{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:RN5QCZU756NKV4MVMJCPCQKQS7","short_pith_number":"pith:RN5QCZU7","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"},"canonical_sha256":"8b7b01669fef9aaaf1956244f1415097f93a693fa7019abb10c9d05a69cd4522","source":{"kind":"arxiv","id":"2508.07876","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.07876","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2508.07876v2","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07876","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"RN5QCZU756NK","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"RN5QCZU756NKV4MV","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"RN5QCZU7","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:RN5QCZU756NKV4MVMJCPCQKQS7","target":"record","payload":{"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"},"canonical_sha256":"8b7b01669fef9aaaf1956244f1415097f93a693fa7019abb10c9d05a69cd4522","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"},"source_kind":"arxiv","source_id":"2508.07876","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0GCdIWCg5acaLRetx6U4c230Rt8S1oFG0/zOMRFdYLskE7kHhalW7o6RB95b78BEeqOaWgapp2/n6uCByKx4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T14:55:42.904090Z"},"content_sha256":"1ff8a90115f870e0853992842d2c5d876e0a4bea8e725668d435e30fff5e8bcd","schema_version":"1.0","event_id":"sha256:1ff8a90115f870e0853992842d2c5d876e0a4bea8e725668d435e30fff5e8bcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:RN5QCZU756NKV4MVMJCPCQKQS7","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ds+0UCaF9FCukAek2y9oCAkpyNIfeOq1Kxd1uNFCKHsSPztexRBGAX1IP8/Gh0GZ7RbAn4W7GUJfHiFRQy1FAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T14:55:42.904743Z"},"content_sha256":"553471046266c5e1f2216e01580fd16db6e4a87966b1c021f136bbfdae98f780","schema_version":"1.0","event_id":"sha256:553471046266c5e1f2216e01580fd16db6e4a87966b1c021f136bbfdae98f780"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7/bundle.json","state_url":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RN5QCZU756NKV4MVMJCPCQKQS7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-21T14:55:42Z","links":{"resolver":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7","bundle":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7/bundle.json","state":"https://pith.science/pith/RN5QCZU756NKV4MVMJCPCQKQS7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RN5QCZU756NKV4MVMJCPCQKQS7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RN5QCZU756NKV4MVMJCPCQKQS7","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":"f1a3fdd2cf26ffc1e9196638d2915e7f4c67940f030a661a916af75a799dd1ee","cross_cats_sorted":["cs.LG","math.DS","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-08-11T11:49:01Z","title_canon_sha256":"10d314585b63db1b1e65985d4b1faedfd2796827735672d7d980fcb679fa5a54"},"schema_version":"1.0","source":{"id":"2508.07876","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.07876","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2508.07876v2","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07876","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"RN5QCZU756NK","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"RN5QCZU756NKV4MV","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"RN5QCZU7","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:553471046266c5e1f2216e01580fd16db6e4a87966b1c021f136bbfdae98f780","target":"graph","created_at":"2026-05-17T23:39:17Z","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":"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","authors_text":"Florian Rossmannek, Juan-Pablo Ortega","cross_cats":["cs.LG","math.DS","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-08-11T11:49:01Z","title":"Stochastic dynamics learning with state-space systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07876","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":"sha256:1ff8a90115f870e0853992842d2c5d876e0a4bea8e725668d435e30fff5e8bcd","target":"record","created_at":"2026-05-17T23:39:17Z","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":"f1a3fdd2cf26ffc1e9196638d2915e7f4c67940f030a661a916af75a799dd1ee","cross_cats_sorted":["cs.LG","math.DS","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-08-11T11:49:01Z","title_canon_sha256":"10d314585b63db1b1e65985d4b1faedfd2796827735672d7d980fcb679fa5a54"},"schema_version":"1.0","source":{"id":"2508.07876","kind":"arxiv","version":2}},"canonical_sha256":"8b7b01669fef9aaaf1956244f1415097f93a693fa7019abb10c9d05a69cd4522","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b7b01669fef9aaaf1956244f1415097f93a693fa7019abb10c9d05a69cd4522","first_computed_at":"2026-05-17T23:39:17.739662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:17.739662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"43e83pVV4WBGr1VnK9q0oSGBEKxu4x+6r5x4gVRrcZeP+Thh4qD64DDE8qy9G8R0G36St0JHdL9fSoUQV0WlCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:17.740347Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.07876","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ff8a90115f870e0853992842d2c5d876e0a4bea8e725668d435e30fff5e8bcd","sha256:553471046266c5e1f2216e01580fd16db6e4a87966b1c021f136bbfdae98f780"],"state_sha256":"01a8aad7c5a18e667118ef21a00f11998474b42209cab3516608efedc5da2776"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FxJVWuHuVpbA5AS443f2lE00ldVnua2jZbTGQi8yUt4rkSFAOOf1AGeoZJAbOTxt7XNW9I+s7233tyAjDqnYAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T14:55:42.908658Z","bundle_sha256":"49cf1ebfd954a55dcd17dc530caf6ac9f0fb5b13821046e4da713593cfa6f7ba"}}