{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OCRPOCTOOA5WBDIVTHIKBWG2HV","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":"b559350480879443c995ddc3bd2ba30acaa25003db99a14a5f6836a9af635109","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-21T01:12:16Z","title_canon_sha256":"9b7d3d86d38661599268e568749a3169d191c070bc774f6529d0372a819c0fe4"},"schema_version":"1.0","source":{"id":"1607.06165","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06165","created_at":"2026-05-18T00:54:57Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06165v2","created_at":"2026-05-18T00:54:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06165","created_at":"2026-05-18T00:54:57Z"},{"alias_kind":"pith_short_12","alias_value":"OCRPOCTOOA5W","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OCRPOCTOOA5WBDIV","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OCRPOCTO","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:6b884f4683a6d45d32093d8a1f25f994868a9d8ae2d7cd38d421f40f87d30a2d","target":"graph","created_at":"2026-05-18T00:54:57Z","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":"In this paper we will consider the concept of $\\mathbb{P}$-weakly hyperbolic iterated function systems on compact metric spaces that generalizes the concept of weakly hyperbolic iterated function systems, as defined by Edalat in \\cite{E} and by Arbieto, Santiago and Junqueira in \\cite{ASJ} for a more general setting where the parameter space is a compact metric space. We prove the existence and uniqueness of the invariant measure of a $\\mathbb{P}$-weakly hyperbolic IFS. Furthermore, we prove an ergodic theorem for $\\mathbb{P}$-weakly hyperbolic IFS with compact parameter space.","authors_text":"\\'Italo Melo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-21T01:12:16Z","title":"On $\\mathbb{P}$-Weakly Hyperbolic Iterated Function Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06165","kind":"arxiv","version":2},"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":"sha256:050f68dd4358cfcdfe89ba09193274f6b943558723350435c253b9fefc4e1ff7","target":"record","created_at":"2026-05-18T00:54:57Z","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":"b559350480879443c995ddc3bd2ba30acaa25003db99a14a5f6836a9af635109","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-21T01:12:16Z","title_canon_sha256":"9b7d3d86d38661599268e568749a3169d191c070bc774f6529d0372a819c0fe4"},"schema_version":"1.0","source":{"id":"1607.06165","kind":"arxiv","version":2}},"canonical_sha256":"70a2f70a6e703b608d1599d0a0d8da3d49faa7640f6171e92ef8bee3b1a6acfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70a2f70a6e703b608d1599d0a0d8da3d49faa7640f6171e92ef8bee3b1a6acfb","first_computed_at":"2026-05-18T00:54:57.880869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:57.880869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2eSuL0qdL/bxwFnWl7r6EEXpu+CePeHcxJ9STE6DiUANVNTq5iOaOhoOfYyOfucttEK0Pa9+BVX4hu/7NPVECA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:57.881361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06165","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:050f68dd4358cfcdfe89ba09193274f6b943558723350435c253b9fefc4e1ff7","sha256:6b884f4683a6d45d32093d8a1f25f994868a9d8ae2d7cd38d421f40f87d30a2d"],"state_sha256":"9aa868c07692a3f3abb4eb82b8a01338b573f9a23a88970622859e825f7df315"}