{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YZOXS3ZNONGMI577DQYFB4P6RL","short_pith_number":"pith:YZOXS3ZN","canonical_record":{"source":{"id":"1109.5171","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-23T19:57:58Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"50eb4bca92e67957e67b1168e23b5e9ff26660cfef55ac66fdd3b5695c66ed17","abstract_canon_sha256":"4c476b9b523bb802d76e4dc90f1cd82ef0b14791c19046763be9e4c672250a36"},"schema_version":"1.0"},"canonical_sha256":"c65d796f2d734cc477ff1c3050f1fe8aea918d7155d1763fd87e48bef909e003","source":{"kind":"arxiv","id":"1109.5171","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5171","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5171v2","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5171","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"pith_short_12","alias_value":"YZOXS3ZNONGM","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YZOXS3ZNONGMI577","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YZOXS3ZN","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YZOXS3ZNONGMI577DQYFB4P6RL","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5171","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-23T19:57:58Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"50eb4bca92e67957e67b1168e23b5e9ff26660cfef55ac66fdd3b5695c66ed17","abstract_canon_sha256":"4c476b9b523bb802d76e4dc90f1cd82ef0b14791c19046763be9e4c672250a36"},"schema_version":"1.0"},"canonical_sha256":"c65d796f2d734cc477ff1c3050f1fe8aea918d7155d1763fd87e48bef909e003","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:52.552711Z","signature_b64":"3mx3/ca5nL0PhY1sdp4OFtKYDYGnZqypx/MDqa8Qa4F/uCYXAWGz8lTnYQxLNQI8IJ72NwGZmQHfCP1VWg12Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c65d796f2d734cc477ff1c3050f1fe8aea918d7155d1763fd87e48bef909e003","last_reissued_at":"2026-05-18T04:02:52.551833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:52.551833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5171","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":"2026-05-18T04:02:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pv8i71QoeeSoZhj7PImDbY92XytVz/Veu0ZAEVKG+u06DjzSLGPVUFvCtmClUtVokGS9g2XWiK23WDPFlZJIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:48:52.783779Z"},"content_sha256":"10975f2c098e00f534260cfd6ebfc7c51991f5cfe820bb8fa20b402d6d48a7dd","schema_version":"1.0","event_id":"sha256:10975f2c098e00f534260cfd6ebfc7c51991f5cfe820bb8fa20b402d6d48a7dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YZOXS3ZNONGMI577DQYFB4P6RL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Open projections in operator algebras I: Comparison theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.OA","authors_text":"David P. Blecher, Matthew Neal","submitted_at":"2011-09-23T19:57:58Z","abstract_excerpt":"We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega, Rordam, and Thiel of studying these equivalences, etc., in terms of open projections or module isomorphisms. We also define and characterize a new class of inner ideals in operator algebras, and develop a matching theory of open partial isometries in operator ideals which simultaneously generalize the open projections in operator algebras (in the sense of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5171","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":"2026-05-18T04:02:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/gkn1vOE4eMsaFCND+SpBWwvpJ6kJ1ZfgLYqzFMDLAVj5aNZbb7IomJ6zpdgRLVuMJuVbIUothhf+rhSsM3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:48:52.784467Z"},"content_sha256":"37dfa1a8ec837309999e99d697b788bf7d2227c0803e7e64f4325bd37f059204","schema_version":"1.0","event_id":"sha256:37dfa1a8ec837309999e99d697b788bf7d2227c0803e7e64f4325bd37f059204"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZOXS3ZNONGMI577DQYFB4P6RL/bundle.json","state_url":"https://pith.science/pith/YZOXS3ZNONGMI577DQYFB4P6RL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZOXS3ZNONGMI577DQYFB4P6RL/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":"2026-06-06T14:48:52Z","links":{"resolver":"https://pith.science/pith/YZOXS3ZNONGMI577DQYFB4P6RL","bundle":"https://pith.science/pith/YZOXS3ZNONGMI577DQYFB4P6RL/bundle.json","state":"https://pith.science/pith/YZOXS3ZNONGMI577DQYFB4P6RL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZOXS3ZNONGMI577DQYFB4P6RL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YZOXS3ZNONGMI577DQYFB4P6RL","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":"4c476b9b523bb802d76e4dc90f1cd82ef0b14791c19046763be9e4c672250a36","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-23T19:57:58Z","title_canon_sha256":"50eb4bca92e67957e67b1168e23b5e9ff26660cfef55ac66fdd3b5695c66ed17"},"schema_version":"1.0","source":{"id":"1109.5171","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5171","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5171v2","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5171","created_at":"2026-05-18T04:02:52Z"},{"alias_kind":"pith_short_12","alias_value":"YZOXS3ZNONGM","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YZOXS3ZNONGMI577","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YZOXS3ZN","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:37dfa1a8ec837309999e99d697b788bf7d2227c0803e7e64f4325bd37f059204","target":"graph","created_at":"2026-05-18T04:02:52Z","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 begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega, Rordam, and Thiel of studying these equivalences, etc., in terms of open projections or module isomorphisms. We also define and characterize a new class of inner ideals in operator algebras, and develop a matching theory of open partial isometries in operator ideals which simultaneously generalize the open projections in operator algebras (in the sense of the ","authors_text":"David P. Blecher, Matthew Neal","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-23T19:57:58Z","title":"Open projections in operator algebras I: Comparison theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5171","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":"sha256:10975f2c098e00f534260cfd6ebfc7c51991f5cfe820bb8fa20b402d6d48a7dd","target":"record","created_at":"2026-05-18T04:02:52Z","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":"4c476b9b523bb802d76e4dc90f1cd82ef0b14791c19046763be9e4c672250a36","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-23T19:57:58Z","title_canon_sha256":"50eb4bca92e67957e67b1168e23b5e9ff26660cfef55ac66fdd3b5695c66ed17"},"schema_version":"1.0","source":{"id":"1109.5171","kind":"arxiv","version":2}},"canonical_sha256":"c65d796f2d734cc477ff1c3050f1fe8aea918d7155d1763fd87e48bef909e003","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c65d796f2d734cc477ff1c3050f1fe8aea918d7155d1763fd87e48bef909e003","first_computed_at":"2026-05-18T04:02:52.551833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:52.551833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3mx3/ca5nL0PhY1sdp4OFtKYDYGnZqypx/MDqa8Qa4F/uCYXAWGz8lTnYQxLNQI8IJ72NwGZmQHfCP1VWg12Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:52.552711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5171","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10975f2c098e00f534260cfd6ebfc7c51991f5cfe820bb8fa20b402d6d48a7dd","sha256:37dfa1a8ec837309999e99d697b788bf7d2227c0803e7e64f4325bd37f059204"],"state_sha256":"3533bdd6307f711d63e1df3672d237664d19a175c35fd6139d03d514e8630a66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbnF4FY3/Lr1+C2Bd4G5mIAWKY0DP2Iw3FoxS/ebwIKJRKuJ3sYadRmTMpNDYV9pqkfFsFne+Jqmwc6rhQ8lAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:48:52.788298Z","bundle_sha256":"27a2cd35bdee413aeb6155b5c0151c096f64c79c63f660ed8e4facce6f6d77a7"}}