{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CWFUHGGUA4TQJVPV22VPH2I7YJ","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":"f5e6ce145fdbd8b226fae02ad311fd5e0ae406c134542f77a450de51887f08db","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-05-25T09:33:07Z","title_canon_sha256":"26d93961a864f9c2e4a0bd0e11ea6a1a22011bd51a387ae41ae0e8bb485736e0"},"schema_version":"1.0","source":{"id":"2605.25633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25633","created_at":"2026-05-26T02:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25633v1","created_at":"2026-05-26T02:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25633","created_at":"2026-05-26T02:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"CWFUHGGUA4TQ","created_at":"2026-05-26T02:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"CWFUHGGUA4TQJVPV","created_at":"2026-05-26T02:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"CWFUHGGU","created_at":"2026-05-26T02:04:47Z"}],"graph_snapshots":[{"event_id":"sha256:efccedbfea15b4084fbcc340d22da660c37438dfd3407bc549f4540726098c53","target":"graph","created_at":"2026-05-26T02:04:47Z","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/2605.25633/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The importance of functional data analysis has increased substantially in recent years. In machine learning, nonlinear function regression based on deep neural networks is referred to as operator learning, and many of its applications involve functional time series data. However, the theoretical understanding of nonlinear models in functional time series analysis remains limited, as most existing works focus on linear models. In this paper, we derive basic properties for analyzing adaptive learning in nonlinear functional autoregressive (NFAR) models. Specifically, we derive sufficient conditi","authors_text":"Shuntarou Suzuki, Yoshikazu Terada","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-05-25T09:33:07Z","title":"Exponential mixing properties of nonlinear functional autoregressive models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25633","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":"sha256:197cbba0d31a2f3f1ff736afbb15c3674e803737f6eb57b95b289febc56bf468","target":"record","created_at":"2026-05-26T02:04:47Z","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":"f5e6ce145fdbd8b226fae02ad311fd5e0ae406c134542f77a450de51887f08db","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-05-25T09:33:07Z","title_canon_sha256":"26d93961a864f9c2e4a0bd0e11ea6a1a22011bd51a387ae41ae0e8bb485736e0"},"schema_version":"1.0","source":{"id":"2605.25633","kind":"arxiv","version":1}},"canonical_sha256":"158b4398d4072704d5f5d6aaf3e91fc25370232208bf3cceb485be01845bd5f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"158b4398d4072704d5f5d6aaf3e91fc25370232208bf3cceb485be01845bd5f3","first_computed_at":"2026-05-26T02:04:47.369879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:47.369879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s2xOyCr849MPY68QXL7NUGb6LImooEPkLep91GtTlybJuGw0XrR3Q+rEujqiJ/Ck9+Q+BYcBeu4esL85d6qJCA==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:47.370478Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:197cbba0d31a2f3f1ff736afbb15c3674e803737f6eb57b95b289febc56bf468","sha256:efccedbfea15b4084fbcc340d22da660c37438dfd3407bc549f4540726098c53"],"state_sha256":"0273dfb82f4dccc5e9b2751cabc6abf2a6d017afb9a346099d3818698b010ac9"}