{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:LL5VAXA2DAMEL4EOZVAIUR24DH","short_pith_number":"pith:LL5VAXA2","canonical_record":{"source":{"id":"2304.03907","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-04-08T04:23:46Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"3417235ce87156851cde5d0fe06f026847e2d465444c3149e211024126c09f7a","abstract_canon_sha256":"2a2a23c81d612ee389fabb8d6daf545e818ab4e15fc1a1eb9562eff0580989b0"},"schema_version":"1.0"},"canonical_sha256":"5afb505c1a181845f08ecd408a475c19d12ba8988030c7271ab00c6860954484","source":{"kind":"arxiv","id":"2304.03907","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.03907","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"2304.03907v6","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.03907","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"LL5VAXA2DAME","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_16","alias_value":"LL5VAXA2DAMEL4EO","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_8","alias_value":"LL5VAXA2","created_at":"2026-07-05T11:59:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:LL5VAXA2DAMEL4EOZVAIUR24DH","target":"record","payload":{"canonical_record":{"source":{"id":"2304.03907","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-04-08T04:23:46Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"3417235ce87156851cde5d0fe06f026847e2d465444c3149e211024126c09f7a","abstract_canon_sha256":"2a2a23c81d612ee389fabb8d6daf545e818ab4e15fc1a1eb9562eff0580989b0"},"schema_version":"1.0"},"canonical_sha256":"5afb505c1a181845f08ecd408a475c19d12ba8988030c7271ab00c6860954484","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:59:02.921600Z","signature_b64":"Zo9C6ip1v0XpjaKMnYRfYJ4BKJVm8kFrp4iKpkVsxgbZ3h48lYTnnnLjD6UnyM9s7bRa1j7Qi04mHQnqmRKtBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5afb505c1a181845f08ecd408a475c19d12ba8988030c7271ab00c6860954484","last_reissued_at":"2026-07-05T11:59:02.921110Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:59:02.921110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.03907","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:59:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mr2D85cSvdkrCYimR9p0NvO1BkvER/1KeCrv1ppnqr3ZB6rBVR0npKgf0AQl3QnXotpAv131iAyZmyDPWaTZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T16:44:14.153734Z"},"content_sha256":"81e9485f78135309aa75db1a5428b49905a42fa8932ff8c8a5272e2db3abe79d","schema_version":"1.0","event_id":"sha256:81e9485f78135309aa75db1a5428b49905a42fa8932ff8c8a5272e2db3abe79d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:LL5VAXA2DAMEL4EOZVAIUR24DH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Bo Dai, Haitong Ma, Na Li, Tongzheng Ren, Zhaolin Ren","submitted_at":"2023-04-08T04:23:46Z","abstract_excerpt":"This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear stochastic dynamics, enabling a linear representation of the state-action value function. For practical implementation, this representation is approximated using finite-dimensional truncations, specifically via two prominent kernel approximation methods: random feature truncation and Nystrom approximation. To characterize the effectiveness of these approximations, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.03907","kind":"arxiv","version":6},"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/2304.03907/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":"2026-07-05T11:59:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uovTrg8ZSeHAtzb62PwJ9TugaGt3B+VUjJ4IYG/HS/ocxJsWBRWyirI0JmWzB127A5t9wy29AV5jd17Hg8JMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T16:44:14.154238Z"},"content_sha256":"00ca4ca5773a7ec023d43adeee7c9bc2e35a7a55ebdd9c759584dcd18fb0b858","schema_version":"1.0","event_id":"sha256:00ca4ca5773a7ec023d43adeee7c9bc2e35a7a55ebdd9c759584dcd18fb0b858"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LL5VAXA2DAMEL4EOZVAIUR24DH/bundle.json","state_url":"https://pith.science/pith/LL5VAXA2DAMEL4EOZVAIUR24DH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LL5VAXA2DAMEL4EOZVAIUR24DH/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":"2026-08-05T16:44:14Z","links":{"resolver":"https://pith.science/pith/LL5VAXA2DAMEL4EOZVAIUR24DH","bundle":"https://pith.science/pith/LL5VAXA2DAMEL4EOZVAIUR24DH/bundle.json","state":"https://pith.science/pith/LL5VAXA2DAMEL4EOZVAIUR24DH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LL5VAXA2DAMEL4EOZVAIUR24DH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LL5VAXA2DAMEL4EOZVAIUR24DH","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":"2a2a23c81d612ee389fabb8d6daf545e818ab4e15fc1a1eb9562eff0580989b0","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-04-08T04:23:46Z","title_canon_sha256":"3417235ce87156851cde5d0fe06f026847e2d465444c3149e211024126c09f7a"},"schema_version":"1.0","source":{"id":"2304.03907","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.03907","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"2304.03907v6","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.03907","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"LL5VAXA2DAME","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_16","alias_value":"LL5VAXA2DAMEL4EO","created_at":"2026-07-05T11:59:02Z"},{"alias_kind":"pith_short_8","alias_value":"LL5VAXA2","created_at":"2026-07-05T11:59:02Z"}],"graph_snapshots":[{"event_id":"sha256:00ca4ca5773a7ec023d43adeee7c9bc2e35a7a55ebdd9c759584dcd18fb0b858","target":"graph","created_at":"2026-07-05T11:59:02Z","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/2304.03907/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear stochastic dynamics, enabling a linear representation of the state-action value function. For practical implementation, this representation is approximated using finite-dimensional truncations, specifically via two prominent kernel approximation methods: random feature truncation and Nystrom approximation. To characterize the effectiveness of these approximations, we","authors_text":"Bo Dai, Haitong Ma, Na Li, Tongzheng Ren, Zhaolin Ren","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-04-08T04:23:46Z","title":"Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.03907","kind":"arxiv","version":6},"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":"sha256:81e9485f78135309aa75db1a5428b49905a42fa8932ff8c8a5272e2db3abe79d","target":"record","created_at":"2026-07-05T11:59:02Z","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":"2a2a23c81d612ee389fabb8d6daf545e818ab4e15fc1a1eb9562eff0580989b0","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-04-08T04:23:46Z","title_canon_sha256":"3417235ce87156851cde5d0fe06f026847e2d465444c3149e211024126c09f7a"},"schema_version":"1.0","source":{"id":"2304.03907","kind":"arxiv","version":6}},"canonical_sha256":"5afb505c1a181845f08ecd408a475c19d12ba8988030c7271ab00c6860954484","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5afb505c1a181845f08ecd408a475c19d12ba8988030c7271ab00c6860954484","first_computed_at":"2026-07-05T11:59:02.921110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:59:02.921110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zo9C6ip1v0XpjaKMnYRfYJ4BKJVm8kFrp4iKpkVsxgbZ3h48lYTnnnLjD6UnyM9s7bRa1j7Qi04mHQnqmRKtBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:59:02.921600Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.03907","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81e9485f78135309aa75db1a5428b49905a42fa8932ff8c8a5272e2db3abe79d","sha256:00ca4ca5773a7ec023d43adeee7c9bc2e35a7a55ebdd9c759584dcd18fb0b858"],"state_sha256":"9f1dfba8c8e5c9bc0d047dd750400b52ab1cd335f281c3bcd1189054459adbcf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3Rl39ceJjti9KenYXdBwhkplYfFe++PjCcW0cESGqVQSReoy5vjNneBL21oFbvKwMTv1MJY92kHJYyEW/+wAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T16:44:14.158167Z","bundle_sha256":"8014176cc930bab838ad2b1b20fc84616dfb858302f10e17f73e7cda05986fa3"}}