{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B5J65QARFPS6RDJ4KT7R6HPZGW","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":"b3e1eaaec2fdded1e2e785ab0167b39c16e3e1415ec12a32e54d8b6ed7a07386","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-03T10:02:18Z","title_canon_sha256":"d79e944bc857c6e25281dd8fead99453addacc836113886770ef28fffa30a6f3"},"schema_version":"1.0","source":{"id":"1403.0361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0361","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0361v1","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0361","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"B5J65QARFPS6","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B5J65QARFPS6RDJ4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B5J65QAR","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:d22f3e070bae1a7cd1482a23ebd3319a70a704f72238267b55423d6e58466db8","target":"graph","created_at":"2026-05-18T02:57:25Z","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 family of kernels for analysis of data generated by dynamical systems. These so-called cone kernels feature an explicit dependence on the dynamical vector field operating in the phase-space manifold, estimated empirically through finite-differences of time-ordered data samples. In particular, cone kernels assign strong affinity to pairs of samples whose relative displacement vector lies within a narrow cone aligned with the dynamical vector field. As a result, in a suitable asymptotic limit, the associated diffusion operator generates diffusions along the dynamical flow, and is in","authors_text":"Dimitrios Giannakis","cross_cats":["physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-03T10:02:18Z","title":"Dynamics-Adapted Cone Kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0361","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":"sha256:8c098c76a89ec822b8016c530257a2229667e34a833fdfe80304a9ae704c1138","target":"record","created_at":"2026-05-18T02:57:25Z","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":"b3e1eaaec2fdded1e2e785ab0167b39c16e3e1415ec12a32e54d8b6ed7a07386","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-03T10:02:18Z","title_canon_sha256":"d79e944bc857c6e25281dd8fead99453addacc836113886770ef28fffa30a6f3"},"schema_version":"1.0","source":{"id":"1403.0361","kind":"arxiv","version":1}},"canonical_sha256":"0f53eec0112be5e88d3c54ff1f1df9359834880cb7744463862bb4aae2943f66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f53eec0112be5e88d3c54ff1f1df9359834880cb7744463862bb4aae2943f66","first_computed_at":"2026-05-18T02:57:25.090256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:25.090256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"815xIbGL8WZWsAKQUNyfxI0HLuo7XiHgrBsiSVuoK9elrDQZru/qyjOhlaR8kUUtUdRIQCjxYldLg2oTDV6CCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:25.090773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c098c76a89ec822b8016c530257a2229667e34a833fdfe80304a9ae704c1138","sha256:d22f3e070bae1a7cd1482a23ebd3319a70a704f72238267b55423d6e58466db8"],"state_sha256":"e9bd073a4c619c8b054e2765c191118b65ae574c58b3cb10bc56c024b196afe6"}