{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:W7IGO63P4GWZ4FSJGM6T7Z3H67","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":"2464bbc0ad9d1d8e7e6818d8c435fa3f33c82a1e7b207388d1fa7df4a1b3b1fe","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-04-07T15:23:26Z","title_canon_sha256":"89181eaed18084328e23dd7e08d7e28f3cc51791768218d63ac78e92ba2e5f1a"},"schema_version":"1.0","source":{"id":"0904.1164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.1164","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"arxiv_version","alias_value":"0904.1164v1","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1164","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"pith_short_12","alias_value":"W7IGO63P4GWZ","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"pith_short_16","alias_value":"W7IGO63P4GWZ4FSJ","created_at":"2026-07-04T15:40:45Z"},{"alias_kind":"pith_short_8","alias_value":"W7IGO63P","created_at":"2026-07-04T15:40:45Z"}],"graph_snapshots":[{"event_id":"sha256:0334ddc1337e9439b3cae9270ec543c554d6e76c3057ce7c0595a66100aaffba","target":"graph","created_at":"2026-07-04T15:40:45Z","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/0904.1164/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $(X, \\{w_j \\}_{j=1}^m, \\{p_j \\}_{j=1}^m)$ ($2 \\leq m < \\infty$) be a contractive iterated function system (IFS), where $X$ is a compact subset of ${\\Bbb{R}}^d$. It is well known that there exists a unique nonempty compact set $K$ such that $K=\\bigcup_{j=1}^m w_j(K)$. Moreover, the Ruelle operator on $C(K)$ determined by the IFS $(X, \\{w_j \\}_{j=1}^m, \\{p_j \\}_{j=1}^m)$ ($2 \\leq m < \\infty$) has been introduced in \\cite{FL}. In the present paper, the Ruelle operators determined by the infinite conformal IFSs are discussed. Some separation properties for the infinite conformal IFSs are inves","authors_text":"Li-Yan Wu, Xiao-Peng Chen, Yuan-Ling Ye","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-04-07T15:23:26Z","title":"Ruelle Operator for Infinite Conformal IFS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1164","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:b2fabf870ce2823f8e2d831a1b697b7186ed1e940a1902e5fca6080470cae4ed","target":"record","created_at":"2026-07-04T15:40:45Z","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":"2464bbc0ad9d1d8e7e6818d8c435fa3f33c82a1e7b207388d1fa7df4a1b3b1fe","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-04-07T15:23:26Z","title_canon_sha256":"89181eaed18084328e23dd7e08d7e28f3cc51791768218d63ac78e92ba2e5f1a"},"schema_version":"1.0","source":{"id":"0904.1164","kind":"arxiv","version":1}},"canonical_sha256":"b7d0677b6fe1ad9e1649333d3fe767f7ca4eba1ff33cd263c724c65c4489216a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7d0677b6fe1ad9e1649333d3fe767f7ca4eba1ff33cd263c724c65c4489216a","first_computed_at":"2026-07-04T15:40:45.423071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:40:45.423071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0bqinXa+6ZTfsdI+gogTq+0OZB/xL3E1Wm9jZCS0uVbcbLcM1GolRwUBj2nCBEsggkl1DAXMDXP7brjnbSZ9DQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:40:45.423486Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.1164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2fabf870ce2823f8e2d831a1b697b7186ed1e940a1902e5fca6080470cae4ed","sha256:0334ddc1337e9439b3cae9270ec543c554d6e76c3057ce7c0595a66100aaffba"],"state_sha256":"3e7b8ac171d3345bbe0c4c42bd960be3dc1d8de9ba0a5b482996cea02490ded3"}