{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RWDXZIFAJEFPKBNOSY2IFA34DT","short_pith_number":"pith:RWDXZIFA","canonical_record":{"source":{"id":"1712.09386","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-26T19:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"a055c9329e8c3080ce60d804131663fb0190673cb59eb5192a4ef842cc101b41","abstract_canon_sha256":"4c11f9415d9ccb4c624454fa912e995fb14a2afe83bc7464cb0951ad1fca3db1"},"schema_version":"1.0"},"canonical_sha256":"8d877ca0a0490af505ae963482837c1ce2eabf88cf81e87ace372e8de7263e0f","source":{"kind":"arxiv","id":"1712.09386","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09386","created_at":"2026-05-18T00:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09386v1","created_at":"2026-05-18T00:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09386","created_at":"2026-05-18T00:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"RWDXZIFAJEFP","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RWDXZIFAJEFPKBNO","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RWDXZIFA","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RWDXZIFAJEFPKBNOSY2IFA34DT","target":"record","payload":{"canonical_record":{"source":{"id":"1712.09386","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-26T19:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"a055c9329e8c3080ce60d804131663fb0190673cb59eb5192a4ef842cc101b41","abstract_canon_sha256":"4c11f9415d9ccb4c624454fa912e995fb14a2afe83bc7464cb0951ad1fca3db1"},"schema_version":"1.0"},"canonical_sha256":"8d877ca0a0490af505ae963482837c1ce2eabf88cf81e87ace372e8de7263e0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:08.605527Z","signature_b64":"UOEREmrBbfNcXNn3/XUYYTbuxz90wErLyMu7AxCCKQO4IGjyFbE/duZ7LjxnA9Cx/PimTFkWLd66omqdH+hdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d877ca0a0490af505ae963482837c1ce2eabf88cf81e87ace372e8de7263e0f","last_reissued_at":"2026-05-18T00:27:08.604849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:08.604849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.09386","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":"2026-05-18T00:27:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x6jTp/cC4yQRhhbsF5u8eCqtImf2naYfTsp3YY7Wd0rbbv5f7vSwcKu9Ycnb09ZnMgCu17Z4CtZcRew77wsNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:51:56.936163Z"},"content_sha256":"6f127c334164c6a397da6e49634e38d0bd2f8b9756b340a8e76dfcbd87ad7574","schema_version":"1.0","event_id":"sha256:6f127c334164c6a397da6e49634e38d0bd2f8b9756b340a8e76dfcbd87ad7574"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RWDXZIFAJEFPKBNOSY2IFA34DT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the geometry of idempotents in von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Adam Sierakowski, Thierry Giordano","submitted_at":"2017-12-26T19:58:52Z","abstract_excerpt":"We consider the general linear group as an invariant of von Neumann factors. We prove that up to complement, a set consisting of all idempotents generating the same right ideal admits a characterisation in terms of properties of the general linear group of a von Neumann factor. We prove that for two Neumann factors, any bijection of their general linear groups induces a bijection of their idempotents with the following additional property: If two idempotents or their two complements generate the same right ideal, then so does their image. This generalises work on regular rings, such include vo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09386","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":"2026-05-18T00:27:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7ejWHZ1eUifvnKaG9/FgAM3Ybsmr7db+nfTPEwUdpo6juW9J2mAqYGXDoV0gdxym6e0g90qRx9camUgAR0RCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:51:56.936898Z"},"content_sha256":"3ee4ca6ec389c9ed42d5175ff8929e813470c8486f0be4a83c37555365980cab","schema_version":"1.0","event_id":"sha256:3ee4ca6ec389c9ed42d5175ff8929e813470c8486f0be4a83c37555365980cab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWDXZIFAJEFPKBNOSY2IFA34DT/bundle.json","state_url":"https://pith.science/pith/RWDXZIFAJEFPKBNOSY2IFA34DT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWDXZIFAJEFPKBNOSY2IFA34DT/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":"2026-05-26T05:51:56Z","links":{"resolver":"https://pith.science/pith/RWDXZIFAJEFPKBNOSY2IFA34DT","bundle":"https://pith.science/pith/RWDXZIFAJEFPKBNOSY2IFA34DT/bundle.json","state":"https://pith.science/pith/RWDXZIFAJEFPKBNOSY2IFA34DT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWDXZIFAJEFPKBNOSY2IFA34DT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RWDXZIFAJEFPKBNOSY2IFA34DT","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":"4c11f9415d9ccb4c624454fa912e995fb14a2afe83bc7464cb0951ad1fca3db1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-26T19:58:52Z","title_canon_sha256":"a055c9329e8c3080ce60d804131663fb0190673cb59eb5192a4ef842cc101b41"},"schema_version":"1.0","source":{"id":"1712.09386","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09386","created_at":"2026-05-18T00:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09386v1","created_at":"2026-05-18T00:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09386","created_at":"2026-05-18T00:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"RWDXZIFAJEFP","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RWDXZIFAJEFPKBNO","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RWDXZIFA","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:3ee4ca6ec389c9ed42d5175ff8929e813470c8486f0be4a83c37555365980cab","target":"graph","created_at":"2026-05-18T00:27:08Z","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":"We consider the general linear group as an invariant of von Neumann factors. We prove that up to complement, a set consisting of all idempotents generating the same right ideal admits a characterisation in terms of properties of the general linear group of a von Neumann factor. We prove that for two Neumann factors, any bijection of their general linear groups induces a bijection of their idempotents with the following additional property: If two idempotents or their two complements generate the same right ideal, then so does their image. This generalises work on regular rings, such include vo","authors_text":"Adam Sierakowski, Thierry Giordano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-26T19:58:52Z","title":"On the geometry of idempotents in von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09386","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":"sha256:6f127c334164c6a397da6e49634e38d0bd2f8b9756b340a8e76dfcbd87ad7574","target":"record","created_at":"2026-05-18T00:27:08Z","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":"4c11f9415d9ccb4c624454fa912e995fb14a2afe83bc7464cb0951ad1fca3db1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-26T19:58:52Z","title_canon_sha256":"a055c9329e8c3080ce60d804131663fb0190673cb59eb5192a4ef842cc101b41"},"schema_version":"1.0","source":{"id":"1712.09386","kind":"arxiv","version":1}},"canonical_sha256":"8d877ca0a0490af505ae963482837c1ce2eabf88cf81e87ace372e8de7263e0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d877ca0a0490af505ae963482837c1ce2eabf88cf81e87ace372e8de7263e0f","first_computed_at":"2026-05-18T00:27:08.604849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:08.604849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UOEREmrBbfNcXNn3/XUYYTbuxz90wErLyMu7AxCCKQO4IGjyFbE/duZ7LjxnA9Cx/PimTFkWLd66omqdH+hdCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:08.605527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09386","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f127c334164c6a397da6e49634e38d0bd2f8b9756b340a8e76dfcbd87ad7574","sha256:3ee4ca6ec389c9ed42d5175ff8929e813470c8486f0be4a83c37555365980cab"],"state_sha256":"4cb64f83c746ef01f51c558a09830816e20e7a8b80ebefb387e347cb5af8a010"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lL7rIhrKiRkbe6GTGtahVp9bwFmocwVcsOeMa8eBh5YlRdBKjWj9jD0RIja8PFx5PLsxR5GWdx5k4IQtgDBgBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:51:56.940978Z","bundle_sha256":"25b028a319ca34abb31f31ba5d35bd8ca1e14b77536cc4f625e50541d394058d"}}