{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WGVQAJDPI674YX3TVDPLTLZRBK","short_pith_number":"pith:WGVQAJDP","schema_version":"1.0","canonical_sha256":"b1ab00246f47bfcc5f73a8deb9af310aa6259a4e2b5db9b08c2ab87542a63251","source":{"kind":"arxiv","id":"1506.01128","version":1},"attestation_state":"computed","paper":{"title":"Exploring the Topology of Dynamical Reconstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Elizabeth Bradley, James D. Meiss, Joshua Garland","submitted_at":"2015-06-03T05:25:11Z","abstract_excerpt":"Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a number of free parameters and the computation of homology for a large number of simplices can be expensive. This paper is a study of how to avoid a full (diffeomorphic) reconstruction and how to decrease the computational burden. Using trajectories from the classic Lorenz system, we reconstruct the dynamics using the method of delays, then build a parsimonious si"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.01128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-03T05:25:11Z","cross_cats_sorted":[],"title_canon_sha256":"ca71a838c5fadfcbd6aa6463b6674dad90585b39bec2ee6f66a62f4440b20ce9","abstract_canon_sha256":"592f3c638a47ec633c66c811c239018d66b4be4ae82000cc32881fbcb3f7b80c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:45.856238Z","signature_b64":"4Tmuxxq7lN8Rru4lSbZvjl9F0hW9oxX1ktQ1XgVe+A0c/UAds0FG3G1PHbfoNACikqLgaiV7I2HVxsg/P9h+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1ab00246f47bfcc5f73a8deb9af310aa6259a4e2b5db9b08c2ab87542a63251","last_reissued_at":"2026-05-18T01:02:45.855622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:45.855622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exploring the Topology of Dynamical Reconstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Elizabeth Bradley, James D. Meiss, Joshua Garland","submitted_at":"2015-06-03T05:25:11Z","abstract_excerpt":"Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a number of free parameters and the computation of homology for a large number of simplices can be expensive. This paper is a study of how to avoid a full (diffeomorphic) reconstruction and how to decrease the computational burden. Using trajectories from the classic Lorenz system, we reconstruct the dynamics using the method of delays, then build a parsimonious si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01128","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.01128","created_at":"2026-05-18T01:02:45.855705+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.01128v1","created_at":"2026-05-18T01:02:45.855705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01128","created_at":"2026-05-18T01:02:45.855705+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGVQAJDPI674","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGVQAJDPI674YX3T","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGVQAJDP","created_at":"2026-05-18T12:29:47.479230+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WGVQAJDPI674YX3TVDPLTLZRBK","json":"https://pith.science/pith/WGVQAJDPI674YX3TVDPLTLZRBK.json","graph_json":"https://pith.science/api/pith-number/WGVQAJDPI674YX3TVDPLTLZRBK/graph.json","events_json":"https://pith.science/api/pith-number/WGVQAJDPI674YX3TVDPLTLZRBK/events.json","paper":"https://pith.science/paper/WGVQAJDP"},"agent_actions":{"view_html":"https://pith.science/pith/WGVQAJDPI674YX3TVDPLTLZRBK","download_json":"https://pith.science/pith/WGVQAJDPI674YX3TVDPLTLZRBK.json","view_paper":"https://pith.science/paper/WGVQAJDP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.01128&json=true","fetch_graph":"https://pith.science/api/pith-number/WGVQAJDPI674YX3TVDPLTLZRBK/graph.json","fetch_events":"https://pith.science/api/pith-number/WGVQAJDPI674YX3TVDPLTLZRBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGVQAJDPI674YX3TVDPLTLZRBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGVQAJDPI674YX3TVDPLTLZRBK/action/storage_attestation","attest_author":"https://pith.science/pith/WGVQAJDPI674YX3TVDPLTLZRBK/action/author_attestation","sign_citation":"https://pith.science/pith/WGVQAJDPI674YX3TVDPLTLZRBK/action/citation_signature","submit_replication":"https://pith.science/pith/WGVQAJDPI674YX3TVDPLTLZRBK/action/replication_record"}},"created_at":"2026-05-18T01:02:45.855705+00:00","updated_at":"2026-05-18T01:02:45.855705+00:00"}