{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:RN5QCZU756NKV4MVMJCPCQKQS7","short_pith_number":"pith:RN5QCZU7","schema_version":"1.0","canonical_sha256":"8b7b01669fef9aaaf1956244f1415097f93a693fa7019abb10c9d05a69cd4522","source":{"kind":"arxiv","id":"2508.07876","version":2},"attestation_state":"computed","paper":{"title":"Stochastic dynamics learning with state-space systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.DS","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Florian Rossmannek, Juan-Pablo Ortega","submitted_at":"2025-08-11T11:49:01Z","abstract_excerpt":"This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space systems, a central model class in time series learning, and establish that fading memory and solution stability hold generically -- even in the absence of the ESP -- offering a robust explanation for the empirical success of RC models without strict contractivity conditions. In the stochastic case, we critically assess stochastic echo states, proposing a novel dist"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2508.07876","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-08-11T11:49:01Z","cross_cats_sorted":["cs.LG","math.DS","math.ST","stat.TH"],"title_canon_sha256":"10d314585b63db1b1e65985d4b1faedfd2796827735672d7d980fcb679fa5a54","abstract_canon_sha256":"f1a3fdd2cf26ffc1e9196638d2915e7f4c67940f030a661a916af75a799dd1ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:17.740347Z","signature_b64":"43e83pVV4WBGr1VnK9q0oSGBEKxu4x+6r5x4gVRrcZeP+Thh4qD64DDE8qy9G8R0G36St0JHdL9fSoUQV0WlCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b7b01669fef9aaaf1956244f1415097f93a693fa7019abb10c9d05a69cd4522","last_reissued_at":"2026-05-17T23:39:17.739662Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:17.739662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic dynamics learning with state-space systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.DS","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Florian Rossmannek, Juan-Pablo Ortega","submitted_at":"2025-08-11T11:49:01Z","abstract_excerpt":"This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space systems, a central model class in time series learning, and establish that fading memory and solution stability hold generically -- even in the absence of the ESP -- offering a robust explanation for the empirical success of RC models without strict contractivity conditions. In the stochastic case, we critically assess stochastic echo states, proposing a novel dist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07876","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2508.07876","created_at":"2026-05-17T23:39:17.739751+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.07876v2","created_at":"2026-05-17T23:39:17.739751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07876","created_at":"2026-05-17T23:39:17.739751+00:00"},{"alias_kind":"pith_short_12","alias_value":"RN5QCZU756NK","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"RN5QCZU756NKV4MV","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"RN5QCZU7","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2508.19145","citing_title":"Echoes of the Past: A Unified Perspective on Fading memory and Echo States","ref_index":29,"is_internal_anchor":true},{"citing_arxiv_id":"2512.15530","citing_title":"Learning the climate of dynamical systems with state-space systems","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7","json":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7.json","graph_json":"https://pith.science/api/pith-number/RN5QCZU756NKV4MVMJCPCQKQS7/graph.json","events_json":"https://pith.science/api/pith-number/RN5QCZU756NKV4MVMJCPCQKQS7/events.json","paper":"https://pith.science/paper/RN5QCZU7"},"agent_actions":{"view_html":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7","download_json":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7.json","view_paper":"https://pith.science/paper/RN5QCZU7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.07876&json=true","fetch_graph":"https://pith.science/api/pith-number/RN5QCZU756NKV4MVMJCPCQKQS7/graph.json","fetch_events":"https://pith.science/api/pith-number/RN5QCZU756NKV4MVMJCPCQKQS7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7/action/storage_attestation","attest_author":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7/action/author_attestation","sign_citation":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7/action/citation_signature","submit_replication":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7/action/replication_record"}},"created_at":"2026-05-17T23:39:17.739751+00:00","updated_at":"2026-05-17T23:39:17.739751+00:00"}