{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KJ6C42OLOXP2AYWK6FTDLQBRRF","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":"05422f3b0d1f03cea1d8bad1806ba6a8bfaba5b710be847a23fb470365b0308f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-06T07:33:46Z","title_canon_sha256":"f108285d068ebba4038bb3c3a0588a62567b7194cf28c3edb472d33e34e95ab6"},"schema_version":"1.0","source":{"id":"1606.01644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01644","created_at":"2026-05-18T00:14:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01644v1","created_at":"2026-05-18T00:14:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01644","created_at":"2026-05-18T00:14:41Z"},{"alias_kind":"pith_short_12","alias_value":"KJ6C42OLOXP2","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KJ6C42OLOXP2AYWK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KJ6C42OL","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:4f32b3bd5c03d25b81d7937280abb1926e3a212a3010a5039421cad89391a050","target":"graph","created_at":"2026-05-18T00:14:41Z","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 study the real, bounded-variables process (X_n) defined by a k-term recurrence relation X_{n+k} ={\\phi}(X_n, ... , X_{n+k-1}). We prove the decay of correlations, mainly under purely analytic hypotheses concerning the function {\\phi} and its partial derivatives.","authors_text":"Alain Ninet, Jules Maes, Lisette Jager","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-06T07:33:46Z","title":"Exponential decay of correlations for a real-valued dynamical system generated by a k dimensional system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01644","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:c31d1514eb529d87a7fe35d57c8e64ac7a5bb6dd97f6539c7e17425c0872dd88","target":"record","created_at":"2026-05-18T00:14:41Z","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":"05422f3b0d1f03cea1d8bad1806ba6a8bfaba5b710be847a23fb470365b0308f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-06T07:33:46Z","title_canon_sha256":"f108285d068ebba4038bb3c3a0588a62567b7194cf28c3edb472d33e34e95ab6"},"schema_version":"1.0","source":{"id":"1606.01644","kind":"arxiv","version":1}},"canonical_sha256":"527c2e69cb75dfa062caf16635c031894a05a29466a74c66f770bbe80b9a3f78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"527c2e69cb75dfa062caf16635c031894a05a29466a74c66f770bbe80b9a3f78","first_computed_at":"2026-05-18T00:14:41.527830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:41.527830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7AWqpHYumITmD1RB8FK7ZtwOOqAq1VdwDGzLSIaz4waEs5EzQkJdLoO9xR90GqmtP9ANX/jmbXmVmBJk8LZ9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:41.528448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c31d1514eb529d87a7fe35d57c8e64ac7a5bb6dd97f6539c7e17425c0872dd88","sha256:4f32b3bd5c03d25b81d7937280abb1926e3a212a3010a5039421cad89391a050"],"state_sha256":"99593d1226ad94f7c63ae7aab36d98f98a7705abf5b41d29e05eec1bb007fa5e"}