{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:N5XZXNXFQ74TFLJEZHQPF4K555","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"925b1c45d07558f36363c8e79a40fd550445a793a7736f764c7b2985a3c6a856","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2002-05-15T03:55:34Z","title_canon_sha256":"82c95f204241c6e7c567054cd5d4be2004b5a28ff79110c3516ebdf0a2aad46d"},"schema_version":"1.0","source":{"id":"math/0205166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205166","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205166v2","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205166","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"pith_short_12","alias_value":"N5XZXNXFQ74T","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"pith_short_16","alias_value":"N5XZXNXFQ74TFLJE","created_at":"2026-07-04T14:36:12Z"},{"alias_kind":"pith_short_8","alias_value":"N5XZXNXF","created_at":"2026-07-04T14:36:12Z"}],"graph_snapshots":[{"event_id":"sha256:ddfbe09e93ea3918825e8679829c872e542a3119f3bf0e458273a2288bee719f","target":"graph","created_at":"2026-07-04T14:36:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0205166/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each vertex in G can be reached by an infinite number of vertices. We use this characterization to realize the stabilization of a graph C*-algebra. Specifically, if G is a graph and F is the graph formed by adding a head to each vertex of G, then C*(F) is the stabilization of C*(G).","authors_text":"Mark Tomforde","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2002-05-15T03:55:34Z","title":"Stability of C*-algebras associated to graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205166","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:880f60508e5782640591f331a7d8602098c5e5a2cc3b22ccde3da0ca1e971e98","target":"record","created_at":"2026-07-04T14:36:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"925b1c45d07558f36363c8e79a40fd550445a793a7736f764c7b2985a3c6a856","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2002-05-15T03:55:34Z","title_canon_sha256":"82c95f204241c6e7c567054cd5d4be2004b5a28ff79110c3516ebdf0a2aad46d"},"schema_version":"1.0","source":{"id":"math/0205166","kind":"arxiv","version":2}},"canonical_sha256":"6f6f9bb6e587f932ad24c9e0f2f15def7b79fd718ae80dbed108c178e0a998a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f6f9bb6e587f932ad24c9e0f2f15def7b79fd718ae80dbed108c178e0a998a4","first_computed_at":"2026-07-04T14:36:12.447391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:12.447391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pP8ul2tVt80YiBaRANi0x0ZNtcqUBaUpoz6OMU2rR1MYvxhjZEhi14LwkqBtc16Y7xlVKNlExBfKpmUOHQSzCA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:12.447750Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0205166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:880f60508e5782640591f331a7d8602098c5e5a2cc3b22ccde3da0ca1e971e98","sha256:ddfbe09e93ea3918825e8679829c872e542a3119f3bf0e458273a2288bee719f"],"state_sha256":"4c0592866345b4ae0618394dd8979092240a6660f254a898402953f4fb99ffb0"}