{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RXYBGISRUDNPSFTSGXDM5QXETN","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":"13839855173966c541f6ae485a02bfb2a90868770f8e9b44c2c6e2e1a464829b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2016-12-26T18:43:23Z","title_canon_sha256":"36ec544c3b935ace4843fe532624d59463f5f2edc1f7cdba978bdf263e5b7836"},"schema_version":"1.0","source":{"id":"1612.08423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08423","created_at":"2026-05-18T00:36:32Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08423v1","created_at":"2026-05-18T00:36:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08423","created_at":"2026-05-18T00:36:32Z"},{"alias_kind":"pith_short_12","alias_value":"RXYBGISRUDNP","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RXYBGISRUDNPSFTS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RXYBGISR","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:a8d86ba8460926ccb4e71adb8a8067208c3f6942137066bbd91be5ae3cbaebc7","target":"graph","created_at":"2026-05-18T00:36:32Z","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":"Most approximations for stochastic differential equations with high-dimensional, non-Gaussian inputs suffer from a rapid (e.g., exponential) increase of computational cost, an issue known as the curse of dimensionality. In astrodynamics, this results in reduced accuracy when propagating an orbit-state probability density function. This paper considers the application of separated representations for orbit uncertainty propagation, where future states are expanded into a sum of products of univariate functions of initial states and other uncertain parameters. An accurate generation of separated ","authors_text":"Alireza Doostan, Brandon Jones, Marc Balducci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2016-12-26T18:43:23Z","title":"Orbit Uncertainty Propagation and Sensitivity Analysis With Separated Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08423","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":"sha256:4da29ddd427d288f51f59be4883c0f78ee501a9c3431ca68274303c3abd8c820","target":"record","created_at":"2026-05-18T00:36:32Z","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":"13839855173966c541f6ae485a02bfb2a90868770f8e9b44c2c6e2e1a464829b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2016-12-26T18:43:23Z","title_canon_sha256":"36ec544c3b935ace4843fe532624d59463f5f2edc1f7cdba978bdf263e5b7836"},"schema_version":"1.0","source":{"id":"1612.08423","kind":"arxiv","version":1}},"canonical_sha256":"8df0132251a0daf9167235c6cec2e49b66d966b7a3fdf6584cc8c26e11df71d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8df0132251a0daf9167235c6cec2e49b66d966b7a3fdf6584cc8c26e11df71d5","first_computed_at":"2026-05-18T00:36:32.791557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:32.791557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rd2eiuQQ8kVm7VKbGORH4gsww9QhHLt9ZxT/VHFuM4ISCa0Q4dCO8m6LAqDZ3trTCX0XkdrZ4LL9UJwVoBAIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:32.792000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.08423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4da29ddd427d288f51f59be4883c0f78ee501a9c3431ca68274303c3abd8c820","sha256:a8d86ba8460926ccb4e71adb8a8067208c3f6942137066bbd91be5ae3cbaebc7"],"state_sha256":"89add95e7c9ff7e90108f592dfdfc7b4d2df202a91117df0a075813bba8db30d"}