-08-21T12:36:49Z","cross_cats_sorted":["math.CO","math.FA"],"title_canon_sha256":"2e341b21ee3bb61f3a531758476f84a1999b28ee64415c81a3d2564cddfbe826","abstract_canon_sha256":"27db491454fb228bf6320432344ed68d0becfa5c3e1b83cf2b0bf4e512cf99a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:52:06.230734Z","signature_b64":"htLQckC4Yv4VXHUAnx0TatHzxG/3T2dQkW4HveftoPJEitTtTweZlHbclBBpGZombtqnnxLcIgzetFOe5MLqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c686fc545d38643218774ffee0407eb70333c9da003a936264f43351a9f9b23f","last_reissued_at":"2026-07-05T00:52:06.230292Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:52:06.230292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-local Algebras and Asymptotic Expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.FA"],"primary_cat":"math.OA","authors_text":"J\\'an \\v{S}pakula, Jiawen Zhang, Kang Li, Piotr Nowak","submitted_at":"2019-08-21T12:36:49Z","abstract_excerpt":"In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being a sequence of asymptotic expanders is a coarse property under certain connectedness condition, and it implies non-uniformly local amenability. Moreover, we also analyse some $C^*$-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07814","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07814/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.07814","created_at":"2026-07-05T00:52:06.230362+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.07814v3","created_at":"2026-07-05T00:52:06.230362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07814","created_at":"2026-07-05T00:52:06.230362+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2DPYVC5HBSD","created_at":"2026-07-05T00:52:06.230362+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2DPYVC5HBSDEGDX","created_at":"2026-07-05T00:52:06.230362+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2DPYVC5","created_at":"2026-07-05T00:52:06.230362+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/Y2DPYVC5HBSDEGDXJ77OAQD6W4","json":"https://pith.science/pith/Y2DPYVC5HBSDEGDXJ77OAQD6W4.json","graph_json":"https://pith.science/api/pith-number/Y2DPYVC5HBSDEGDXJ77OAQD6W4/graph.json","events_json":"https://pith.science/api/pith-number/Y2DPYVC5HBSDEGDXJ77OAQD6W4/events.json","paper":"https://pith.science/paper/Y2DPYVC5"},"agent_actions":{"view_html":"https://pith.science/pith/Y2DPYVC5HBSDEGDXJ77OAQD6W4","download_json":"https://pith.science/pith/Y2DPYVC5HBSDEGDXJ77OAQD6W4.json","view_paper":"https://pith.science/paper/Y2DPYVC5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.07814&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2DPYVC5HBSDEGDXJ77OAQD6W4/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2DPYVC5HBSDEGDXJ77OAQD6W4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2DPYVC5HBSDEGDXJ77OAQD6W4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2DPYVC5HBSDEGDXJ77OAQD6W4/action/storage_attestation","attest_author":"https://pith.science/pith/Y2DPYVC5HBSDEGDXJ77OAQD6W4/action/author_attestation","sign_citation":"https://pith.science/pith/Y2DPYVC5HBSDEGDXJ77OAQD6W4/action/citation_signature","submit_replication":"https://pith.science/pith/Y2DPYVC5HBSDEGDXJ77OAQD6W4/action/replication_record"}},"created_at":"2026-07-05T00:52:06.230362+00:00","updated_at":"2026-07-05T00:52:06.230362+00:00"}