{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:O34EFEUEOUS7S7RI5U2VTFVI4K","short_pith_number":"pith:O34EFEUE","canonical_record":{"source":{"id":"2501.13329","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-23T02:18:13Z","cross_cats_sorted":["cs.AI","math.DS"],"title_canon_sha256":"0bf702f289de4f9b8502f34c4fb7bd5a343cf426d3593de3682379102f010dd8","abstract_canon_sha256":"d3621d8fbf25c5ddcddbe3cb31db8ec5279698d0a30a4941972ef04bc5ed5a40"},"schema_version":"1.0"},"canonical_sha256":"76f84292847525f97e28ed355996a8e2948891f625b1016b1bc317b834e69854","source":{"kind":"arxiv","id":"2501.13329","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13329","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13329v2","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13329","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"O34EFEUEOUS7","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"pith_short_16","alias_value":"O34EFEUEOUS7S7RI","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"pith_short_8","alias_value":"O34EFEUE","created_at":"2026-07-05T10:42:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:O34EFEUEOUS7S7RI5U2VTFVI4K","target":"record","payload":{"canonical_record":{"source":{"id":"2501.13329","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-23T02:18:13Z","cross_cats_sorted":["cs.AI","math.DS"],"title_canon_sha256":"0bf702f289de4f9b8502f34c4fb7bd5a343cf426d3593de3682379102f010dd8","abstract_canon_sha256":"d3621d8fbf25c5ddcddbe3cb31db8ec5279698d0a30a4941972ef04bc5ed5a40"},"schema_version":"1.0"},"canonical_sha256":"76f84292847525f97e28ed355996a8e2948891f625b1016b1bc317b834e69854","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:42:14.667444Z","signature_b64":"DRX28PYcNWSAv8qd0pfsCqLtIWL10/zeBB1W0lKfzoe/jzH1qOa5kzP655u/V8hl+9h3RMJdKFsp2ZkOgdy5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76f84292847525f97e28ed355996a8e2948891f625b1016b1bc317b834e69854","last_reissued_at":"2026-07-05T10:42:14.666894Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:42:14.666894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.13329","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":"2026-07-05T10:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wz1IwCezKFB+WqqGc5fK08Zykx9LlTWT2nBQPBaXhqlX+CVTaBqVj6iO8FrdrEidXSLtt3NFHypoe51byrE5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:42:57.687950Z"},"content_sha256":"1a83c5c106e2c84d90c50fe5bf6acb27eb2a266f8da282ef2eadb5b485b5d09e","schema_version":"1.0","event_id":"sha256:1a83c5c106e2c84d90c50fe5bf6acb27eb2a266f8da282ef2eadb5b485b5d09e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:O34EFEUEOUS7S7RI5U2VTFVI4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.DS"],"primary_cat":"cs.LG","authors_text":"Jan P. Williams, J. Nathan Kutz, Mars Liyao Gao","submitted_at":"2025-01-23T02:18:13Z","abstract_excerpt":"Modeling real-world spatio-temporal data is exceptionally difficult due to inherent high dimensionality, measurement noise, partial observations, and often expensive data collection procedures. In this paper, we present Sparse Identification of Nonlinear Dynamics with SHallow REcurrent Decoder networks (SINDy-SHRED), a method to jointly solve the sensing and model identification problems with simple implementation, efficient computation, and robust performance. SINDy-SHRED uses Gated Recurrent Units to model the temporal sequence of sparse sensor measurements along with a shallow decoder netwo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13329","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.13329/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d1RWPpVuteTMxmG8AcGGgZ9jUWMPdclte5w/N+VHDbDO2eqPHHTv/SfQfcYafmMcPncU9Vh+PwBjz5cdkt+NDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:42:57.688456Z"},"content_sha256":"bfbd3e99d5cf6a835971691863728282602ae7438cb0af7a6674580df53c7b7c","schema_version":"1.0","event_id":"sha256:bfbd3e99d5cf6a835971691863728282602ae7438cb0af7a6674580df53c7b7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O34EFEUEOUS7S7RI5U2VTFVI4K/bundle.json","state_url":"https://pith.science/pith/O34EFEUEOUS7S7RI5U2VTFVI4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O34EFEUEOUS7S7RI5U2VTFVI4K/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":"2026-08-08T17:42:57Z","links":{"resolver":"https://pith.science/pith/O34EFEUEOUS7S7RI5U2VTFVI4K","bundle":"https://pith.science/pith/O34EFEUEOUS7S7RI5U2VTFVI4K/bundle.json","state":"https://pith.science/pith/O34EFEUEOUS7S7RI5U2VTFVI4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O34EFEUEOUS7S7RI5U2VTFVI4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:O34EFEUEOUS7S7RI5U2VTFVI4K","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":"d3621d8fbf25c5ddcddbe3cb31db8ec5279698d0a30a4941972ef04bc5ed5a40","cross_cats_sorted":["cs.AI","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-23T02:18:13Z","title_canon_sha256":"0bf702f289de4f9b8502f34c4fb7bd5a343cf426d3593de3682379102f010dd8"},"schema_version":"1.0","source":{"id":"2501.13329","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13329","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13329v2","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13329","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"O34EFEUEOUS7","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"pith_short_16","alias_value":"O34EFEUEOUS7S7RI","created_at":"2026-07-05T10:42:14Z"},{"alias_kind":"pith_short_8","alias_value":"O34EFEUE","created_at":"2026-07-05T10:42:14Z"}],"graph_snapshots":[{"event_id":"sha256:bfbd3e99d5cf6a835971691863728282602ae7438cb0af7a6674580df53c7b7c","target":"graph","created_at":"2026-07-05T10:42:14Z","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/2501.13329/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Modeling real-world spatio-temporal data is exceptionally difficult due to inherent high dimensionality, measurement noise, partial observations, and often expensive data collection procedures. In this paper, we present Sparse Identification of Nonlinear Dynamics with SHallow REcurrent Decoder networks (SINDy-SHRED), a method to jointly solve the sensing and model identification problems with simple implementation, efficient computation, and robust performance. SINDy-SHRED uses Gated Recurrent Units to model the temporal sequence of sparse sensor measurements along with a shallow decoder netwo","authors_text":"Jan P. Williams, J. Nathan Kutz, Mars Liyao Gao","cross_cats":["cs.AI","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-23T02:18:13Z","title":"Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13329","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":"sha256:1a83c5c106e2c84d90c50fe5bf6acb27eb2a266f8da282ef2eadb5b485b5d09e","target":"record","created_at":"2026-07-05T10:42:14Z","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":"d3621d8fbf25c5ddcddbe3cb31db8ec5279698d0a30a4941972ef04bc5ed5a40","cross_cats_sorted":["cs.AI","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-23T02:18:13Z","title_canon_sha256":"0bf702f289de4f9b8502f34c4fb7bd5a343cf426d3593de3682379102f010dd8"},"schema_version":"1.0","source":{"id":"2501.13329","kind":"arxiv","version":2}},"canonical_sha256":"76f84292847525f97e28ed355996a8e2948891f625b1016b1bc317b834e69854","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76f84292847525f97e28ed355996a8e2948891f625b1016b1bc317b834e69854","first_computed_at":"2026-07-05T10:42:14.666894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:42:14.666894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DRX28PYcNWSAv8qd0pfsCqLtIWL10/zeBB1W0lKfzoe/jzH1qOa5kzP655u/V8hl+9h3RMJdKFsp2ZkOgdy5AA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:42:14.667444Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13329","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a83c5c106e2c84d90c50fe5bf6acb27eb2a266f8da282ef2eadb5b485b5d09e","sha256:bfbd3e99d5cf6a835971691863728282602ae7438cb0af7a6674580df53c7b7c"],"state_sha256":"36e1771317131034224c343fbb747357fcd4385de837f9cd96c284e103668a80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QL/mi7Qxfq5bhwVK2xJesEE7zdF8orDlkpsvGkwQrEWMdZxd3W9ngCwu0j7KMXsnazNGKxqt4GpcAtQQYjnAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T17:42:57.691966Z","bundle_sha256":"8c2e6965bbe4a23e9ebc8e1b0afa5cd51f40057e97b0e4af7da5529fd3b6b49b"}}