{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CZ6NS6WQRYC4E45KKNMI7D2IGM","short_pith_number":"pith:CZ6NS6WQ","schema_version":"1.0","canonical_sha256":"167cd97ad08e05c273aa53588f8f483307221eded1a18d0592db050449642671","source":{"kind":"arxiv","id":"1104.0725","version":1},"attestation_state":"computed","paper":{"title":"Noisy dynamic simulations in the presence of symmetry: data alignment and model reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Amit Singer, Benjamin E. Sonday, Ioannis G. Kevrekidis","submitted_at":"2011-04-05T03:05:07Z","abstract_excerpt":"We process snapshots of trajectories of evolution equations with intrinsic symmetries, and demonstrate the use of recently developed eigenvector-based techniques to successfully quotient out the degrees of freedom associated with the symmetries in the presence of noise. Our illustrative examples include a one-dimensional evolutionary partial differential (the Kuramoto-Sivashinsky) equation with periodic boundary conditions, as well as a stochastic simulation of nematic liquid crystals which can be effectively modeled through a nonlinear Smoluchowski equation on the surface of a sphere. This is"},"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":"1104.0725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-04-05T03:05:07Z","cross_cats_sorted":[],"title_canon_sha256":"163a0a8a60a38f92480fca19254a9f92e1f0874c4a665e2e237ea7bce34affe8","abstract_canon_sha256":"f00cd813de0f0cbdcce5bb316251119e22a3e806c98f75e27a2511993a0b0457"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:11.067540Z","signature_b64":"1uoL7DgIvn0ufxiLBhH8lp4DILwAcJjAzHPw+EqvFiw3pMKBp5Tao6eu5XkgwbuZG8EJzeBz/TmSO5LIpk4FAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"167cd97ad08e05c273aa53588f8f483307221eded1a18d0592db050449642671","last_reissued_at":"2026-05-18T02:22:11.066858Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:11.066858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noisy dynamic simulations in the presence of symmetry: data alignment and model reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Amit Singer, Benjamin E. Sonday, Ioannis G. Kevrekidis","submitted_at":"2011-04-05T03:05:07Z","abstract_excerpt":"We process snapshots of trajectories of evolution equations with intrinsic symmetries, and demonstrate the use of recently developed eigenvector-based techniques to successfully quotient out the degrees of freedom associated with the symmetries in the presence of noise. Our illustrative examples include a one-dimensional evolutionary partial differential (the Kuramoto-Sivashinsky) equation with periodic boundary conditions, as well as a stochastic simulation of nematic liquid crystals which can be effectively modeled through a nonlinear Smoluchowski equation on the surface of a sphere. This is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0725","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":"1104.0725","created_at":"2026-05-18T02:22:11.066953+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.0725v1","created_at":"2026-05-18T02:22:11.066953+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0725","created_at":"2026-05-18T02:22:11.066953+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZ6NS6WQRYC4","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZ6NS6WQRYC4E45K","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZ6NS6WQ","created_at":"2026-05-18T12:26:26.731475+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/CZ6NS6WQRYC4E45KKNMI7D2IGM","json":"https://pith.science/pith/CZ6NS6WQRYC4E45KKNMI7D2IGM.json","graph_json":"https://pith.science/api/pith-number/CZ6NS6WQRYC4E45KKNMI7D2IGM/graph.json","events_json":"https://pith.science/api/pith-number/CZ6NS6WQRYC4E45KKNMI7D2IGM/events.json","paper":"https://pith.science/paper/CZ6NS6WQ"},"agent_actions":{"view_html":"https://pith.science/pith/CZ6NS6WQRYC4E45KKNMI7D2IGM","download_json":"https://pith.science/pith/CZ6NS6WQRYC4E45KKNMI7D2IGM.json","view_paper":"https://pith.science/paper/CZ6NS6WQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.0725&json=true","fetch_graph":"https://pith.science/api/pith-number/CZ6NS6WQRYC4E45KKNMI7D2IGM/graph.json","fetch_events":"https://pith.science/api/pith-number/CZ6NS6WQRYC4E45KKNMI7D2IGM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZ6NS6WQRYC4E45KKNMI7D2IGM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZ6NS6WQRYC4E45KKNMI7D2IGM/action/storage_attestation","attest_author":"https://pith.science/pith/CZ6NS6WQRYC4E45KKNMI7D2IGM/action/author_attestation","sign_citation":"https://pith.science/pith/CZ6NS6WQRYC4E45KKNMI7D2IGM/action/citation_signature","submit_replication":"https://pith.science/pith/CZ6NS6WQRYC4E45KKNMI7D2IGM/action/replication_record"}},"created_at":"2026-05-18T02:22:11.066953+00:00","updated_at":"2026-05-18T02:22:11.066953+00:00"}