{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6DWFRIVCGRGPSCO4SNT7NXTA5D","short_pith_number":"pith:6DWFRIVC","canonical_record":{"source":{"id":"1212.0361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-12-03T12:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"119b3aa0766c5d4f85306d0c9887df6889075064332552a5fac4e5d96965026f","abstract_canon_sha256":"a8503edae626f06654c95776528b06e9963f7be6a1b8039408972f6f8a716142"},"schema_version":"1.0"},"canonical_sha256":"f0ec58a2a2344cf909dc9367f6de60e8cad6ab85e611a4166ca85a4ac66aeb1b","source":{"kind":"arxiv","id":"1212.0361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0361","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0361v1","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0361","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"6DWFRIVCGRGP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6DWFRIVCGRGPSCO4","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6DWFRIVC","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6DWFRIVCGRGPSCO4SNT7NXTA5D","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-12-03T12:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"119b3aa0766c5d4f85306d0c9887df6889075064332552a5fac4e5d96965026f","abstract_canon_sha256":"a8503edae626f06654c95776528b06e9963f7be6a1b8039408972f6f8a716142"},"schema_version":"1.0"},"canonical_sha256":"f0ec58a2a2344cf909dc9367f6de60e8cad6ab85e611a4166ca85a4ac66aeb1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:47.638507Z","signature_b64":"X/rNOT6QeUziP+plyKRKuovi5AyQltDJl1c9WRtGidLSImG/NqSdzryM1qi8aDauN0CLJ6lRA/97armm0ScvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0ec58a2a2344cf909dc9367f6de60e8cad6ab85e611a4166ca85a4ac66aeb1b","last_reissued_at":"2026-05-18T02:40:47.637861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:47.637861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0361","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":"2026-05-18T02:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qNXgqYe2fawhj+r4BbYktowOdqqI5/2JPUZA8N7cdTxTTSDSII1AzgbJNzIn/kx9o4EDbuynlwDloOxE6WLoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:05:20.380533Z"},"content_sha256":"f6dedd2d128bffc2ba8c1a202d6da3c34e00bf4807564964bd4297000bc6344a","schema_version":"1.0","event_id":"sha256:f6dedd2d128bffc2ba8c1a202d6da3c34e00bf4807564964bd4297000bc6344a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6DWFRIVCGRGPSCO4SNT7NXTA5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological freeness for Hilbert bimodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"B. K. Kwasniewski","submitted_at":"2012-12-03T12:24:40Z","abstract_excerpt":"It is shown that topological freeness of Rieffel's induced representation functor implies that any $C^*$-algebra generated by a faithful covariant representation of a Hilbert bimodule $X$ over a $C^*$-algebra $A$ is canonically isomorphic to the crossed product $A\\rtimes_X \\mathbb{Z}$. An ideal lattice description and a simplicity criterion for $A\\rtimes_X \\mathbb{Z}$ are established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0361","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":"2026-05-18T02:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uf1p8zAHAnzMayiGtcT1nw/LncXRGb64Op7xlH+VxAOPMHJOsyceyjt3iWcEr/yBI6mqocBPA35l6B9S5YGBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:05:20.380870Z"},"content_sha256":"e2b1e7f134ff321d522a7833d5254bbd360a910fe2a90ecc7e13e432e2347d00","schema_version":"1.0","event_id":"sha256:e2b1e7f134ff321d522a7833d5254bbd360a910fe2a90ecc7e13e432e2347d00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DWFRIVCGRGPSCO4SNT7NXTA5D/bundle.json","state_url":"https://pith.science/pith/6DWFRIVCGRGPSCO4SNT7NXTA5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DWFRIVCGRGPSCO4SNT7NXTA5D/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":"2026-06-01T20:05:20Z","links":{"resolver":"https://pith.science/pith/6DWFRIVCGRGPSCO4SNT7NXTA5D","bundle":"https://pith.science/pith/6DWFRIVCGRGPSCO4SNT7NXTA5D/bundle.json","state":"https://pith.science/pith/6DWFRIVCGRGPSCO4SNT7NXTA5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DWFRIVCGRGPSCO4SNT7NXTA5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6DWFRIVCGRGPSCO4SNT7NXTA5D","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":"a8503edae626f06654c95776528b06e9963f7be6a1b8039408972f6f8a716142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-12-03T12:24:40Z","title_canon_sha256":"119b3aa0766c5d4f85306d0c9887df6889075064332552a5fac4e5d96965026f"},"schema_version":"1.0","source":{"id":"1212.0361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0361","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0361v1","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0361","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"6DWFRIVCGRGP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6DWFRIVCGRGPSCO4","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6DWFRIVC","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:e2b1e7f134ff321d522a7833d5254bbd360a910fe2a90ecc7e13e432e2347d00","target":"graph","created_at":"2026-05-18T02:40:47Z","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":"It is shown that topological freeness of Rieffel's induced representation functor implies that any $C^*$-algebra generated by a faithful covariant representation of a Hilbert bimodule $X$ over a $C^*$-algebra $A$ is canonically isomorphic to the crossed product $A\\rtimes_X \\mathbb{Z}$. An ideal lattice description and a simplicity criterion for $A\\rtimes_X \\mathbb{Z}$ are established.","authors_text":"B. K. Kwasniewski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-12-03T12:24:40Z","title":"Topological freeness for Hilbert bimodules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0361","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:f6dedd2d128bffc2ba8c1a202d6da3c34e00bf4807564964bd4297000bc6344a","target":"record","created_at":"2026-05-18T02:40:47Z","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":"a8503edae626f06654c95776528b06e9963f7be6a1b8039408972f6f8a716142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-12-03T12:24:40Z","title_canon_sha256":"119b3aa0766c5d4f85306d0c9887df6889075064332552a5fac4e5d96965026f"},"schema_version":"1.0","source":{"id":"1212.0361","kind":"arxiv","version":1}},"canonical_sha256":"f0ec58a2a2344cf909dc9367f6de60e8cad6ab85e611a4166ca85a4ac66aeb1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0ec58a2a2344cf909dc9367f6de60e8cad6ab85e611a4166ca85a4ac66aeb1b","first_computed_at":"2026-05-18T02:40:47.637861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:47.637861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X/rNOT6QeUziP+plyKRKuovi5AyQltDJl1c9WRtGidLSImG/NqSdzryM1qi8aDauN0CLJ6lRA/97armm0ScvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:47.638507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6dedd2d128bffc2ba8c1a202d6da3c34e00bf4807564964bd4297000bc6344a","sha256:e2b1e7f134ff321d522a7833d5254bbd360a910fe2a90ecc7e13e432e2347d00"],"state_sha256":"379067e69fa95ab9bc9152d6d48d5f2b3bbd9e5917048129c195e370aa5e8540"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CgMHzBQrAq26HN9VLR/SQJa3tSNgUZxOqbTPrz0F+TNAegIsAqVGWb1nibLMUbW1ZfjlZRgBDH5QnX1+VF1HCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:05:20.382733Z","bundle_sha256":"51c88f70813556a91f98584b67f9b84ae0deb9de348a01b88b39b0f0b38dca8e"}}