{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:67X6WUGA222ZK3SO3T3NDW5TC6","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":"72aed5b7853fdc13eec0be0ef3a3e57527aa190ecc031179eac7c98ac515ea4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-07T12:30:54Z","title_canon_sha256":"95240010b0aceabcd2656a760279e9b405cee9f24b137b85fa6e7b5f51da02cb"},"schema_version":"1.0","source":{"id":"1302.1728","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1728","created_at":"2026-05-18T03:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1728v1","created_at":"2026-05-18T03:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1728","created_at":"2026-05-18T03:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"67X6WUGA222Z","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"67X6WUGA222ZK3SO","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"67X6WUGA","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:452a1380fddeea30450353b5c6736722023b1ff886490bb333fedff2f439191a","target":"graph","created_at":"2026-05-18T03:34:14Z","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"},"paper":{"abstract_excerpt":"Given a second-countable, Hausdorff, \\'etale, amenable groupoid G with compact unit space, we show that an element a in C*(G) is invertible if and only if \\lambda_x(a) is invertible for every x in the unit space of G, where \\lambda_x refers to the \"regular representation\" of C*(G) on l_2(G_x). We also prove that, for every a in C*(G), there exists some x in G^{(0)} such that ||a|| = ||\\lambda_x(a)||.","authors_text":"Ruy Exel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-07T12:30:54Z","title":"Invertibility in groupoid C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1728","kind":"arxiv","version":1},"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:b204802dd9e506cab5fbd027a2c54e7a3c87885f5993207d2cea160cad9a23a1","target":"record","created_at":"2026-05-18T03:34:14Z","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":"72aed5b7853fdc13eec0be0ef3a3e57527aa190ecc031179eac7c98ac515ea4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-07T12:30:54Z","title_canon_sha256":"95240010b0aceabcd2656a760279e9b405cee9f24b137b85fa6e7b5f51da02cb"},"schema_version":"1.0","source":{"id":"1302.1728","kind":"arxiv","version":1}},"canonical_sha256":"f7efeb50c0d6b5956e4edcf6d1dbb317b79c9f8e10f9ec880aad7b165b0d6fa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7efeb50c0d6b5956e4edcf6d1dbb317b79c9f8e10f9ec880aad7b165b0d6fa5","first_computed_at":"2026-05-18T03:34:14.809853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:14.809853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b9Dtqx6Fw4w+615ShtZQD6M5ho/z/e8fLcPvoC82NEs4c/ZDk/kHDfOHJHjvh35TffbBLymnb7idaSYBC4rWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:14.810593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1728","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b204802dd9e506cab5fbd027a2c54e7a3c87885f5993207d2cea160cad9a23a1","sha256:452a1380fddeea30450353b5c6736722023b1ff886490bb333fedff2f439191a"],"state_sha256":"3c633bdf15d0d5aa0301f4c2fcc28a1c15edb0cc0dbc76898773c33e9be3aea7"}