{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:J4F7ZIMWE6ATHPKNHDQ24W7B3D","short_pith_number":"pith:J4F7ZIMW","canonical_record":{"source":{"id":"1110.1532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-10-07T13:57:19Z","cross_cats_sorted":[],"title_canon_sha256":"31b2ffd067352c964a20967665d67d851aabb2ca2e3c58e6b84be3d4df1b0a7d","abstract_canon_sha256":"630e4b4ece9f2d84a46dc83cd0f293fbac05fdf9270fe2dc7fb6d7df07080d86"},"schema_version":"1.0"},"canonical_sha256":"4f0bfca196278133bd4d38e1ae5be1d8df9aa69191fce27a349515041e0b8f60","source":{"kind":"arxiv","id":"1110.1532","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1532","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1532v2","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1532","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"J4F7ZIMWE6AT","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J4F7ZIMWE6ATHPKN","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J4F7ZIMW","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:J4F7ZIMWE6ATHPKNHDQ24W7B3D","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-10-07T13:57:19Z","cross_cats_sorted":[],"title_canon_sha256":"31b2ffd067352c964a20967665d67d851aabb2ca2e3c58e6b84be3d4df1b0a7d","abstract_canon_sha256":"630e4b4ece9f2d84a46dc83cd0f293fbac05fdf9270fe2dc7fb6d7df07080d86"},"schema_version":"1.0"},"canonical_sha256":"4f0bfca196278133bd4d38e1ae5be1d8df9aa69191fce27a349515041e0b8f60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:35.330216Z","signature_b64":"Nrh4cbQBpJYVkR0DL5zj+w/dryVxg6KF1wA5Xmt1ad3Gx2S//LVNzDrzddBChxLmZ3O+enig8/zubgs/zkgjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f0bfca196278133bd4d38e1ae5be1d8df9aa69191fce27a349515041e0b8f60","last_reissued_at":"2026-05-18T03:12:35.329517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:35.329517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1532","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q+fSRP2bsVQiS2n0tYzZe59vzZQK/INbGOrmXmwrQZM0V/2axIQWvrLrvTqD8QT1zB+0OKtzhblg+kkEOqXrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:24:57.140268Z"},"content_sha256":"b0fa9ad9c2f1230c778f390922a21cab6f8e238c39669e37c01a259755124f01","schema_version":"1.0","event_id":"sha256:b0fa9ad9c2f1230c778f390922a21cab6f8e238c39669e37c01a259755124f01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:J4F7ZIMWE6ATHPKNHDQ24W7B3D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Rigidity of Roe algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jan Spakula, Rufus Willett","submitted_at":"2011-10-07T13:57:19Z","abstract_excerpt":"Roe algebras are C*-algebras built using large-scale (or 'coarse') aspects of a metric space (X,d). In the special case that X=G is a finitely generated group and d is a word metric, the simplest Roe algebra associated to (G,d) is isomorphic to the reduced crossed product C*-algebra l^\\infty(G)\\rtimes G.\n  Roe algebras are 'coarse invariants', in the sense that if X and Y are coarsely equivalent metric spaces, then their Roe algebras are isomorphic. Motivated in part by the coarse Baum-Connes conjecture, we ask if there is a converse to the above statement: that is, if X and Y are metric space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1532","kind":"arxiv","version":2},"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":"2026-05-18T03:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JsEyL23tFmnuEsOtNS3f617pwDY3+fx2wcUA4CD/s9hH7MaR58GCxfx7PPKaRBksAiHdnfpS0cVYjnAX3vf+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:24:57.140641Z"},"content_sha256":"b0cb7fdcd39a6c04173d4343ea5df3d046336b0d635dab386fc4ae8bf0cb7de9","schema_version":"1.0","event_id":"sha256:b0cb7fdcd39a6c04173d4343ea5df3d046336b0d635dab386fc4ae8bf0cb7de9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4F7ZIMWE6ATHPKNHDQ24W7B3D/bundle.json","state_url":"https://pith.science/pith/J4F7ZIMWE6ATHPKNHDQ24W7B3D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4F7ZIMWE6ATHPKNHDQ24W7B3D/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":"2026-06-23T13:24:57Z","links":{"resolver":"https://pith.science/pith/J4F7ZIMWE6ATHPKNHDQ24W7B3D","bundle":"https://pith.science/pith/J4F7ZIMWE6ATHPKNHDQ24W7B3D/bundle.json","state":"https://pith.science/pith/J4F7ZIMWE6ATHPKNHDQ24W7B3D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4F7ZIMWE6ATHPKNHDQ24W7B3D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J4F7ZIMWE6ATHPKNHDQ24W7B3D","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":"630e4b4ece9f2d84a46dc83cd0f293fbac05fdf9270fe2dc7fb6d7df07080d86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-10-07T13:57:19Z","title_canon_sha256":"31b2ffd067352c964a20967665d67d851aabb2ca2e3c58e6b84be3d4df1b0a7d"},"schema_version":"1.0","source":{"id":"1110.1532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1532","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1532v2","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1532","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"J4F7ZIMWE6AT","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J4F7ZIMWE6ATHPKN","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J4F7ZIMW","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:b0cb7fdcd39a6c04173d4343ea5df3d046336b0d635dab386fc4ae8bf0cb7de9","target":"graph","created_at":"2026-05-18T03:12:35Z","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":"Roe algebras are C*-algebras built using large-scale (or 'coarse') aspects of a metric space (X,d). In the special case that X=G is a finitely generated group and d is a word metric, the simplest Roe algebra associated to (G,d) is isomorphic to the reduced crossed product C*-algebra l^\\infty(G)\\rtimes G.\n  Roe algebras are 'coarse invariants', in the sense that if X and Y are coarsely equivalent metric spaces, then their Roe algebras are isomorphic. Motivated in part by the coarse Baum-Connes conjecture, we ask if there is a converse to the above statement: that is, if X and Y are metric space","authors_text":"Jan Spakula, Rufus Willett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-10-07T13:57:19Z","title":"On Rigidity of Roe algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1532","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:b0fa9ad9c2f1230c778f390922a21cab6f8e238c39669e37c01a259755124f01","target":"record","created_at":"2026-05-18T03:12:35Z","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":"630e4b4ece9f2d84a46dc83cd0f293fbac05fdf9270fe2dc7fb6d7df07080d86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-10-07T13:57:19Z","title_canon_sha256":"31b2ffd067352c964a20967665d67d851aabb2ca2e3c58e6b84be3d4df1b0a7d"},"schema_version":"1.0","source":{"id":"1110.1532","kind":"arxiv","version":2}},"canonical_sha256":"4f0bfca196278133bd4d38e1ae5be1d8df9aa69191fce27a349515041e0b8f60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f0bfca196278133bd4d38e1ae5be1d8df9aa69191fce27a349515041e0b8f60","first_computed_at":"2026-05-18T03:12:35.329517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:35.329517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nrh4cbQBpJYVkR0DL5zj+w/dryVxg6KF1wA5Xmt1ad3Gx2S//LVNzDrzddBChxLmZ3O+enig8/zubgs/zkgjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:35.330216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0fa9ad9c2f1230c778f390922a21cab6f8e238c39669e37c01a259755124f01","sha256:b0cb7fdcd39a6c04173d4343ea5df3d046336b0d635dab386fc4ae8bf0cb7de9"],"state_sha256":"bbe656959c18e89b12444714603cb14d959f7c71db93199aee8855785af91b37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/WISa1OxNCJr6O+GgNBT55yBsvJ+NXt8xYWZ/tCoiy/re48YBXoolDi7L3gEvA1QX0U54tb4OD1yH+wyyo/sBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:24:57.142565Z","bundle_sha256":"20bd8f60824f68dc7620b64d7d0861f027992426d3c5c2c4260300e7cb6e876a"}}