{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:MYOT7P63EE4KSRZCSM2KAEKSQM","short_pith_number":"pith:MYOT7P63","canonical_record":{"source":{"id":"math/9707228","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"1997-07-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"ced93335fe06b65cfa486f7b28dba3245e42b1297404241cb1ad70ab79e35847","abstract_canon_sha256":"fd5d33719aed0443000ba9b7e7eed2ecf247c7ab68e169edaad25931b34c58dc"},"schema_version":"1.0"},"canonical_sha256":"661d3fbfdb2138a947229334a011528306af002e6bee0f57450319b353614bc5","source":{"kind":"arxiv","id":"math/9707228","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9707228","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/9707228v1","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9707228","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"pith_short_12","alias_value":"MYOT7P63EE4K","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"pith_short_16","alias_value":"MYOT7P63EE4KSRZC","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"pith_short_8","alias_value":"MYOT7P63","created_at":"2026-07-04T15:51:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:MYOT7P63EE4KSRZCSM2KAEKSQM","target":"record","payload":{"canonical_record":{"source":{"id":"math/9707228","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"1997-07-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"ced93335fe06b65cfa486f7b28dba3245e42b1297404241cb1ad70ab79e35847","abstract_canon_sha256":"fd5d33719aed0443000ba9b7e7eed2ecf247c7ab68e169edaad25931b34c58dc"},"schema_version":"1.0"},"canonical_sha256":"661d3fbfdb2138a947229334a011528306af002e6bee0f57450319b353614bc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:51:31.358091Z","signature_b64":"wjwlp4T8JDrLCjDeUrUKuVSr6I0Suv4fEGtuRP/gwcneOugVYzcKTqqja3nZ+3izOVGIWXPRBFpBbarnuB2LBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"661d3fbfdb2138a947229334a011528306af002e6bee0f57450319b353614bc5","last_reissued_at":"2026-07-04T15:51:31.357666Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:51:31.357666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9707228","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":"2026-07-04T15:51:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zgBEYJVcRDp/p84SdXxV7ChFnWYMCskuggl1YqKqotjF55QAj+Zy4ke4cZYTdb05JdVlbjxd141QT6LfUQM/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T13:43:23.733431Z"},"content_sha256":"a2bfb5fa9d512d27d64aab932c298b405be77854987bb1b2cc59b87c069578cd","schema_version":"1.0","event_id":"sha256:a2bfb5fa9d512d27d64aab932c298b405be77854987bb1b2cc59b87c069578cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:MYOT7P63EE4KSRZCSM2KAEKSQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonstable K-theory for Z-stable C*-algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Xinhui Jiang (Fields Institute)","submitted_at":"1997-07-01T00:00:00Z","abstract_excerpt":"Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants, namely, \\pi_i(U(A)) = K_{i-1}(A) for all integers i >= 0. Furthermore, A has cancellation for full projections, and satisfies the comparability question for full projections. Analogous results hold for non-unital Z-stable C^*-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9707228","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/9707228/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":"2026-07-04T15:51:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tPHEKRi8LNAQg4H4epUo3BvethQyMRdoHXU1A7k/ey1TkLNtFaHYO7zFTjsXHqMbHCVMiK6bmL+oXK5LChi4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T13:43:23.733943Z"},"content_sha256":"be4570cc6423985f4756d8731b519e67e30b9ad38a40c782e67712d50c94a12a","schema_version":"1.0","event_id":"sha256:be4570cc6423985f4756d8731b519e67e30b9ad38a40c782e67712d50c94a12a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MYOT7P63EE4KSRZCSM2KAEKSQM/bundle.json","state_url":"https://pith.science/pith/MYOT7P63EE4KSRZCSM2KAEKSQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MYOT7P63EE4KSRZCSM2KAEKSQM/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":"2026-08-15T13:43:23Z","links":{"resolver":"https://pith.science/pith/MYOT7P63EE4KSRZCSM2KAEKSQM","bundle":"https://pith.science/pith/MYOT7P63EE4KSRZCSM2KAEKSQM/bundle.json","state":"https://pith.science/pith/MYOT7P63EE4KSRZCSM2KAEKSQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MYOT7P63EE4KSRZCSM2KAEKSQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:MYOT7P63EE4KSRZCSM2KAEKSQM","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":"fd5d33719aed0443000ba9b7e7eed2ecf247c7ab68e169edaad25931b34c58dc","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"1997-07-01T00:00:00Z","title_canon_sha256":"ced93335fe06b65cfa486f7b28dba3245e42b1297404241cb1ad70ab79e35847"},"schema_version":"1.0","source":{"id":"math/9707228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9707228","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/9707228v1","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9707228","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"pith_short_12","alias_value":"MYOT7P63EE4K","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"pith_short_16","alias_value":"MYOT7P63EE4KSRZC","created_at":"2026-07-04T15:51:31Z"},{"alias_kind":"pith_short_8","alias_value":"MYOT7P63","created_at":"2026-07-04T15:51:31Z"}],"graph_snapshots":[{"event_id":"sha256:be4570cc6423985f4756d8731b519e67e30b9ad38a40c782e67712d50c94a12a","target":"graph","created_at":"2026-07-04T15:51:31Z","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/9707228/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants, namely, \\pi_i(U(A)) = K_{i-1}(A) for all integers i >= 0. Furthermore, A has cancellation for full projections, and satisfies the comparability question for full projections. Analogous results hold for non-unital Z-stable C^*-algebras.","authors_text":"Xinhui Jiang (Fields Institute)","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"1997-07-01T00:00:00Z","title":"Nonstable K-theory for Z-stable C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9707228","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:a2bfb5fa9d512d27d64aab932c298b405be77854987bb1b2cc59b87c069578cd","target":"record","created_at":"2026-07-04T15:51:31Z","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":"fd5d33719aed0443000ba9b7e7eed2ecf247c7ab68e169edaad25931b34c58dc","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"1997-07-01T00:00:00Z","title_canon_sha256":"ced93335fe06b65cfa486f7b28dba3245e42b1297404241cb1ad70ab79e35847"},"schema_version":"1.0","source":{"id":"math/9707228","kind":"arxiv","version":1}},"canonical_sha256":"661d3fbfdb2138a947229334a011528306af002e6bee0f57450319b353614bc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"661d3fbfdb2138a947229334a011528306af002e6bee0f57450319b353614bc5","first_computed_at":"2026-07-04T15:51:31.357666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:51:31.357666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wjwlp4T8JDrLCjDeUrUKuVSr6I0Suv4fEGtuRP/gwcneOugVYzcKTqqja3nZ+3izOVGIWXPRBFpBbarnuB2LBA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:51:31.358091Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9707228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2bfb5fa9d512d27d64aab932c298b405be77854987bb1b2cc59b87c069578cd","sha256:be4570cc6423985f4756d8731b519e67e30b9ad38a40c782e67712d50c94a12a"],"state_sha256":"f102b67ea3fd165a6514cf3f34be23f475d4270375bbda1d1c82c11f953d778f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sxUEHsIiMqBU1BWbOm4Khleq3lhOKnh/cegf6Djp2a/lNNp2IPGX5Avn66E0n9AUkRr+TKbRLN6bCBNqFzJpAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T13:43:23.737619Z","bundle_sha256":"2d7ed90c5cc66af5a4bbc48ff3683d946f21c3e2035b8501dd57af99f08e7a5b"}}