{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YWL4TQZJ7CH6ONJEB65G2LVWUJ","short_pith_number":"pith:YWL4TQZJ","canonical_record":{"source":{"id":"1503.03263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-11T10:36:41Z","cross_cats_sorted":[],"title_canon_sha256":"364291c46927b49917584f01c310b0896462ec7b3da47aeaa2b99f0a78726a8c","abstract_canon_sha256":"bef8869aa1be9687f168bc238fcbbca6080cc144a2765053b1a29c60012ef842"},"schema_version":"1.0"},"canonical_sha256":"c597c9c329f88fe735240fba6d2eb6a27773f019bb330c6d8080e3f49852b6d0","source":{"kind":"arxiv","id":"1503.03263","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03263","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03263v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03263","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"YWL4TQZJ7CH6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YWL4TQZJ7CH6ONJE","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YWL4TQZJ","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YWL4TQZJ7CH6ONJEB65G2LVWUJ","target":"record","payload":{"canonical_record":{"source":{"id":"1503.03263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-11T10:36:41Z","cross_cats_sorted":[],"title_canon_sha256":"364291c46927b49917584f01c310b0896462ec7b3da47aeaa2b99f0a78726a8c","abstract_canon_sha256":"bef8869aa1be9687f168bc238fcbbca6080cc144a2765053b1a29c60012ef842"},"schema_version":"1.0"},"canonical_sha256":"c597c9c329f88fe735240fba6d2eb6a27773f019bb330c6d8080e3f49852b6d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:08.672867Z","signature_b64":"eEdEoJ/iyCxwtCoP9ewiYYU9e1HoxvbuWJuYdCZ0ydRRB43yZMB5MrrNKZeBzJsaIussZTvkz49IK2zq3ZqGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c597c9c329f88fe735240fba6d2eb6a27773f019bb330c6d8080e3f49852b6d0","last_reissued_at":"2026-05-18T01:12:08.672447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:08.672447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.03263","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HCltWG8Qe5EQH0R7QHeA/8Y3vNO1lhV/Evtd8fsLFfKl71SOimF5HK6rouoy91AeNQk0kDO/TjqVEKJSPFdPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:12:46.323324Z"},"content_sha256":"f2350524d50ae0efefb6211da8c3cc2c8718ace69cc8f7b9f5a9a851142b04a7","schema_version":"1.0","event_id":"sha256:f2350524d50ae0efefb6211da8c3cc2c8718ace69cc8f7b9f5a9a851142b04a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YWL4TQZJ7CH6ONJEB65G2LVWUJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of Lie groupoid C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Claire Debord, Georges Skandalis","submitted_at":"2015-03-11T10:36:41Z","abstract_excerpt":"In this paper we generalize a theorem of M. Hilsum and G. Skandalis stating that the $C^*$- algebra of any foliation of non zero dimension is stable. Precisely, we show that the C*-algebra of a Lie groupoid is stable whenever the groupoid has no orbit of dimension zero. We also prove an analogous theorem for singular foliations for which the holonomy groupoid as defined by I. Androulidakis and G. Skandalis is not Lie in general."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03263","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y3QkJ5HCLk+V9USKDvzmP+ll1TdRnOMh8Q3kp4U2yFvLsqcCRwb6EkB+X/jLNf5Xyy++hqknAZWEUFDDBYHeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:12:46.323668Z"},"content_sha256":"f4b86731e2ce07ec13403a8b7b91d2f0568e56d10cf8d45587a04ffd45c9bcaa","schema_version":"1.0","event_id":"sha256:f4b86731e2ce07ec13403a8b7b91d2f0568e56d10cf8d45587a04ffd45c9bcaa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWL4TQZJ7CH6ONJEB65G2LVWUJ/bundle.json","state_url":"https://pith.science/pith/YWL4TQZJ7CH6ONJEB65G2LVWUJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWL4TQZJ7CH6ONJEB65G2LVWUJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T05:12:46Z","links":{"resolver":"https://pith.science/pith/YWL4TQZJ7CH6ONJEB65G2LVWUJ","bundle":"https://pith.science/pith/YWL4TQZJ7CH6ONJEB65G2LVWUJ/bundle.json","state":"https://pith.science/pith/YWL4TQZJ7CH6ONJEB65G2LVWUJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWL4TQZJ7CH6ONJEB65G2LVWUJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YWL4TQZJ7CH6ONJEB65G2LVWUJ","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":"bef8869aa1be9687f168bc238fcbbca6080cc144a2765053b1a29c60012ef842","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-11T10:36:41Z","title_canon_sha256":"364291c46927b49917584f01c310b0896462ec7b3da47aeaa2b99f0a78726a8c"},"schema_version":"1.0","source":{"id":"1503.03263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03263","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03263v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03263","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"YWL4TQZJ7CH6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YWL4TQZJ7CH6ONJE","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YWL4TQZJ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:f4b86731e2ce07ec13403a8b7b91d2f0568e56d10cf8d45587a04ffd45c9bcaa","target":"graph","created_at":"2026-05-18T01:12:08Z","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":"In this paper we generalize a theorem of M. Hilsum and G. Skandalis stating that the $C^*$- algebra of any foliation of non zero dimension is stable. Precisely, we show that the C*-algebra of a Lie groupoid is stable whenever the groupoid has no orbit of dimension zero. We also prove an analogous theorem for singular foliations for which the holonomy groupoid as defined by I. Androulidakis and G. Skandalis is not Lie in general.","authors_text":"Claire Debord, Georges Skandalis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-11T10:36:41Z","title":"Stability of Lie groupoid C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03263","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:f2350524d50ae0efefb6211da8c3cc2c8718ace69cc8f7b9f5a9a851142b04a7","target":"record","created_at":"2026-05-18T01:12:08Z","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":"bef8869aa1be9687f168bc238fcbbca6080cc144a2765053b1a29c60012ef842","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-11T10:36:41Z","title_canon_sha256":"364291c46927b49917584f01c310b0896462ec7b3da47aeaa2b99f0a78726a8c"},"schema_version":"1.0","source":{"id":"1503.03263","kind":"arxiv","version":1}},"canonical_sha256":"c597c9c329f88fe735240fba6d2eb6a27773f019bb330c6d8080e3f49852b6d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c597c9c329f88fe735240fba6d2eb6a27773f019bb330c6d8080e3f49852b6d0","first_computed_at":"2026-05-18T01:12:08.672447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:08.672447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eEdEoJ/iyCxwtCoP9ewiYYU9e1HoxvbuWJuYdCZ0ydRRB43yZMB5MrrNKZeBzJsaIussZTvkz49IK2zq3ZqGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:08.672867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2350524d50ae0efefb6211da8c3cc2c8718ace69cc8f7b9f5a9a851142b04a7","sha256:f4b86731e2ce07ec13403a8b7b91d2f0568e56d10cf8d45587a04ffd45c9bcaa"],"state_sha256":"204326232af1096e54db0c0038365085d9d9d1d796c230ee5ea1023063c9c555"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSlCDcCxA2J9+YXu+mGRMscLQhU9jPrXrvemuleAh5aU5HAamgRcgZ18WynEZ1gUlRD4cFEgiy/iTUX2m+MwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:12:46.325767Z","bundle_sha256":"e4b9e12c7274ab54b5ffb1a174e256f71850f4f47ce81b094d9d4449dda853a3"}}