{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:RS64OW4WFQK4EAHSUZWZDSCEUU","short_pith_number":"pith:RS64OW4W","canonical_record":{"source":{"id":"math/0309293","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2003-09-18T00:31:51Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"c1a45a980e2d1a9942e327a7e30cff8d75de3722bc4812b1d62125f7f72bec03","abstract_canon_sha256":"1d709c01f43fc4358cbde3214563b1d38c87282643fcf3cf61c7577bb7b70908"},"schema_version":"1.0"},"canonical_sha256":"8cbdc75b962c15c200f2a66d91c844a509d1f3075fa260d8d4e29c355fd7c0d7","source":{"kind":"arxiv","id":"math/0309293","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0309293","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0309293v1","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0309293","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"RS64OW4WFQK4","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"pith_short_16","alias_value":"RS64OW4WFQK4EAHS","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"pith_short_8","alias_value":"RS64OW4W","created_at":"2026-07-04T14:37:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:RS64OW4WFQK4EAHSUZWZDSCEUU","target":"record","payload":{"canonical_record":{"source":{"id":"math/0309293","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2003-09-18T00:31:51Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"c1a45a980e2d1a9942e327a7e30cff8d75de3722bc4812b1d62125f7f72bec03","abstract_canon_sha256":"1d709c01f43fc4358cbde3214563b1d38c87282643fcf3cf61c7577bb7b70908"},"schema_version":"1.0"},"canonical_sha256":"8cbdc75b962c15c200f2a66d91c844a509d1f3075fa260d8d4e29c355fd7c0d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:43.923087Z","signature_b64":"p+ItPAHX41xW+QhA0+YhMkee6ffOQyR61aDl0mWiH6/5NVPcdPYE3i7AXaPxna0kK5jTtjkjdo0taU5c8UyaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cbdc75b962c15c200f2a66d91c844a509d1f3075fa260d8d4e29c355fd7c0d7","last_reissued_at":"2026-07-04T14:37:43.922697Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:43.922697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0309293","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":"2026-07-04T14:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ca3le8pR/ZPRpf8DTYrR4Veg4CmAlTrEDqkzXqqtgsuwvDpkZFH6CB6QoY2JferEPnmJVzBcT2AoAG5jt/tFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:22:31.280543Z"},"content_sha256":"b4952b1edcad462eb7fcb5e96eb2e13f8012c9c2c50afb0b6586fffa7cd2e184","schema_version":"1.0","event_id":"sha256:b4952b1edcad462eb7fcb5e96eb2e13f8012c9c2c50afb0b6586fffa7cd2e184"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:RS64OW4WFQK4EAHSUZWZDSCEUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"C^*-algebras associated with complex dynamical systems","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Tsuyoshi Kajiwara, Yasuo Watatani","submitted_at":"2003-09-18T00:31:51Z","abstract_excerpt":"Iteration of a rational function $R$ gives a complex dynamical system on the Riemann sphere. We introduce a $C^*$-algebra ${\\mathcal O}_R$ associated with $R$ as a Cuntz-Pimsner algebra of a Hilbert bimodule over the algebra $A = C(J_R)$ of continuous functions on the Julia set $J_R$ of $R$. The algebra ${\\mathcal O}_R$ is a certain analog of the crossed product by a boundary action. We show that if the degree of $R$ is at least two, then $C^*$-algebra ${\\mathcal O}_R$ is simple and purely infinite. For example if $R(z) = z^2 - 2$, then the Julia set $J_R = [-2,2]$ and the restriction $R : J_R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309293","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0309293/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dIvKQxL/LwsmRfbQ5KTzzxMLxIhyyhoqMOvvHnd38U1EaI9LSujZR++t3KoZ0qpaDB/SPH7UYL14LnlcXtC5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:22:31.280916Z"},"content_sha256":"2490e4911f91b9340dedc89dbbc9c299a0fa7ae8d0276bf4eefa821cde39b377","schema_version":"1.0","event_id":"sha256:2490e4911f91b9340dedc89dbbc9c299a0fa7ae8d0276bf4eefa821cde39b377"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RS64OW4WFQK4EAHSUZWZDSCEUU/bundle.json","state_url":"https://pith.science/pith/RS64OW4WFQK4EAHSUZWZDSCEUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RS64OW4WFQK4EAHSUZWZDSCEUU/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":"2026-07-05T07:22:31Z","links":{"resolver":"https://pith.science/pith/RS64OW4WFQK4EAHSUZWZDSCEUU","bundle":"https://pith.science/pith/RS64OW4WFQK4EAHSUZWZDSCEUU/bundle.json","state":"https://pith.science/pith/RS64OW4WFQK4EAHSUZWZDSCEUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RS64OW4WFQK4EAHSUZWZDSCEUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:RS64OW4WFQK4EAHSUZWZDSCEUU","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":"1d709c01f43fc4358cbde3214563b1d38c87282643fcf3cf61c7577bb7b70908","cross_cats_sorted":["math.DS"],"license":"","primary_cat":"math.OA","submitted_at":"2003-09-18T00:31:51Z","title_canon_sha256":"c1a45a980e2d1a9942e327a7e30cff8d75de3722bc4812b1d62125f7f72bec03"},"schema_version":"1.0","source":{"id":"math/0309293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0309293","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0309293v1","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0309293","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"RS64OW4WFQK4","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"pith_short_16","alias_value":"RS64OW4WFQK4EAHS","created_at":"2026-07-04T14:37:43Z"},{"alias_kind":"pith_short_8","alias_value":"RS64OW4W","created_at":"2026-07-04T14:37:43Z"}],"graph_snapshots":[{"event_id":"sha256:2490e4911f91b9340dedc89dbbc9c299a0fa7ae8d0276bf4eefa821cde39b377","target":"graph","created_at":"2026-07-04T14:37:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0309293/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Iteration of a rational function $R$ gives a complex dynamical system on the Riemann sphere. We introduce a $C^*$-algebra ${\\mathcal O}_R$ associated with $R$ as a Cuntz-Pimsner algebra of a Hilbert bimodule over the algebra $A = C(J_R)$ of continuous functions on the Julia set $J_R$ of $R$. The algebra ${\\mathcal O}_R$ is a certain analog of the crossed product by a boundary action. We show that if the degree of $R$ is at least two, then $C^*$-algebra ${\\mathcal O}_R$ is simple and purely infinite. For example if $R(z) = z^2 - 2$, then the Julia set $J_R = [-2,2]$ and the restriction $R : J_R","authors_text":"Tsuyoshi Kajiwara, Yasuo Watatani","cross_cats":["math.DS"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2003-09-18T00:31:51Z","title":"C^*-algebras associated with complex dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309293","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:b4952b1edcad462eb7fcb5e96eb2e13f8012c9c2c50afb0b6586fffa7cd2e184","target":"record","created_at":"2026-07-04T14:37:43Z","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":"1d709c01f43fc4358cbde3214563b1d38c87282643fcf3cf61c7577bb7b70908","cross_cats_sorted":["math.DS"],"license":"","primary_cat":"math.OA","submitted_at":"2003-09-18T00:31:51Z","title_canon_sha256":"c1a45a980e2d1a9942e327a7e30cff8d75de3722bc4812b1d62125f7f72bec03"},"schema_version":"1.0","source":{"id":"math/0309293","kind":"arxiv","version":1}},"canonical_sha256":"8cbdc75b962c15c200f2a66d91c844a509d1f3075fa260d8d4e29c355fd7c0d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cbdc75b962c15c200f2a66d91c844a509d1f3075fa260d8d4e29c355fd7c0d7","first_computed_at":"2026-07-04T14:37:43.922697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:37:43.922697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p+ItPAHX41xW+QhA0+YhMkee6ffOQyR61aDl0mWiH6/5NVPcdPYE3i7AXaPxna0kK5jTtjkjdo0taU5c8UyaAA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:37:43.923087Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0309293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4952b1edcad462eb7fcb5e96eb2e13f8012c9c2c50afb0b6586fffa7cd2e184","sha256:2490e4911f91b9340dedc89dbbc9c299a0fa7ae8d0276bf4eefa821cde39b377"],"state_sha256":"bdc3b3d3c8946720511a07ec80c2f3d806e7d5d11aacf0689c758d3edc5e59f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5KPkRCvywcdDIRb4SlyLFrJZZ3QYTeJtWATcv0eSCrWmJqkGHfSeDyfiQefWOGfgzE0BNCuR5u534WmiKdalDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T07:22:31.284201Z","bundle_sha256":"937605806c11b1757479a7a4d36d0b852826019e8b0bb1efe9aa981704449468"}}