{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NWCRWIIGDQURMEGKPYZEVKS6US","short_pith_number":"pith:NWCRWIIG","schema_version":"1.0","canonical_sha256":"6d851b21061c291610ca7e324aaa5ea4a0e0b7c592105cf5c703b342db21543d","source":{"kind":"arxiv","id":"2606.11586","version":1},"attestation_state":"computed","paper":{"title":"Ideal structure of $\\ell^p$ uniform Roe algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Xinhui Du, Yeong Chyuan Chung","submitted_at":"2026-06-10T02:27:27Z","abstract_excerpt":"For a uniformly locally finite coarse space $(X,\\mathcal{E})$, we prove that for every $p\\in\\{0\\}\\cup[1,\\infty]$, the lattice of geometric ideals in the $\\ell^p$ uniform Roe algebra $B^p_u(X,\\mathcal{E})$ is isomorphic to the lattice of ideals of $\\mathcal{E}$ (equivalently, to the lattice of ideals in the associated family of controlled partial coverings of $X$). In particular, the lattices of geometric ideals for different values of $p$ coincide. Using limit operators, we establish a canonical isometric isomorphism between $B^p_u(X,\\mathcal{E})$ and the reduced $L^p$ operator algebra of 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":"2606.11586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-10T02:27:27Z","cross_cats_sorted":[],"title_canon_sha256":"01452610a2b8b5dfa0c6d6290a6480dd1edb49da894b64ac0a5536975771ab79","abstract_canon_sha256":"8dd3c8e1bc8dea584748f2e64f76422bf93fe6c9d59b48d5237e1de097b123ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:09:57.589051Z","signature_b64":"36wBcA2V5ybjVBkrKatQY3fDEBQJdHQ5UX5TCM4QnDQn1p8zUF+ySesoYl29wAx52SbBOFcuasqWgo+xjG3GDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d851b21061c291610ca7e324aaa5ea4a0e0b7c592105cf5c703b342db21543d","last_reissued_at":"2026-06-11T01:09:57.588183Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:09:57.588183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ideal structure of $\\ell^p$ uniform Roe algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Xinhui Du, Yeong Chyuan Chung","submitted_at":"2026-06-10T02:27:27Z","abstract_excerpt":"For a uniformly locally finite coarse space $(X,\\mathcal{E})$, we prove that for every $p\\in\\{0\\}\\cup[1,\\infty]$, the lattice of geometric ideals in the $\\ell^p$ uniform Roe algebra $B^p_u(X,\\mathcal{E})$ is isomorphic to the lattice of ideals of $\\mathcal{E}$ (equivalently, to the lattice of ideals in the associated family of controlled partial coverings of $X$). In particular, the lattices of geometric ideals for different values of $p$ coincide. Using limit operators, we establish a canonical isometric isomorphism between $B^p_u(X,\\mathcal{E})$ and the reduced $L^p$ operator algebra of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11586","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11586/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":"2606.11586","created_at":"2026-06-11T01:09:57.588341+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.11586v1","created_at":"2026-06-11T01:09:57.588341+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11586","created_at":"2026-06-11T01:09:57.588341+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWCRWIIGDQUR","created_at":"2026-06-11T01:09:57.588341+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWCRWIIGDQURMEGK","created_at":"2026-06-11T01:09:57.588341+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWCRWIIG","created_at":"2026-06-11T01:09:57.588341+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/NWCRWIIGDQURMEGKPYZEVKS6US","json":"https://pith.science/pith/NWCRWIIGDQURMEGKPYZEVKS6US.json","graph_json":"https://pith.science/api/pith-number/NWCRWIIGDQURMEGKPYZEVKS6US/graph.json","events_json":"https://pith.science/api/pith-number/NWCRWIIGDQURMEGKPYZEVKS6US/events.json","paper":"https://pith.science/paper/NWCRWIIG"},"agent_actions":{"view_html":"https://pith.science/pith/NWCRWIIGDQURMEGKPYZEVKS6US","download_json":"https://pith.science/pith/NWCRWIIGDQURMEGKPYZEVKS6US.json","view_paper":"https://pith.science/paper/NWCRWIIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.11586&json=true","fetch_graph":"https://pith.science/api/pith-number/NWCRWIIGDQURMEGKPYZEVKS6US/graph.json","fetch_events":"https://pith.science/api/pith-number/NWCRWIIGDQURMEGKPYZEVKS6US/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWCRWIIGDQURMEGKPYZEVKS6US/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWCRWIIGDQURMEGKPYZEVKS6US/action/storage_attestation","attest_author":"https://pith.science/pith/NWCRWIIGDQURMEGKPYZEVKS6US/action/author_attestation","sign_citation":"https://pith.science/pith/NWCRWIIGDQURMEGKPYZEVKS6US/action/citation_signature","submit_replication":"https://pith.science/pith/NWCRWIIGDQURMEGKPYZEVKS6US/action/replication_record"}},"created_at":"2026-06-11T01:09:57.588341+00:00","updated_at":"2026-06-11T01:09:57.588341+00:00"}