{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CK7T6W6NYS2AGNJF6KYAC7NL57","short_pith_number":"pith:CK7T6W6N","canonical_record":{"source":{"id":"1809.07131","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-19T11:47:49Z","cross_cats_sorted":["cs.CG","math.AT"],"title_canon_sha256":"621a270e3787bb932e2c4dd2addfb956831b673ff8a54fcf5cd49af4388558f6","abstract_canon_sha256":"9380d1f19056ec35d0c482a8e1cb43554064b61e6d207a8e7656e45df5e2e155"},"schema_version":"1.0"},"canonical_sha256":"12bf3f5bcdc4b4033525f2b0017dabeffdf5cc420aeddf20f0ace6e1b1d88b70","source":{"kind":"arxiv","id":"1809.07131","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07131","created_at":"2026-05-17T23:47:02Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07131v3","created_at":"2026-05-17T23:47:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07131","created_at":"2026-05-17T23:47:02Z"},{"alias_kind":"pith_short_12","alias_value":"CK7T6W6NYS2A","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CK7T6W6NYS2AGNJF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CK7T6W6N","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CK7T6W6NYS2AGNJF6KYAC7NL57","target":"record","payload":{"canonical_record":{"source":{"id":"1809.07131","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-19T11:47:49Z","cross_cats_sorted":["cs.CG","math.AT"],"title_canon_sha256":"621a270e3787bb932e2c4dd2addfb956831b673ff8a54fcf5cd49af4388558f6","abstract_canon_sha256":"9380d1f19056ec35d0c482a8e1cb43554064b61e6d207a8e7656e45df5e2e155"},"schema_version":"1.0"},"canonical_sha256":"12bf3f5bcdc4b4033525f2b0017dabeffdf5cc420aeddf20f0ace6e1b1d88b70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:02.831977Z","signature_b64":"yYW8qgNVzzEza1/BVYuh58INh+7/5QzB9WKcbv4sA168lZJdjOe0HofbeoPz9/hczuPDQudqWCXpUoJ/Bi98Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12bf3f5bcdc4b4033525f2b0017dabeffdf5cc420aeddf20f0ace6e1b1d88b70","last_reissued_at":"2026-05-17T23:47:02.831361Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:02.831361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.07131","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eB70g1kg7mAJQMPcLLctElNiTB4bk+yhZSPldjRZ9KSl/p9HS2EMFOhHP61JQzj5BnWgQws9VscXC9ekdPQ+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:28:59.323301Z"},"content_sha256":"815da0d694a905c6fc80ee3d2d585acac0d5490d00cb04cc343ba14b1384a93a","schema_version":"1.0","event_id":"sha256:815da0d694a905c6fc80ee3d2d585acac0d5490d00cb04cc343ba14b1384a93a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CK7T6W6NYS2AGNJF6KYAC7NL57","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisty Takens: A Geometric Characterization of Good Observations on Dense Trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.AT"],"primary_cat":"math.DS","authors_text":"Alice Antia, Boyan Xu, Christopher J. Tralie, Jose A. Perea, Michael Lin","submitted_at":"2018-09-19T11:47:49Z","abstract_excerpt":"In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics. This can be used, for instance, to show that sliding window embeddings of periodic signals recover topological loops, and that sliding window embeddings of quasiperiodic signals recover high-dimensional torii. However, in spite of these motivating examples, Takens' theorem does not in general prescribe how to choose such an observation function given particu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07131","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:47:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PyQcWO/eJTb+b2bX/JZWpnoahurq5OI9Hw3M1a2x3JidCBAxQ4phXoX5RTcLaPecbWO0jTIhk9sVz/0VsIneCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:28:59.323667Z"},"content_sha256":"7c0527e9ce3246d0820361cd490bb5cb5a7b4a9985301492987954a551b3f6c9","schema_version":"1.0","event_id":"sha256:7c0527e9ce3246d0820361cd490bb5cb5a7b4a9985301492987954a551b3f6c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CK7T6W6NYS2AGNJF6KYAC7NL57/bundle.json","state_url":"https://pith.science/pith/CK7T6W6NYS2AGNJF6KYAC7NL57/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CK7T6W6NYS2AGNJF6KYAC7NL57/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":"2026-06-01T08:28:59Z","links":{"resolver":"https://pith.science/pith/CK7T6W6NYS2AGNJF6KYAC7NL57","bundle":"https://pith.science/pith/CK7T6W6NYS2AGNJF6KYAC7NL57/bundle.json","state":"https://pith.science/pith/CK7T6W6NYS2AGNJF6KYAC7NL57/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CK7T6W6NYS2AGNJF6KYAC7NL57/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CK7T6W6NYS2AGNJF6KYAC7NL57","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":"9380d1f19056ec35d0c482a8e1cb43554064b61e6d207a8e7656e45df5e2e155","cross_cats_sorted":["cs.CG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-19T11:47:49Z","title_canon_sha256":"621a270e3787bb932e2c4dd2addfb956831b673ff8a54fcf5cd49af4388558f6"},"schema_version":"1.0","source":{"id":"1809.07131","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07131","created_at":"2026-05-17T23:47:02Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07131v3","created_at":"2026-05-17T23:47:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07131","created_at":"2026-05-17T23:47:02Z"},{"alias_kind":"pith_short_12","alias_value":"CK7T6W6NYS2A","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CK7T6W6NYS2AGNJF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CK7T6W6N","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:7c0527e9ce3246d0820361cd490bb5cb5a7b4a9985301492987954a551b3f6c9","target":"graph","created_at":"2026-05-17T23:47:02Z","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"},"paper":{"abstract_excerpt":"In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics. This can be used, for instance, to show that sliding window embeddings of periodic signals recover topological loops, and that sliding window embeddings of quasiperiodic signals recover high-dimensional torii. However, in spite of these motivating examples, Takens' theorem does not in general prescribe how to choose such an observation function given particu","authors_text":"Alice Antia, Boyan Xu, Christopher J. Tralie, Jose A. Perea, Michael Lin","cross_cats":["cs.CG","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-19T11:47:49Z","title":"Twisty Takens: A Geometric Characterization of Good Observations on Dense Trajectories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07131","kind":"arxiv","version":3},"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":"sha256:815da0d694a905c6fc80ee3d2d585acac0d5490d00cb04cc343ba14b1384a93a","target":"record","created_at":"2026-05-17T23:47:02Z","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":"9380d1f19056ec35d0c482a8e1cb43554064b61e6d207a8e7656e45df5e2e155","cross_cats_sorted":["cs.CG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-19T11:47:49Z","title_canon_sha256":"621a270e3787bb932e2c4dd2addfb956831b673ff8a54fcf5cd49af4388558f6"},"schema_version":"1.0","source":{"id":"1809.07131","kind":"arxiv","version":3}},"canonical_sha256":"12bf3f5bcdc4b4033525f2b0017dabeffdf5cc420aeddf20f0ace6e1b1d88b70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12bf3f5bcdc4b4033525f2b0017dabeffdf5cc420aeddf20f0ace6e1b1d88b70","first_computed_at":"2026-05-17T23:47:02.831361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:02.831361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yYW8qgNVzzEza1/BVYuh58INh+7/5QzB9WKcbv4sA168lZJdjOe0HofbeoPz9/hczuPDQudqWCXpUoJ/Bi98Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:02.831977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07131","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:815da0d694a905c6fc80ee3d2d585acac0d5490d00cb04cc343ba14b1384a93a","sha256:7c0527e9ce3246d0820361cd490bb5cb5a7b4a9985301492987954a551b3f6c9"],"state_sha256":"b861d5478464b25dc20d9b11ac9e504fe8d5d585d23e1500d3e3d1bd55d78cd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JmfckLv45uBAE/BsfCSJ767bDl8muXQVTrcFymX4YR9zNK3ufZvx9s8kliDFZ8rrVtQXFZeKPOwZSbdpENhlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:28:59.325641Z","bundle_sha256":"fa81f3126dbff5190889fc3b6b94adf457798da6fa8c41e56afba5029d6966c5"}}