{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DGKJZVR33J3LXEOQFMRN7252V3","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":"7488259cb39d10a94585acfb32efca3ae9e574e117c607066a5cc7d6591bd2a8","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2012-02-28T01:53:01Z","title_canon_sha256":"4b4b2081d0753823d99baf85596f7af564d829b5a65a539007e0bfef592114d1"},"schema_version":"1.0","source":{"id":"1202.6103","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6103","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6103v2","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6103","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"DGKJZVR33J3L","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DGKJZVR33J3LXEOQ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DGKJZVR3","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:10b8c12b36609a4874492dc5bef72bb7f9c07c264b13d5ee3dbbb275de3bd5b5","target":"graph","created_at":"2026-05-18T03:50:50Z","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":"We present a technique for spatiotemporal data analysis called nonlinear Laplacian spectral analysis (NLSA), which generalizes singular spectrum analysis (SSA) to take into account the nonlinear manifold structure of complex data sets. The key principle underlying NLSA is that the functions used to represent temporal patterns should exhibit a degree of smoothness on the nonlinear data manifold M; a constraint absent from classical SSA. NLSA enforces such a notion of smoothness by requiring that temporal patterns belong in low-dimensional Hilbert spaces V_l spanned by the leading l Laplace-Belt","authors_text":"Andrew J. Majda, Dimitrios Giannakis","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2012-02-28T01:53:01Z","title":"Nonlinear Laplacian spectral analysis: Capturing intermittent and low-frequency spatiotemporal patterns in high-dimensional data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6103","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:bec4199d2ee181b2e696a818aa0428abf4d44f3aaa2eb4288c04106179ba6f1e","target":"record","created_at":"2026-05-18T03:50:50Z","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":"7488259cb39d10a94585acfb32efca3ae9e574e117c607066a5cc7d6591bd2a8","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2012-02-28T01:53:01Z","title_canon_sha256":"4b4b2081d0753823d99baf85596f7af564d829b5a65a539007e0bfef592114d1"},"schema_version":"1.0","source":{"id":"1202.6103","kind":"arxiv","version":2}},"canonical_sha256":"19949cd63bda76bb91d02b22dfebbaaee4ac6a1152a5da0674f7b68d89796a93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19949cd63bda76bb91d02b22dfebbaaee4ac6a1152a5da0674f7b68d89796a93","first_computed_at":"2026-05-18T03:50:50.227127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:50.227127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"koUzEgXCAUUqcDU/heWsx7bbs+lZwerSQ5LTRdGgq8cNIg1rdtZKCNXDdSlyXH6/URzAbU/mLq4cujWWMb9QCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:50.227728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6103","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bec4199d2ee181b2e696a818aa0428abf4d44f3aaa2eb4288c04106179ba6f1e","sha256:10b8c12b36609a4874492dc5bef72bb7f9c07c264b13d5ee3dbbb275de3bd5b5"],"state_sha256":"e97bd00098a852303bca4d4f96165c12b53dbf44e73adaabc78bca6927031b38"}