{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:DY6JBWXWICEAYEY37QTFR3RD4T","short_pith_number":"pith:DY6JBWXW","canonical_record":{"source":{"id":"math/0301214","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2003-01-20T14:07:17Z","cross_cats_sorted":["math.CT","math.KT"],"title_canon_sha256":"05bf7ee4d7cd5043c0d577625263d928f559e626d8959e2c88edbe62f4980c9e","abstract_canon_sha256":"f448a3dff0c8d8035bcd20a21298ba749c2f3148d582a554caa2ecb29e305a2d"},"schema_version":"1.0"},"canonical_sha256":"1e3c90daf640880c131bfc2658ee23e4c314f6f119c336db3568b5ed19669499","source":{"kind":"arxiv","id":"math/0301214","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301214","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301214v4","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301214","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"DY6JBWXWICEA","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"DY6JBWXWICEAYEY3","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"DY6JBWXW","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:DY6JBWXWICEAYEY37QTFR3RD4T","target":"record","payload":{"canonical_record":{"source":{"id":"math/0301214","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2003-01-20T14:07:17Z","cross_cats_sorted":["math.CT","math.KT"],"title_canon_sha256":"05bf7ee4d7cd5043c0d577625263d928f559e626d8959e2c88edbe62f4980c9e","abstract_canon_sha256":"f448a3dff0c8d8035bcd20a21298ba749c2f3148d582a554caa2ecb29e305a2d"},"schema_version":"1.0"},"canonical_sha256":"1e3c90daf640880c131bfc2658ee23e4c314f6f119c336db3568b5ed19669499","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:04.344700Z","signature_b64":"JyASFpdt7p7N2mEgb0hdjrSXhUTmRet48WKvbj91TI4zdY8GmnJpxhu465xZzAdpvcM5d+yUaYjuohOrOaNyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e3c90daf640880c131bfc2658ee23e4c314f6f119c336db3568b5ed19669499","last_reissued_at":"2026-05-18T04:08:04.344147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:04.344147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0301214","source_version":4,"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":"GIsLp8yrSn9K5f/0N8F4VEl1bGjRaRkpH8O3+s7vV5C4t9CU3z5fUU3fMwPRKa2Z9azGqHkdD/c3IgL9AljJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T22:27:39.551177Z"},"content_sha256":"83af38ee8a241f76c12a6132cb8ce5c8aefa19783da7c4827ae8d7b939d4f328","schema_version":"1.0","event_id":"sha256:83af38ee8a241f76c12a6132cb8ce5c8aefa19783da7c4827ae8d7b939d4f328"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:DY6JBWXWICEAYEY37QTFR3RD4T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Crossed Products by Endomorphisms, Vector Bundles and Group Duality","license":"","headline":"","cross_cats":["math.CT","math.KT"],"primary_cat":"math.OA","authors_text":"Ezio Vasselli","submitted_at":"2003-01-20T14:07:17Z","abstract_excerpt":"We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that the endomorphism itself becomes induced by the bimodule of continuous sections of a vector bundle. Some motivating examples for such a construction are given. Furthermore, we study the C*-algebra of G-invariant elements of the Cuntz-Pimsner algebra associated with a G-vector bundle, where G is a (noncompact, in general) group. In particular, the C*-algebra of invariant elements w.r.t. the action of the group of special unitaries of the given vector bundle is a crossed product in the above sense. We also s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301214","kind":"arxiv","version":4},"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":"G+noF3pxocyyVyE3B72QC4mIqvb+epzm7f8CYz17IBYvrHWuwjJJ7j/IeGiZ6PibDfA9w2FDSTlWofFA8LQ8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T22:27:39.551534Z"},"content_sha256":"13b44b04cb0fdfdc9a9701b7639372905a8393275c7b3d2a920640906d1c6fa4","schema_version":"1.0","event_id":"sha256:13b44b04cb0fdfdc9a9701b7639372905a8393275c7b3d2a920640906d1c6fa4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DY6JBWXWICEAYEY37QTFR3RD4T/bundle.json","state_url":"https://pith.science/pith/DY6JBWXWICEAYEY37QTFR3RD4T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DY6JBWXWICEAYEY37QTFR3RD4T/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":"2026-06-28T22:27:39Z","links":{"resolver":"https://pith.science/pith/DY6JBWXWICEAYEY37QTFR3RD4T","bundle":"https://pith.science/pith/DY6JBWXWICEAYEY37QTFR3RD4T/bundle.json","state":"https://pith.science/pith/DY6JBWXWICEAYEY37QTFR3RD4T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DY6JBWXWICEAYEY37QTFR3RD4T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:DY6JBWXWICEAYEY37QTFR3RD4T","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":"f448a3dff0c8d8035bcd20a21298ba749c2f3148d582a554caa2ecb29e305a2d","cross_cats_sorted":["math.CT","math.KT"],"license":"","primary_cat":"math.OA","submitted_at":"2003-01-20T14:07:17Z","title_canon_sha256":"05bf7ee4d7cd5043c0d577625263d928f559e626d8959e2c88edbe62f4980c9e"},"schema_version":"1.0","source":{"id":"math/0301214","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301214","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301214v4","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301214","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"DY6JBWXWICEA","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"DY6JBWXWICEAYEY3","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"DY6JBWXW","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:13b44b04cb0fdfdc9a9701b7639372905a8393275c7b3d2a920640906d1c6fa4","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":"We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that the endomorphism itself becomes induced by the bimodule of continuous sections of a vector bundle. Some motivating examples for such a construction are given. Furthermore, we study the C*-algebra of G-invariant elements of the Cuntz-Pimsner algebra associated with a G-vector bundle, where G is a (noncompact, in general) group. In particular, the C*-algebra of invariant elements w.r.t. the action of the group of special unitaries of the given vector bundle is a crossed product in the above sense. We also s","authors_text":"Ezio Vasselli","cross_cats":["math.CT","math.KT"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2003-01-20T14:07:17Z","title":"Crossed Products by Endomorphisms, Vector Bundles and Group Duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301214","kind":"arxiv","version":4},"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":"sha256:83af38ee8a241f76c12a6132cb8ce5c8aefa19783da7c4827ae8d7b939d4f328","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":"f448a3dff0c8d8035bcd20a21298ba749c2f3148d582a554caa2ecb29e305a2d","cross_cats_sorted":["math.CT","math.KT"],"license":"","primary_cat":"math.OA","submitted_at":"2003-01-20T14:07:17Z","title_canon_sha256":"05bf7ee4d7cd5043c0d577625263d928f559e626d8959e2c88edbe62f4980c9e"},"schema_version":"1.0","source":{"id":"math/0301214","kind":"arxiv","version":4}},"canonical_sha256":"1e3c90daf640880c131bfc2658ee23e4c314f6f119c336db3568b5ed19669499","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e3c90daf640880c131bfc2658ee23e4c314f6f119c336db3568b5ed19669499","first_computed_at":"2026-05-18T04:08:04.344147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:04.344147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JyASFpdt7p7N2mEgb0hdjrSXhUTmRet48WKvbj91TI4zdY8GmnJpxhu465xZzAdpvcM5d+yUaYjuohOrOaNyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:04.344700Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0301214","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83af38ee8a241f76c12a6132cb8ce5c8aefa19783da7c4827ae8d7b939d4f328","sha256:13b44b04cb0fdfdc9a9701b7639372905a8393275c7b3d2a920640906d1c6fa4"],"state_sha256":"b67ea7f3e2e1ad0b365821bcdddabf2530e98a8baea6545acad69c1f8217b677"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tE5389tkG4hjjcAi+8zzQqzNPE7J5cmq3xwpwO/uQp2JC5FdEbu6VH8Jjrub7IpHnKUmhx2JLrCgK53Kufn5Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T22:27:39.553502Z","bundle_sha256":"8d2e352e99537593862899fed1f389bf11b4f843d2826c0d4c55419c99256d3b"}}