{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:6NINLHKS7FRPLJMMA7ZNAY3VLE","short_pith_number":"pith:6NINLHKS","canonical_record":{"source":{"id":"0807.2940","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-07-18T10:18:39Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"d8172221633e089803e12a9552e0b28d3875fe49b918c1d81b0a51f96dc3a003","abstract_canon_sha256":"2f47208bae30c065ca83ed261a62aa2b79d85a98398858f8ae6178e39ba7460c"},"schema_version":"1.0"},"canonical_sha256":"f350d59d52f962f5a58c07f2d063755905f7f52b7204b75f58266e6307020c16","source":{"kind":"arxiv","id":"0807.2940","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.2940","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"0807.2940v3","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.2940","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"6NINLHKS7FRP","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"6NINLHKS7FRPLJMM","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"6NINLHKS","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:6NINLHKS7FRPLJMMA7ZNAY3VLE","target":"record","payload":{"canonical_record":{"source":{"id":"0807.2940","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-07-18T10:18:39Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"d8172221633e089803e12a9552e0b28d3875fe49b918c1d81b0a51f96dc3a003","abstract_canon_sha256":"2f47208bae30c065ca83ed261a62aa2b79d85a98398858f8ae6178e39ba7460c"},"schema_version":"1.0"},"canonical_sha256":"f350d59d52f962f5a58c07f2d063755905f7f52b7204b75f58266e6307020c16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:04.279594Z","signature_b64":"dIHbjoQkdUV3T62Rzb195xgXWEN82Aj4vjLPFD6Flq9wVLE+cyjfBHT2+CVaMfbgXLgCK36epua/Uqx8fOsfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f350d59d52f962f5a58c07f2d063755905f7f52b7204b75f58266e6307020c16","last_reissued_at":"2026-05-18T04:08:04.279137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:04.279137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.2940","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YFeLVPJGOXBem8xFaqRj+cD8Mcu1bGDjgmLAzmv536W9hEOHx3gHTSBCHFaA/Stmpd8o21SeLsQsTwILEOrgCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:28:53.946193Z"},"content_sha256":"afb5f4efca398bde7441aa2c8358c0ebb48ad0d1941cf4ddcd7a620bc5c431b7","schema_version":"1.0","event_id":"sha256:afb5f4efca398bde7441aa2c8358c0ebb48ad0d1941cf4ddcd7a620bc5c431b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:6NINLHKS7FRPLJMMA7ZNAY3VLE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the commutant of $C(X)$ in $C^*$-crossed products by $\\mathbb{Z}$ and their representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Christian Svensson, Jun Tomiyama","submitted_at":"2008-07-18T10:18:39Z","abstract_excerpt":"For the $C^*$-crossed product $C^*(\\Sigma)$ associated with an arbitrary topological dynamical system $\\Sigma = (X, \\sigma)$, we provide a detailed analysis of the commutant, in $C^* (\\Sigma)$, of $C(X)$ and the commutant of the image of $C(X)$ under an arbitrary Hilbert space representation $\\tilde{\\pi}$ of $C^* (\\Sigma)$. In particular, we give a concrete description of these commutants, and also determine their spectra. We show that, regardless of the system $\\Sigma$, the commutant of $C(X)$ has non-zero intersection with every non-zero, not necessarily closed or self-adjoint, ideal of $C^*"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.2940","kind":"arxiv","version":3},"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":"2026-05-18T04:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nR8/kdYG3FFjuz74CEd1oYBJGI5QYWUIPwb2HtJ0gWM+gjAWeuVUlfsH/hCg31kL+eDoeij2mFoD7F0WrsVkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:28:53.946583Z"},"content_sha256":"cf3fa3b12b929c95710ac40877abc3e67f214c835e4a6be00abfdd7645ce62a6","schema_version":"1.0","event_id":"sha256:cf3fa3b12b929c95710ac40877abc3e67f214c835e4a6be00abfdd7645ce62a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NINLHKS7FRPLJMMA7ZNAY3VLE/bundle.json","state_url":"https://pith.science/pith/6NINLHKS7FRPLJMMA7ZNAY3VLE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NINLHKS7FRPLJMMA7ZNAY3VLE/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":"2026-06-21T21:28:53Z","links":{"resolver":"https://pith.science/pith/6NINLHKS7FRPLJMMA7ZNAY3VLE","bundle":"https://pith.science/pith/6NINLHKS7FRPLJMMA7ZNAY3VLE/bundle.json","state":"https://pith.science/pith/6NINLHKS7FRPLJMMA7ZNAY3VLE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NINLHKS7FRPLJMMA7ZNAY3VLE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:6NINLHKS7FRPLJMMA7ZNAY3VLE","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":"2f47208bae30c065ca83ed261a62aa2b79d85a98398858f8ae6178e39ba7460c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-07-18T10:18:39Z","title_canon_sha256":"d8172221633e089803e12a9552e0b28d3875fe49b918c1d81b0a51f96dc3a003"},"schema_version":"1.0","source":{"id":"0807.2940","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.2940","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"0807.2940v3","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.2940","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"6NINLHKS7FRP","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"6NINLHKS7FRPLJMM","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"6NINLHKS","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:cf3fa3b12b929c95710ac40877abc3e67f214c835e4a6be00abfdd7645ce62a6","target":"graph","created_at":"2026-05-18T04:08:04Z","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":"For the $C^*$-crossed product $C^*(\\Sigma)$ associated with an arbitrary topological dynamical system $\\Sigma = (X, \\sigma)$, we provide a detailed analysis of the commutant, in $C^* (\\Sigma)$, of $C(X)$ and the commutant of the image of $C(X)$ under an arbitrary Hilbert space representation $\\tilde{\\pi}$ of $C^* (\\Sigma)$. In particular, we give a concrete description of these commutants, and also determine their spectra. We show that, regardless of the system $\\Sigma$, the commutant of $C(X)$ has non-zero intersection with every non-zero, not necessarily closed or self-adjoint, ideal of $C^*","authors_text":"Christian Svensson, Jun Tomiyama","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-07-18T10:18:39Z","title":"On the commutant of $C(X)$ in $C^*$-crossed products by $\\mathbb{Z}$ and their representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.2940","kind":"arxiv","version":3},"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:afb5f4efca398bde7441aa2c8358c0ebb48ad0d1941cf4ddcd7a620bc5c431b7","target":"record","created_at":"2026-05-18T04:08:04Z","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":"2f47208bae30c065ca83ed261a62aa2b79d85a98398858f8ae6178e39ba7460c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-07-18T10:18:39Z","title_canon_sha256":"d8172221633e089803e12a9552e0b28d3875fe49b918c1d81b0a51f96dc3a003"},"schema_version":"1.0","source":{"id":"0807.2940","kind":"arxiv","version":3}},"canonical_sha256":"f350d59d52f962f5a58c07f2d063755905f7f52b7204b75f58266e6307020c16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f350d59d52f962f5a58c07f2d063755905f7f52b7204b75f58266e6307020c16","first_computed_at":"2026-05-18T04:08:04.279137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:04.279137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dIHbjoQkdUV3T62Rzb195xgXWEN82Aj4vjLPFD6Flq9wVLE+cyjfBHT2+CVaMfbgXLgCK36epua/Uqx8fOsfAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:04.279594Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.2940","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afb5f4efca398bde7441aa2c8358c0ebb48ad0d1941cf4ddcd7a620bc5c431b7","sha256:cf3fa3b12b929c95710ac40877abc3e67f214c835e4a6be00abfdd7645ce62a6"],"state_sha256":"a2d693e99e07a023d1e181b4c59e4aab95fdef9e37dd158c881d36a23dd0609b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s+Ub3wYo6Op85yuBsw4o06xAA2qGkKmMfMTNbd9YAqI75u/Tz6ahkVugYZEk7zqe0NyeYfvuowIq0wGHbF1nAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:28:53.948584Z","bundle_sha256":"87606d56e1fbda72c765c3942d47834ce5838fec48b4e90d3e2e3485c715976b"}}