{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CCN6XEP35PJFMNLQSCIRCSMUBY","short_pith_number":"pith:CCN6XEP3","canonical_record":{"source":{"id":"1105.4526","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-05-23T15:02:51Z","cross_cats_sorted":[],"title_canon_sha256":"2c1b4e9138ea77acadb3a9ebc7b9e9f27bf81534f36a071c35a9843b418e29f8","abstract_canon_sha256":"42615a5a6dcce828c89bc30fcbb331de6fd58b98eccaafc5150c7070b49e909f"},"schema_version":"1.0"},"canonical_sha256":"109beb91fbebd256357090911149940e14c94f6c737a9affdcfd3d0b98b107b8","source":{"kind":"arxiv","id":"1105.4526","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4526","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4526v3","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4526","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"pith_short_12","alias_value":"CCN6XEP35PJF","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CCN6XEP35PJFMNLQ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CCN6XEP3","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CCN6XEP35PJFMNLQSCIRCSMUBY","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4526","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-05-23T15:02:51Z","cross_cats_sorted":[],"title_canon_sha256":"2c1b4e9138ea77acadb3a9ebc7b9e9f27bf81534f36a071c35a9843b418e29f8","abstract_canon_sha256":"42615a5a6dcce828c89bc30fcbb331de6fd58b98eccaafc5150c7070b49e909f"},"schema_version":"1.0"},"canonical_sha256":"109beb91fbebd256357090911149940e14c94f6c737a9affdcfd3d0b98b107b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:52.317252Z","signature_b64":"gX3RUMtxkrRZQak5solPAOxB1RH/lygd0k+jT2G6ru4/x0TpUMDR51qNu3jY7ImvmxuAewg9gfhkzsdDsHwFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"109beb91fbebd256357090911149940e14c94f6c737a9affdcfd3d0b98b107b8","last_reissued_at":"2026-05-18T04:20:52.316791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:52.316791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4526","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":"2026-05-18T04:20:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fynIvFDfLIGMx/T9vaUXB31IqNa5xrjxcVsjeSVzbfHJaWc5SsH9FAAW/47AzNk3uS+DjP491Sr4W6OuqrZYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:44:19.437349Z"},"content_sha256":"30f871870d3ffb89b5364ec16f47fccdd1920f5b4063e34874c6feb1a936801e","schema_version":"1.0","event_id":"sha256:30f871870d3ffb89b5364ec16f47fccdd1920f5b4063e34874c6feb1a936801e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CCN6XEP35PJFMNLQSCIRCSMUBY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The crossed-product structure of C*-algebras arising from topological dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Cynthia Farthing, Nura Patani, Paulette N. Willis","submitted_at":"2011-05-23T15:02:51Z","abstract_excerpt":"We show that every topological k-graph constructed from a locally compact Hausdorff space {\\Omega} and a family of pairwise commuting local homeomorphisms on {\\Omega} satisfying a uniform boundedness condition on the cardinalities of inverse images may be realized as a semigroup crossed product in the sense of Larsen."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4526","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":"2026-05-18T04:20:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7kZai5JqSLWnB0mHOr5gKTj/vN4e9h/T3YOaDDeHhvMVbs62wTaicHfQWoa35pHee1SD5D/lvA+QLOFwZRQvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:44:19.437693Z"},"content_sha256":"8cc96484538484a262af8568fe3dd69b16054038f8cc2a1b2982bf5b1aa8e83e","schema_version":"1.0","event_id":"sha256:8cc96484538484a262af8568fe3dd69b16054038f8cc2a1b2982bf5b1aa8e83e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CCN6XEP35PJFMNLQSCIRCSMUBY/bundle.json","state_url":"https://pith.science/pith/CCN6XEP35PJFMNLQSCIRCSMUBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CCN6XEP35PJFMNLQSCIRCSMUBY/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":"2026-05-28T10:44:19Z","links":{"resolver":"https://pith.science/pith/CCN6XEP35PJFMNLQSCIRCSMUBY","bundle":"https://pith.science/pith/CCN6XEP35PJFMNLQSCIRCSMUBY/bundle.json","state":"https://pith.science/pith/CCN6XEP35PJFMNLQSCIRCSMUBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CCN6XEP35PJFMNLQSCIRCSMUBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CCN6XEP35PJFMNLQSCIRCSMUBY","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":"42615a5a6dcce828c89bc30fcbb331de6fd58b98eccaafc5150c7070b49e909f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-05-23T15:02:51Z","title_canon_sha256":"2c1b4e9138ea77acadb3a9ebc7b9e9f27bf81534f36a071c35a9843b418e29f8"},"schema_version":"1.0","source":{"id":"1105.4526","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4526","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4526v3","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4526","created_at":"2026-05-18T04:20:52Z"},{"alias_kind":"pith_short_12","alias_value":"CCN6XEP35PJF","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CCN6XEP35PJFMNLQ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CCN6XEP3","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:8cc96484538484a262af8568fe3dd69b16054038f8cc2a1b2982bf5b1aa8e83e","target":"graph","created_at":"2026-05-18T04:20:52Z","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 show that every topological k-graph constructed from a locally compact Hausdorff space {\\Omega} and a family of pairwise commuting local homeomorphisms on {\\Omega} satisfying a uniform boundedness condition on the cardinalities of inverse images may be realized as a semigroup crossed product in the sense of Larsen.","authors_text":"Cynthia Farthing, Nura Patani, Paulette N. Willis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-05-23T15:02:51Z","title":"The crossed-product structure of C*-algebras arising from topological dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4526","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":"sha256:30f871870d3ffb89b5364ec16f47fccdd1920f5b4063e34874c6feb1a936801e","target":"record","created_at":"2026-05-18T04:20:52Z","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":"42615a5a6dcce828c89bc30fcbb331de6fd58b98eccaafc5150c7070b49e909f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-05-23T15:02:51Z","title_canon_sha256":"2c1b4e9138ea77acadb3a9ebc7b9e9f27bf81534f36a071c35a9843b418e29f8"},"schema_version":"1.0","source":{"id":"1105.4526","kind":"arxiv","version":3}},"canonical_sha256":"109beb91fbebd256357090911149940e14c94f6c737a9affdcfd3d0b98b107b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"109beb91fbebd256357090911149940e14c94f6c737a9affdcfd3d0b98b107b8","first_computed_at":"2026-05-18T04:20:52.316791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:52.316791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gX3RUMtxkrRZQak5solPAOxB1RH/lygd0k+jT2G6ru4/x0TpUMDR51qNu3jY7ImvmxuAewg9gfhkzsdDsHwFDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:52.317252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4526","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30f871870d3ffb89b5364ec16f47fccdd1920f5b4063e34874c6feb1a936801e","sha256:8cc96484538484a262af8568fe3dd69b16054038f8cc2a1b2982bf5b1aa8e83e"],"state_sha256":"eb19c7bbae0158ff627e68613a833151ad5618c776363af993372f3dc6921dd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h1QSkHo3OUTBEeDjomE8EN3tQ7/8PjEQJPqplIVZImGoxjtULcpzkRlD60pRVqu/S2JTaeYQaFApTYKugiEnBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:44:19.439734Z","bundle_sha256":"9a8ca629b475107fa1f0966dae5e99b0b1d9f0b195af9b75fb9ad0412c6a90d5"}}