{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VET53B2R7E6IK6R7IFEL7VMHFY","short_pith_number":"pith:VET53B2R","canonical_record":{"source":{"id":"2503.01077","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-03T00:40:53Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"35bcb5beb4ebe50b4755836bfce88a0a3f26a79f26af73d36713914dd77d4731","abstract_canon_sha256":"e5e3c80d70575b921b37337bd89d8787a48aaaa888a5f3a9b3a6bf8e61d12879"},"schema_version":"1.0"},"canonical_sha256":"a927dd8751f93c857a3f4148bfd5872e28ebd977d850ccc77d256794b704ca86","source":{"kind":"arxiv","id":"2503.01077","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.01077","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"arxiv_version","alias_value":"2503.01077v1","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.01077","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"pith_short_12","alias_value":"VET53B2R7E6I","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"pith_short_16","alias_value":"VET53B2R7E6IK6R7","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"pith_short_8","alias_value":"VET53B2R","created_at":"2026-07-05T10:22:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VET53B2R7E6IK6R7IFEL7VMHFY","target":"record","payload":{"canonical_record":{"source":{"id":"2503.01077","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-03T00:40:53Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"35bcb5beb4ebe50b4755836bfce88a0a3f26a79f26af73d36713914dd77d4731","abstract_canon_sha256":"e5e3c80d70575b921b37337bd89d8787a48aaaa888a5f3a9b3a6bf8e61d12879"},"schema_version":"1.0"},"canonical_sha256":"a927dd8751f93c857a3f4148bfd5872e28ebd977d850ccc77d256794b704ca86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:22:35.519655Z","signature_b64":"jRCy2C9rk1NyFtXHl58g08d4kbOm62vzX8Idp5D6R8cK0MFGoeYz98+2SJ2AR/9XFtp+RZypwdh5DMDOQDDZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a927dd8751f93c857a3f4148bfd5872e28ebd977d850ccc77d256794b704ca86","last_reissued_at":"2026-07-05T10:22:35.519140Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:22:35.519140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.01077","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:22:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qre48dgEFCpOHsFsT7OhJhWpu6MSySaqwsbF36AIQVsQ/bLbDF6VP6wzl21YdO0YMh+mO9viIDGWvgZ78ojwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T07:59:21.673923Z"},"content_sha256":"b91cc6fff512bfc1449b028d119b516d6587f1f23e889e469a582ca3ea90bd11","schema_version":"1.0","event_id":"sha256:b91cc6fff512bfc1449b028d119b516d6587f1f23e889e469a582ca3ea90bd11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VET53B2R7E6IK6R7IFEL7VMHFY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Stochastic Dynamical Systems with Structured Noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"stat.ML","authors_text":"James Greene, Ming Zhong, Ziheng Guo","submitted_at":"2025-03-03T00:40:53Z","abstract_excerpt":"Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest in learning mechanistic models from observations with stochastic noise. In this work, we present a nonparametric framework to learn both the drift and diffusion terms in systems of SDEs where the stochastic noise is singular. Specifically, inspired by second-order equations from classical physics, we consider systems which possess structured noise, i.e. nois"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.01077","kind":"arxiv","version":1},"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/2503.01077/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":"2026-07-05T10:22:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JfxclBhSyc8fJ+36lbLvm3G0z0646FVxyKiw/lXXjzVk/wZWiHv8ftgyeb0jnzgj9psOgp2dyCaAdnpP1NOFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T07:59:21.674497Z"},"content_sha256":"cb0a2887bcfc5343ff2303d10096d5a5d877d836a1ce9c2deebf0f95df361bc6","schema_version":"1.0","event_id":"sha256:cb0a2887bcfc5343ff2303d10096d5a5d877d836a1ce9c2deebf0f95df361bc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VET53B2R7E6IK6R7IFEL7VMHFY/bundle.json","state_url":"https://pith.science/pith/VET53B2R7E6IK6R7IFEL7VMHFY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VET53B2R7E6IK6R7IFEL7VMHFY/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":"2026-08-01T07:59:21Z","links":{"resolver":"https://pith.science/pith/VET53B2R7E6IK6R7IFEL7VMHFY","bundle":"https://pith.science/pith/VET53B2R7E6IK6R7IFEL7VMHFY/bundle.json","state":"https://pith.science/pith/VET53B2R7E6IK6R7IFEL7VMHFY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VET53B2R7E6IK6R7IFEL7VMHFY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VET53B2R7E6IK6R7IFEL7VMHFY","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":"e5e3c80d70575b921b37337bd89d8787a48aaaa888a5f3a9b3a6bf8e61d12879","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-03T00:40:53Z","title_canon_sha256":"35bcb5beb4ebe50b4755836bfce88a0a3f26a79f26af73d36713914dd77d4731"},"schema_version":"1.0","source":{"id":"2503.01077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.01077","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"arxiv_version","alias_value":"2503.01077v1","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.01077","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"pith_short_12","alias_value":"VET53B2R7E6I","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"pith_short_16","alias_value":"VET53B2R7E6IK6R7","created_at":"2026-07-05T10:22:35Z"},{"alias_kind":"pith_short_8","alias_value":"VET53B2R","created_at":"2026-07-05T10:22:35Z"}],"graph_snapshots":[{"event_id":"sha256:cb0a2887bcfc5343ff2303d10096d5a5d877d836a1ce9c2deebf0f95df361bc6","target":"graph","created_at":"2026-07-05T10:22:35Z","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/2503.01077/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest in learning mechanistic models from observations with stochastic noise. In this work, we present a nonparametric framework to learn both the drift and diffusion terms in systems of SDEs where the stochastic noise is singular. Specifically, inspired by second-order equations from classical physics, we consider systems which possess structured noise, i.e. nois","authors_text":"James Greene, Ming Zhong, Ziheng Guo","cross_cats":["cs.LG","cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-03T00:40:53Z","title":"Learning Stochastic Dynamical Systems with Structured Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.01077","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:b91cc6fff512bfc1449b028d119b516d6587f1f23e889e469a582ca3ea90bd11","target":"record","created_at":"2026-07-05T10:22:35Z","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":"e5e3c80d70575b921b37337bd89d8787a48aaaa888a5f3a9b3a6bf8e61d12879","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-03T00:40:53Z","title_canon_sha256":"35bcb5beb4ebe50b4755836bfce88a0a3f26a79f26af73d36713914dd77d4731"},"schema_version":"1.0","source":{"id":"2503.01077","kind":"arxiv","version":1}},"canonical_sha256":"a927dd8751f93c857a3f4148bfd5872e28ebd977d850ccc77d256794b704ca86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a927dd8751f93c857a3f4148bfd5872e28ebd977d850ccc77d256794b704ca86","first_computed_at":"2026-07-05T10:22:35.519140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:22:35.519140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jRCy2C9rk1NyFtXHl58g08d4kbOm62vzX8Idp5D6R8cK0MFGoeYz98+2SJ2AR/9XFtp+RZypwdh5DMDOQDDZDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:22:35.519655Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.01077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b91cc6fff512bfc1449b028d119b516d6587f1f23e889e469a582ca3ea90bd11","sha256:cb0a2887bcfc5343ff2303d10096d5a5d877d836a1ce9c2deebf0f95df361bc6"],"state_sha256":"aabff74a4e544f13dc6c4cdf1c496e2b0c70d55a84245351fc9e2958b246ce2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xdu6aWWO5yQa1VhKb/VbxamRFvz8Liq8OZtIIUmNuorygVDzOWtZMNi0oN0WPEuY7MeMZ03kLQxSz2PZ2PapBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T07:59:21.679841Z","bundle_sha256":"8a2c15a14d5113b6e29a74f64bab2e948f7462a207445974fee646f588544ab4"}}