{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:QJEVVMPWWJORQMLKT5JINBR6XF","short_pith_number":"pith:QJEVVMPW","schema_version":"1.0","canonical_sha256":"82495ab1f6b25d18316a9f5286863eb9558cc844cc8131fc7e7984f6037d2e5b","source":{"kind":"arxiv","id":"1904.07050","version":1},"attestation_state":"computed","paper":{"title":"Structure and $K$-theory of $\\ell^p$ uniform Roe algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Kang Li, Yeong Chyuan Chung","submitted_at":"2019-04-15T13:56:49Z","abstract_excerpt":"In this paper, we characterize when the $\\ell^p$ uniform Roe algebra of a metric space with bounded geometry is (stably) finite and when it is properly infinite in standard form for $p\\in [1,\\infty)$. Moreover, we show that the $\\ell^p$ uniform Roe algebra is a (non-sequential) spatial $L^p$ AF algebra in the sense of Phillips and Viola if and only if the underlying metric space has asymptotic dimension zero.\n  We also consider the ordered $K_0$ groups of $\\ell^p$ uniform Roe algebras for metric spaces with low asymptotic dimension, showing that (1) the ordered $K_0$ group is trivial when the "},"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":"1904.07050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-15T13:56:49Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"50fb4c58bd9a3f2d0a44d66fd56f73edce5a8c8d52672bb15f3afae02f01343f","abstract_canon_sha256":"b6e4beb4379a377fda2ece7a5b681f310aece54a58821741919eeb8a1a713d85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:35.403927Z","signature_b64":"Uz0+rpD9knL7KgdcMupbyap+IgU75PSJrHzGkrmmEZJ4WGfGSeL3HjgmyoX5+BvXbGO1V0XNTADjo/0znRUHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82495ab1f6b25d18316a9f5286863eb9558cc844cc8131fc7e7984f6037d2e5b","last_reissued_at":"2026-05-17T23:48:35.403421Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:35.403421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure and $K$-theory of $\\ell^p$ uniform Roe algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Kang Li, Yeong Chyuan Chung","submitted_at":"2019-04-15T13:56:49Z","abstract_excerpt":"In this paper, we characterize when the $\\ell^p$ uniform Roe algebra of a metric space with bounded geometry is (stably) finite and when it is properly infinite in standard form for $p\\in [1,\\infty)$. Moreover, we show that the $\\ell^p$ uniform Roe algebra is a (non-sequential) spatial $L^p$ AF algebra in the sense of Phillips and Viola if and only if the underlying metric space has asymptotic dimension zero.\n  We also consider the ordered $K_0$ groups of $\\ell^p$ uniform Roe algebras for metric spaces with low asymptotic dimension, showing that (1) the ordered $K_0$ group is trivial when the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07050","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":"1904.07050","created_at":"2026-05-17T23:48:35.403503+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.07050v1","created_at":"2026-05-17T23:48:35.403503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07050","created_at":"2026-05-17T23:48:35.403503+00:00"},{"alias_kind":"pith_short_12","alias_value":"QJEVVMPWWJOR","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"QJEVVMPWWJORQMLK","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"QJEVVMPW","created_at":"2026-05-18T12:33:27.125529+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/QJEVVMPWWJORQMLKT5JINBR6XF","json":"https://pith.science/pith/QJEVVMPWWJORQMLKT5JINBR6XF.json","graph_json":"https://pith.science/api/pith-number/QJEVVMPWWJORQMLKT5JINBR6XF/graph.json","events_json":"https://pith.science/api/pith-number/QJEVVMPWWJORQMLKT5JINBR6XF/events.json","paper":"https://pith.science/paper/QJEVVMPW"},"agent_actions":{"view_html":"https://pith.science/pith/QJEVVMPWWJORQMLKT5JINBR6XF","download_json":"https://pith.science/pith/QJEVVMPWWJORQMLKT5JINBR6XF.json","view_paper":"https://pith.science/paper/QJEVVMPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.07050&json=true","fetch_graph":"https://pith.science/api/pith-number/QJEVVMPWWJORQMLKT5JINBR6XF/graph.json","fetch_events":"https://pith.science/api/pith-number/QJEVVMPWWJORQMLKT5JINBR6XF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QJEVVMPWWJORQMLKT5JINBR6XF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QJEVVMPWWJORQMLKT5JINBR6XF/action/storage_attestation","attest_author":"https://pith.science/pith/QJEVVMPWWJORQMLKT5JINBR6XF/action/author_attestation","sign_citation":"https://pith.science/pith/QJEVVMPWWJORQMLKT5JINBR6XF/action/citation_signature","submit_replication":"https://pith.science/pith/QJEVVMPWWJORQMLKT5JINBR6XF/action/replication_record"}},"created_at":"2026-05-17T23:48:35.403503+00:00","updated_at":"2026-05-17T23:48:35.403503+00:00"}