{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:6LRZZAEWWZCFWZPTUSNLJJBT3G","short_pith_number":"pith:6LRZZAEW","canonical_record":{"source":{"id":"0811.0056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-11-01T03:22:04Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"c240c266336546a40c0c2d9fafb45ffde8cdcf8ce05d42b269673d4ae046d9d2","abstract_canon_sha256":"e8678f82467364ef077df4351eeb18e7727213fe0535cf34ec35ea07789cf8f3"},"schema_version":"1.0"},"canonical_sha256":"f2e39c8096b6445b65f3a49ab4a433d9892a979dc4f4bacdd53a5cd66e9dfbeb","source":{"kind":"arxiv","id":"0811.0056","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.0056","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"0811.0056v1","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0056","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"6LRZZAEWWZCF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"6LRZZAEWWZCFWZPT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"6LRZZAEW","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:6LRZZAEWWZCFWZPTUSNLJJBT3G","target":"record","payload":{"canonical_record":{"source":{"id":"0811.0056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-11-01T03:22:04Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"c240c266336546a40c0c2d9fafb45ffde8cdcf8ce05d42b269673d4ae046d9d2","abstract_canon_sha256":"e8678f82467364ef077df4351eeb18e7727213fe0535cf34ec35ea07789cf8f3"},"schema_version":"1.0"},"canonical_sha256":"f2e39c8096b6445b65f3a49ab4a433d9892a979dc4f4bacdd53a5cd66e9dfbeb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:47.845054Z","signature_b64":"WOQRUsH12syPmuPK1aCCQFf6CHL57jOHPJV1/hTAFpeGvZMWdhbrO3+9cjvDD4I+nuOCISrcNyPVtVq87fyUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2e39c8096b6445b65f3a49ab4a433d9892a979dc4f4bacdd53a5cd66e9dfbeb","last_reissued_at":"2026-05-18T02:40:47.844560Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:47.844560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.0056","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":"vA6+1xN53HP/uC8QlgvKbRlmzIyDvatUDi80BIAGdnReAj76vu81Z6z9gAbhB0NHP8Tuk0gruWnVpo44md2TDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:22:04.473464Z"},"content_sha256":"cafd423f5203683a3b8c1a2911a2ef8c3436b78920e910426d80b01c9f2c0d31","schema_version":"1.0","event_id":"sha256:cafd423f5203683a3b8c1a2911a2ef8c3436b78920e910426d80b01c9f2c0d31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:6LRZZAEWWZCFWZPTUSNLJJBT3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Exel crossed product of topological covering maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Sergei Silvestrov, Toke Meier Carlsen","submitted_at":"2008-11-01T03:22:04Z","abstract_excerpt":"For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the associated crossed product $C^*$-algebras $\\cros$ introduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering map is topologically free; the canonical imbedding of $C(X)$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0056","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":"6TWAIm7BaNZYl0kQHWHLy58Mp9Exm8X3tP/uF+kXSNai5oLCg41RJpGKllaEtPHFRx00gfXb0K5B0C/ysTTjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:22:04.474093Z"},"content_sha256":"03b0b3a57b3cd646e1d18847a2a2bbf01f727a99015b2a702e63f3b82fa60518","schema_version":"1.0","event_id":"sha256:03b0b3a57b3cd646e1d18847a2a2bbf01f727a99015b2a702e63f3b82fa60518"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LRZZAEWWZCFWZPTUSNLJJBT3G/bundle.json","state_url":"https://pith.science/pith/6LRZZAEWWZCFWZPTUSNLJJBT3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LRZZAEWWZCFWZPTUSNLJJBT3G/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":"2026-05-26T21:22:04Z","links":{"resolver":"https://pith.science/pith/6LRZZAEWWZCFWZPTUSNLJJBT3G","bundle":"https://pith.science/pith/6LRZZAEWWZCFWZPTUSNLJJBT3G/bundle.json","state":"https://pith.science/pith/6LRZZAEWWZCFWZPTUSNLJJBT3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LRZZAEWWZCFWZPTUSNLJJBT3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:6LRZZAEWWZCFWZPTUSNLJJBT3G","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":"e8678f82467364ef077df4351eeb18e7727213fe0535cf34ec35ea07789cf8f3","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-11-01T03:22:04Z","title_canon_sha256":"c240c266336546a40c0c2d9fafb45ffde8cdcf8ce05d42b269673d4ae046d9d2"},"schema_version":"1.0","source":{"id":"0811.0056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.0056","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"0811.0056v1","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0056","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"6LRZZAEWWZCF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"6LRZZAEWWZCFWZPT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"6LRZZAEW","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:03b0b3a57b3cd646e1d18847a2a2bbf01f727a99015b2a702e63f3b82fa60518","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":"For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the associated crossed product $C^*$-algebras $\\cros$ introduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering map is topologically free; the canonical imbedding of $C(X)$ i","authors_text":"Sergei Silvestrov, Toke Meier Carlsen","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-11-01T03:22:04Z","title":"On the Exel crossed product of topological covering maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0056","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:cafd423f5203683a3b8c1a2911a2ef8c3436b78920e910426d80b01c9f2c0d31","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":"e8678f82467364ef077df4351eeb18e7727213fe0535cf34ec35ea07789cf8f3","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-11-01T03:22:04Z","title_canon_sha256":"c240c266336546a40c0c2d9fafb45ffde8cdcf8ce05d42b269673d4ae046d9d2"},"schema_version":"1.0","source":{"id":"0811.0056","kind":"arxiv","version":1}},"canonical_sha256":"f2e39c8096b6445b65f3a49ab4a433d9892a979dc4f4bacdd53a5cd66e9dfbeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2e39c8096b6445b65f3a49ab4a433d9892a979dc4f4bacdd53a5cd66e9dfbeb","first_computed_at":"2026-05-18T02:40:47.844560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:47.844560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WOQRUsH12syPmuPK1aCCQFf6CHL57jOHPJV1/hTAFpeGvZMWdhbrO3+9cjvDD4I+nuOCISrcNyPVtVq87fyUBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:47.845054Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.0056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cafd423f5203683a3b8c1a2911a2ef8c3436b78920e910426d80b01c9f2c0d31","sha256:03b0b3a57b3cd646e1d18847a2a2bbf01f727a99015b2a702e63f3b82fa60518"],"state_sha256":"c32a4038aa394ec4b7726ab7226255f127860327a2c2d668e4b050f6514f396a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wjFwwZoZvTbZmpKVl7e1+ekpgpn7ZH/L4s7d/hCM9bv+UKGOlFki29+Ujyd3QetWtk7/krnn8CM14CP+0fc9BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:22:04.477457Z","bundle_sha256":"df62f860137203a134ea44644a1e269373f101aa4ffe39b3b08f77a85237360c"}}