{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6WKKOOB3JSR57K6OM7D6FUWS4D","short_pith_number":"pith:6WKKOOB3","schema_version":"1.0","canonical_sha256":"f594a7383b4ca3dfabce67c7e2d2d2e0d8ccd37d3412fa34361eae5d21151ae2","source":{"kind":"arxiv","id":"2607.27691","version":1},"attestation_state":"computed","paper":{"title":"Nuclear dimension, pure infiniteness and real rank for higher rank graph $C^*$-algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"David Pask","submitted_at":"2026-07-30T05:24:18Z","abstract_excerpt":"We study the structure and regularity of higher rank graph $C^*$-algebras, with particular emphasis on their nuclear dimension. For a row-finite, locally convex $k$-graph $\\Lambda$ with no sources, we characterise pure infiniteness of $C^*(\\Lambda)$ in terms of generalised cycles, maximal tails, and strong aperiodicity, and we relate these conditions to topological dimension zero of the primitive ideal space and to the structure of gauge-invariant ideals. Our main application is that whenever $C^*(\\Lambda)$ is purely infinite of topological dimension zero---in particular whenever its ideal lat"},"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":"2607.27691","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-07-30T05:24:18Z","cross_cats_sorted":[],"title_canon_sha256":"d2000ed3103ffaca61e0ae703a2d8200a220eed06aa95960be58a6e8f8cb6875","abstract_canon_sha256":"8c5963efcc5ca81edb9740b7d190cc4d777214a33d78148235336764e28ea785"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f594a7383b4ca3dfabce67c7e2d2d2e0d8ccd37d3412fa34361eae5d21151ae2","last_reissued_at":"2026-07-31T01:29:44.613313Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:29:44.613313Z"},"graph_snapshot":{"paper":{"title":"Nuclear dimension, pure infiniteness and real rank for higher rank graph $C^*$-algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"David Pask","submitted_at":"2026-07-30T05:24:18Z","abstract_excerpt":"We study the structure and regularity of higher rank graph $C^*$-algebras, with particular emphasis on their nuclear dimension. For a row-finite, locally convex $k$-graph $\\Lambda$ with no sources, we characterise pure infiniteness of $C^*(\\Lambda)$ in terms of generalised cycles, maximal tails, and strong aperiodicity, and we relate these conditions to topological dimension zero of the primitive ideal space and to the structure of gauge-invariant ideals. Our main application is that whenever $C^*(\\Lambda)$ is purely infinite of topological dimension zero---in particular whenever its ideal lat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27691","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/2607.27691/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":"2607.27691","created_at":"2026-07-31T01:29:44.616447+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.27691v1","created_at":"2026-07-31T01:29:44.616447+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27691","created_at":"2026-07-31T01:29:44.616447+00:00"},{"alias_kind":"pith_short_12","alias_value":"6WKKOOB3JSR5","created_at":"2026-07-31T01:29:44.616447+00:00"},{"alias_kind":"pith_short_16","alias_value":"6WKKOOB3JSR57K6O","created_at":"2026-07-31T01:29:44.616447+00:00"},{"alias_kind":"pith_short_8","alias_value":"6WKKOOB3","created_at":"2026-07-31T01:29:44.616447+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/6WKKOOB3JSR57K6OM7D6FUWS4D","json":"https://pith.science/pith/6WKKOOB3JSR57K6OM7D6FUWS4D.json","graph_json":"https://pith.science/api/pith-number/6WKKOOB3JSR57K6OM7D6FUWS4D/graph.json","events_json":"https://pith.science/api/pith-number/6WKKOOB3JSR57K6OM7D6FUWS4D/events.json","paper":"https://pith.science/paper/6WKKOOB3"},"agent_actions":{"view_html":"https://pith.science/pith/6WKKOOB3JSR57K6OM7D6FUWS4D","download_json":"https://pith.science/pith/6WKKOOB3JSR57K6OM7D6FUWS4D.json","view_paper":"https://pith.science/paper/6WKKOOB3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.27691&json=true","fetch_graph":"https://pith.science/api/pith-number/6WKKOOB3JSR57K6OM7D6FUWS4D/graph.json","fetch_events":"https://pith.science/api/pith-number/6WKKOOB3JSR57K6OM7D6FUWS4D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6WKKOOB3JSR57K6OM7D6FUWS4D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6WKKOOB3JSR57K6OM7D6FUWS4D/action/storage_attestation","attest_author":"https://pith.science/pith/6WKKOOB3JSR57K6OM7D6FUWS4D/action/author_attestation","sign_citation":"https://pith.science/pith/6WKKOOB3JSR57K6OM7D6FUWS4D/action/citation_signature","submit_replication":"https://pith.science/pith/6WKKOOB3JSR57K6OM7D6FUWS4D/action/replication_record"}},"created_at":"2026-07-31T01:29:44.616447+00:00","updated_at":"2026-07-31T01:29:44.616447+00:00"}