{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TKE46QF7TBGHPD5WWLORLOQAIH","short_pith_number":"pith:TKE46QF7","canonical_record":{"source":{"id":"1212.4866","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-19T21:53:47Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b94b6e3adba2a15d2c4f518454077e10986860683a9b967718db6a993a6c28ef","abstract_canon_sha256":"f0b7381b382fc467de0fc930fef72ac4bef263aefc4d0000ab1ddbb602ac56b7"},"schema_version":"1.0"},"canonical_sha256":"9a89cf40bf984c778fb6b2dd15ba0041fa8a991512c7034234c2c47e6ab2af10","source":{"kind":"arxiv","id":"1212.4866","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4866","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4866v4","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4866","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"TKE46QF7TBGH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TKE46QF7TBGHPD5W","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TKE46QF7","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TKE46QF7TBGHPD5WWLORLOQAIH","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4866","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-19T21:53:47Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b94b6e3adba2a15d2c4f518454077e10986860683a9b967718db6a993a6c28ef","abstract_canon_sha256":"f0b7381b382fc467de0fc930fef72ac4bef263aefc4d0000ab1ddbb602ac56b7"},"schema_version":"1.0"},"canonical_sha256":"9a89cf40bf984c778fb6b2dd15ba0041fa8a991512c7034234c2c47e6ab2af10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:45.794338Z","signature_b64":"ourtx4SNz7EmiSRVoHGDRj9zdyGkFWGzCpUvjfdQt7MEEHp4p41fv1WBECZj+UYJaXY+v5KLgLjp6YmSaSRXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a89cf40bf984c778fb6b2dd15ba0041fa8a991512c7034234c2c47e6ab2af10","last_reissued_at":"2026-05-18T02:29:45.793766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:45.793766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4866","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uDlsxJQ+xQUp27kxtNNol9OZHSforq6ndRt45g1PR4hneLI7p4Ir7Oy11JYB0Qb+NR6SgXe1XISBpOCPGZFzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:43:37.429276Z"},"content_sha256":"09f6ffa58536c7da9f98ebf9ced84f16fcebc8d9e52ac4ab6ce63c193c80ba0f","schema_version":"1.0","event_id":"sha256:09f6ffa58536c7da9f98ebf9ced84f16fcebc8d9e52ac4ab6ce63c193c80ba0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TKE46QF7TBGHPD5WWLORLOQAIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinitely presented small cancellation groups have the Haagerup property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GR","authors_text":"Damian Osajda, Goulnara Arzhantseva","submitted_at":"2012-12-19T21:53:47Z","abstract_excerpt":"We prove the Haagerup property (= Gromov's a-T-menability) for finitely generated groups defined by infinite presentations satisfying the C'(1/6)-small cancellation condition. We deduce that these groups are coarsely embeddable into a Hilbert space and that the strong Baum-Connes conjecture holds for them. The result is a first non-trivial advancement in understanding groups with such properties among infinitely presented non-amenable direct limits of hyperbolic groups. The proof uses the structure of a space with walls introduced by Wise. As the main step we show that C'(1/6)-complexes satisf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4866","kind":"arxiv","version":4},"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":"2026-05-18T02:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYQGkVc12u76J1lT6M4PlmuUUCVvO+ApAA+UC6ZQ22pzJk1xJhKccVb4opLfvUzi9smYrUQY3tXOYg5BwV4FBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:43:37.429667Z"},"content_sha256":"de5c881d6fc200e0288966c0e7e33e0e0eb3302e946acb93b565f2d30c8adebf","schema_version":"1.0","event_id":"sha256:de5c881d6fc200e0288966c0e7e33e0e0eb3302e946acb93b565f2d30c8adebf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKE46QF7TBGHPD5WWLORLOQAIH/bundle.json","state_url":"https://pith.science/pith/TKE46QF7TBGHPD5WWLORLOQAIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKE46QF7TBGHPD5WWLORLOQAIH/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":"2026-06-04T03:43:37Z","links":{"resolver":"https://pith.science/pith/TKE46QF7TBGHPD5WWLORLOQAIH","bundle":"https://pith.science/pith/TKE46QF7TBGHPD5WWLORLOQAIH/bundle.json","state":"https://pith.science/pith/TKE46QF7TBGHPD5WWLORLOQAIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKE46QF7TBGHPD5WWLORLOQAIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TKE46QF7TBGHPD5WWLORLOQAIH","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":"f0b7381b382fc467de0fc930fef72ac4bef263aefc4d0000ab1ddbb602ac56b7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-19T21:53:47Z","title_canon_sha256":"b94b6e3adba2a15d2c4f518454077e10986860683a9b967718db6a993a6c28ef"},"schema_version":"1.0","source":{"id":"1212.4866","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4866","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4866v4","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4866","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"TKE46QF7TBGH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TKE46QF7TBGHPD5W","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TKE46QF7","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:de5c881d6fc200e0288966c0e7e33e0e0eb3302e946acb93b565f2d30c8adebf","target":"graph","created_at":"2026-05-18T02:29:45Z","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":"We prove the Haagerup property (= Gromov's a-T-menability) for finitely generated groups defined by infinite presentations satisfying the C'(1/6)-small cancellation condition. We deduce that these groups are coarsely embeddable into a Hilbert space and that the strong Baum-Connes conjecture holds for them. The result is a first non-trivial advancement in understanding groups with such properties among infinitely presented non-amenable direct limits of hyperbolic groups. The proof uses the structure of a space with walls introduced by Wise. As the main step we show that C'(1/6)-complexes satisf","authors_text":"Damian Osajda, Goulnara Arzhantseva","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-19T21:53:47Z","title":"Infinitely presented small cancellation groups have the Haagerup property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4866","kind":"arxiv","version":4},"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":"sha256:09f6ffa58536c7da9f98ebf9ced84f16fcebc8d9e52ac4ab6ce63c193c80ba0f","target":"record","created_at":"2026-05-18T02:29:45Z","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":"f0b7381b382fc467de0fc930fef72ac4bef263aefc4d0000ab1ddbb602ac56b7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-19T21:53:47Z","title_canon_sha256":"b94b6e3adba2a15d2c4f518454077e10986860683a9b967718db6a993a6c28ef"},"schema_version":"1.0","source":{"id":"1212.4866","kind":"arxiv","version":4}},"canonical_sha256":"9a89cf40bf984c778fb6b2dd15ba0041fa8a991512c7034234c2c47e6ab2af10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a89cf40bf984c778fb6b2dd15ba0041fa8a991512c7034234c2c47e6ab2af10","first_computed_at":"2026-05-18T02:29:45.793766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:45.793766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ourtx4SNz7EmiSRVoHGDRj9zdyGkFWGzCpUvjfdQt7MEEHp4p41fv1WBECZj+UYJaXY+v5KLgLjp6YmSaSRXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:45.794338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4866","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09f6ffa58536c7da9f98ebf9ced84f16fcebc8d9e52ac4ab6ce63c193c80ba0f","sha256:de5c881d6fc200e0288966c0e7e33e0e0eb3302e946acb93b565f2d30c8adebf"],"state_sha256":"3537d75955cc264c913c327476b120114918e67c25e8d01e95a116949cc77142"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4KxGxHBz9SRoMhdXZ/OuVOJ5azpaVxPCHeH/jf6/qPvQfGHlCfzfiruHl2baXeG65o5JLI5mym7pGvt5bT7DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:43:37.432229Z","bundle_sha256":"9f33e6331d964ec7345d32670a137a7c0e40ac1fb857a60cf44ba2e8d80c9812"}}