{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:N3A2CW5B7WIQMRTQDFFY2ZFJBO","short_pith_number":"pith:N3A2CW5B","canonical_record":{"source":{"id":"math/9911133","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"1999-11-17T19:57:11Z","cross_cats_sorted":[],"title_canon_sha256":"52b11a3f7f6fa5ea462643e5c24ea8b79ba0825ccffd29ec2f6c0bd6cd4836a0","abstract_canon_sha256":"09b53a02dfbc3d47371f4f02657c295c4a13345cd37f0a6ccf3efe1c397992f3"},"schema_version":"1.0"},"canonical_sha256":"6ec1a15ba1fd91064670194b8d64a90b9a73996231eb3c473e45e45b01b92ec8","source":{"kind":"arxiv","id":"math/9911133","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9911133","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/9911133v2","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9911133","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"N3A2CW5B7WIQ","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"pith_short_16","alias_value":"N3A2CW5B7WIQMRTQ","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"pith_short_8","alias_value":"N3A2CW5B","created_at":"2026-07-04T14:41:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:N3A2CW5B7WIQMRTQDFFY2ZFJBO","target":"record","payload":{"canonical_record":{"source":{"id":"math/9911133","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"1999-11-17T19:57:11Z","cross_cats_sorted":[],"title_canon_sha256":"52b11a3f7f6fa5ea462643e5c24ea8b79ba0825ccffd29ec2f6c0bd6cd4836a0","abstract_canon_sha256":"09b53a02dfbc3d47371f4f02657c295c4a13345cd37f0a6ccf3efe1c397992f3"},"schema_version":"1.0"},"canonical_sha256":"6ec1a15ba1fd91064670194b8d64a90b9a73996231eb3c473e45e45b01b92ec8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:41:23.183252Z","signature_b64":"RXMw9xo7uFu9icJkgM1tp+coFEpAWyyz1Fq8vOkffQkxa6cAd2pVs8ggph6dDW87/O95XQabGAy2aVmwQ7+oBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ec1a15ba1fd91064670194b8d64a90b9a73996231eb3c473e45e45b01b92ec8","last_reissued_at":"2026-07-04T14:41:23.182865Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:41:23.182865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9911133","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":"2026-07-04T14:41:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1QxfmDD8KxPLUQ6G0MFIT1ySCXvFFyWqZs1DO56ESeP0Ru53nE85enqVAKOZRLz94Bg2QOBqAwvr0/bjqfyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:20:17.825591Z"},"content_sha256":"561fed1a9d87b30281b1cae996dafe56b9d240ce0cc2796510cfd2a301a5d1da","schema_version":"1.0","event_id":"sha256:561fed1a9d87b30281b1cae996dafe56b9d240ce0cc2796510cfd2a301a5d1da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:N3A2CW5B7WIQMRTQDFFY2ZFJBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometry of oblique projections","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"D. Stojanoff, E. Andruchow, G. Corach","submitted_at":"1999-11-17T19:57:11Z","abstract_excerpt":"Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections P_a determined by the different involutions #_a induced by positive invertible elements a in A. The maps f_p: P \\to P_a sending p to the unique q in P_a with the same range as p and \\Omega_a: P_a \\to P sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q, r in A with |q-r|<1 such that there exists a positive element a in A verifying that q, r are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9911133","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/9911133/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:41:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ph2hYt2HjeJd7JDn2M7QELyfZFQQH2zhWelT3HsZ5Qp9pf8pVJHcOlT5Pdt0BK38Q5v7lyyl+/CnWnjN2o7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:20:17.826938Z"},"content_sha256":"555acb2e573d6e0e1921a49c0903fbf56ecfe7f874eebc17159763968061c9cc","schema_version":"1.0","event_id":"sha256:555acb2e573d6e0e1921a49c0903fbf56ecfe7f874eebc17159763968061c9cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N3A2CW5B7WIQMRTQDFFY2ZFJBO/bundle.json","state_url":"https://pith.science/pith/N3A2CW5B7WIQMRTQDFFY2ZFJBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N3A2CW5B7WIQMRTQDFFY2ZFJBO/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":"2026-08-16T13:20:17Z","links":{"resolver":"https://pith.science/pith/N3A2CW5B7WIQMRTQDFFY2ZFJBO","bundle":"https://pith.science/pith/N3A2CW5B7WIQMRTQDFFY2ZFJBO/bundle.json","state":"https://pith.science/pith/N3A2CW5B7WIQMRTQDFFY2ZFJBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N3A2CW5B7WIQMRTQDFFY2ZFJBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:N3A2CW5B7WIQMRTQDFFY2ZFJBO","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":"09b53a02dfbc3d47371f4f02657c295c4a13345cd37f0a6ccf3efe1c397992f3","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"1999-11-17T19:57:11Z","title_canon_sha256":"52b11a3f7f6fa5ea462643e5c24ea8b79ba0825ccffd29ec2f6c0bd6cd4836a0"},"schema_version":"1.0","source":{"id":"math/9911133","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9911133","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/9911133v2","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9911133","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"N3A2CW5B7WIQ","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"pith_short_16","alias_value":"N3A2CW5B7WIQMRTQ","created_at":"2026-07-04T14:41:23Z"},{"alias_kind":"pith_short_8","alias_value":"N3A2CW5B","created_at":"2026-07-04T14:41:23Z"}],"graph_snapshots":[{"event_id":"sha256:555acb2e573d6e0e1921a49c0903fbf56ecfe7f874eebc17159763968061c9cc","target":"graph","created_at":"2026-07-04T14:41:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/9911133/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections P_a determined by the different involutions #_a induced by positive invertible elements a in A. The maps f_p: P \\to P_a sending p to the unique q in P_a with the same range as p and \\Omega_a: P_a \\to P sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q, r in A with |q-r|<1 such that there exists a positive element a in A verifying that q, r are","authors_text":"D. Stojanoff, E. Andruchow, G. Corach","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"1999-11-17T19:57:11Z","title":"Geometry of oblique projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9911133","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":"sha256:561fed1a9d87b30281b1cae996dafe56b9d240ce0cc2796510cfd2a301a5d1da","target":"record","created_at":"2026-07-04T14:41:23Z","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":"09b53a02dfbc3d47371f4f02657c295c4a13345cd37f0a6ccf3efe1c397992f3","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"1999-11-17T19:57:11Z","title_canon_sha256":"52b11a3f7f6fa5ea462643e5c24ea8b79ba0825ccffd29ec2f6c0bd6cd4836a0"},"schema_version":"1.0","source":{"id":"math/9911133","kind":"arxiv","version":2}},"canonical_sha256":"6ec1a15ba1fd91064670194b8d64a90b9a73996231eb3c473e45e45b01b92ec8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ec1a15ba1fd91064670194b8d64a90b9a73996231eb3c473e45e45b01b92ec8","first_computed_at":"2026-07-04T14:41:23.182865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:41:23.182865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RXMw9xo7uFu9icJkgM1tp+coFEpAWyyz1Fq8vOkffQkxa6cAd2pVs8ggph6dDW87/O95XQabGAy2aVmwQ7+oBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:41:23.183252Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9911133","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:561fed1a9d87b30281b1cae996dafe56b9d240ce0cc2796510cfd2a301a5d1da","sha256:555acb2e573d6e0e1921a49c0903fbf56ecfe7f874eebc17159763968061c9cc"],"state_sha256":"ef8407b1b9238f2ec59542fe58830de41fca73086b9ee0aa063bddaa4897e3c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sginZ7QIqu+D73HyAV7SUSJCb7GksGdaQOTGkhtvr8qokadYRZgc48jO0p2vjtnhlO0ZdoV1GmKtLG9yyUkrDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:20:17.833345Z","bundle_sha256":"1e66c1c60f31d848811b3d825ae4bb0a19c0ef15af700aea136538120dcbf541"}}