{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PDFKUWA5XZABJLEBJQNJVPPL64","short_pith_number":"pith:PDFKUWA5","canonical_record":{"source":{"id":"1110.6353","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-28T14:43:20Z","cross_cats_sorted":["math.CV","math.DS"],"title_canon_sha256":"77c99ab4e5ea98f6f9e7c60b71162d7dac274688e10ff44b508cc77b9878b0d0","abstract_canon_sha256":"8092327ae3643f46a8310e8c1b28595b13ecef806a925e31e60320e5759c02fd"},"schema_version":"1.0"},"canonical_sha256":"78caaa581dbe4014ac814c1a9abdebf721fdf9c6cf04b286e518c8f6ad21795c","source":{"kind":"arxiv","id":"1110.6353","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6353","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6353v3","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6353","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"PDFKUWA5XZAB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PDFKUWA5XZABJLEB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PDFKUWA5","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PDFKUWA5XZABJLEBJQNJVPPL64","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6353","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-28T14:43:20Z","cross_cats_sorted":["math.CV","math.DS"],"title_canon_sha256":"77c99ab4e5ea98f6f9e7c60b71162d7dac274688e10ff44b508cc77b9878b0d0","abstract_canon_sha256":"8092327ae3643f46a8310e8c1b28595b13ecef806a925e31e60320e5759c02fd"},"schema_version":"1.0"},"canonical_sha256":"78caaa581dbe4014ac814c1a9abdebf721fdf9c6cf04b286e518c8f6ad21795c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:45.339570Z","signature_b64":"8R3EOMbYvoLX7muzZeBhTGpxx4hx6c6NLTSLCqgFbQ3aVGeUrlZwO0zH9qLLmyFp/7r6Wq1v8Ma94HiiOKOdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78caaa581dbe4014ac814c1a9abdebf721fdf9c6cf04b286e518c8f6ad21795c","last_reissued_at":"2026-05-18T02:59:45.338750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:45.338750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6353","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:59:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKGeQCjpLymVQ4wTn9WiimQcmpUH0Fen572eR9gkhfiPPzAgwGiTwtKF42g4jaVFV7LE5oRcfn70UDlJDOWbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:23:36.015330Z"},"content_sha256":"2430c408709b47e230f7bbf57a90d6f506c6059d75f1b060d65fc192f9a2d6e1","schema_version":"1.0","event_id":"sha256:2430c408709b47e230f7bbf57a90d6f506c6059d75f1b060d65fc192f9a2d6e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PDFKUWA5XZABJLEBJQNJVPPL64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reversibility and Banach Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.GR","authors_text":"Anthony G. O'Farrell","submitted_at":"2011-10-28T14:43:20Z","abstract_excerpt":"An element $g$ of a group is called {\\em reversible} if it is conjugate in the group to its inverse. In this paper we review some results about the structure of groups involving the reversible elements and we pose some questions about groups associated to a Banach algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6353","kind":"arxiv","version":3},"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":"2026-05-18T02:59:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3xBeylaVGN1NhQrXju8tRaIoQi+o2cg/5JaFcDKgK0yMfnm7pTt0ZRcQ8G/hiKj5B87kiiUdFzSpyhPBrTDFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:23:36.015733Z"},"content_sha256":"783b1f95bda67abb9f31f3f72a294686b8aa711b4a90897971271bcb783415ed","schema_version":"1.0","event_id":"sha256:783b1f95bda67abb9f31f3f72a294686b8aa711b4a90897971271bcb783415ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PDFKUWA5XZABJLEBJQNJVPPL64/bundle.json","state_url":"https://pith.science/pith/PDFKUWA5XZABJLEBJQNJVPPL64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PDFKUWA5XZABJLEBJQNJVPPL64/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":"2026-06-01T11:23:36Z","links":{"resolver":"https://pith.science/pith/PDFKUWA5XZABJLEBJQNJVPPL64","bundle":"https://pith.science/pith/PDFKUWA5XZABJLEBJQNJVPPL64/bundle.json","state":"https://pith.science/pith/PDFKUWA5XZABJLEBJQNJVPPL64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PDFKUWA5XZABJLEBJQNJVPPL64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PDFKUWA5XZABJLEBJQNJVPPL64","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":"8092327ae3643f46a8310e8c1b28595b13ecef806a925e31e60320e5759c02fd","cross_cats_sorted":["math.CV","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-28T14:43:20Z","title_canon_sha256":"77c99ab4e5ea98f6f9e7c60b71162d7dac274688e10ff44b508cc77b9878b0d0"},"schema_version":"1.0","source":{"id":"1110.6353","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6353","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6353v3","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6353","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"PDFKUWA5XZAB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PDFKUWA5XZABJLEB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PDFKUWA5","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:783b1f95bda67abb9f31f3f72a294686b8aa711b4a90897971271bcb783415ed","target":"graph","created_at":"2026-05-18T02:59:45Z","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":"An element $g$ of a group is called {\\em reversible} if it is conjugate in the group to its inverse. In this paper we review some results about the structure of groups involving the reversible elements and we pose some questions about groups associated to a Banach algebra.","authors_text":"Anthony G. O'Farrell","cross_cats":["math.CV","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-28T14:43:20Z","title":"Reversibility and Banach Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6353","kind":"arxiv","version":3},"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":"sha256:2430c408709b47e230f7bbf57a90d6f506c6059d75f1b060d65fc192f9a2d6e1","target":"record","created_at":"2026-05-18T02:59:45Z","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":"8092327ae3643f46a8310e8c1b28595b13ecef806a925e31e60320e5759c02fd","cross_cats_sorted":["math.CV","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-28T14:43:20Z","title_canon_sha256":"77c99ab4e5ea98f6f9e7c60b71162d7dac274688e10ff44b508cc77b9878b0d0"},"schema_version":"1.0","source":{"id":"1110.6353","kind":"arxiv","version":3}},"canonical_sha256":"78caaa581dbe4014ac814c1a9abdebf721fdf9c6cf04b286e518c8f6ad21795c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78caaa581dbe4014ac814c1a9abdebf721fdf9c6cf04b286e518c8f6ad21795c","first_computed_at":"2026-05-18T02:59:45.338750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:45.338750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8R3EOMbYvoLX7muzZeBhTGpxx4hx6c6NLTSLCqgFbQ3aVGeUrlZwO0zH9qLLmyFp/7r6Wq1v8Ma94HiiOKOdDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:45.339570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6353","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2430c408709b47e230f7bbf57a90d6f506c6059d75f1b060d65fc192f9a2d6e1","sha256:783b1f95bda67abb9f31f3f72a294686b8aa711b4a90897971271bcb783415ed"],"state_sha256":"0fc6bec897adda540fbf9f2a565db2c8ecf4dd880cf19f194d2c25ff1f56b81d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wtdLegt1tMsLSEaSxsYQdfx0pBXh7TLVHFF1d4UiGDnEratUQY4j5Fb7ZhYYJPq+AEclwlYXxUI0WDcdhHObBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:23:36.018390Z","bundle_sha256":"02d2a7279125cc25b09773d95bf51474805bd6d339acf8dbcc75cbcfe2d4161d"}}