{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GKZ2PTVDV2TFLHA6CG46O6C62Q","short_pith_number":"pith:GKZ2PTVD","schema_version":"1.0","canonical_sha256":"32b3a7cea3aea6559c1e11b9e7785ed42986835b601aeca5e2b33572090a5726","source":{"kind":"arxiv","id":"1512.06527","version":2},"attestation_state":"computed","paper":{"title":"Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christof Sch\\\"utte, Stefan Klus","submitted_at":"2015-12-21T08:47:26Z","abstract_excerpt":"The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the system's behavior are the Perron-Frobenius operator and the Koopman operator. Due to the curse of dimensionality, computing the eigenfunctions of high-dimensional systems is in general infeasible. We will propose a tensor-based reformulation of two numerical methods for computing finite-dimensional approximations of the aforementioned infinite-dimensional o"},"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":"1512.06527","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-21T08:47:26Z","cross_cats_sorted":[],"title_canon_sha256":"2f30fd5a40487e78769cf8354e6c564e77e758b09f4f8cd26cd3ee26f79d05eb","abstract_canon_sha256":"3226b413e2bbadb6cb124154a087ee75b14fa686962113ee075945ddb0c7f4ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:29.416932Z","signature_b64":"i95TKuvHBmplSwG/QK6+8VaHQExSuf51opmcNpl97FvQ3XNrMFs+aoBQ/EbVklf/WoglK2UX+QZLw3esobdABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32b3a7cea3aea6559c1e11b9e7785ed42986835b601aeca5e2b33572090a5726","last_reissued_at":"2026-05-18T00:52:29.416458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:29.416458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christof Sch\\\"utte, Stefan Klus","submitted_at":"2015-12-21T08:47:26Z","abstract_excerpt":"The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the system's behavior are the Perron-Frobenius operator and the Koopman operator. Due to the curse of dimensionality, computing the eigenfunctions of high-dimensional systems is in general infeasible. We will propose a tensor-based reformulation of two numerical methods for computing finite-dimensional approximations of the aforementioned infinite-dimensional o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06527","kind":"arxiv","version":2},"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":"1512.06527","created_at":"2026-05-18T00:52:29.416532+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.06527v2","created_at":"2026-05-18T00:52:29.416532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06527","created_at":"2026-05-18T00:52:29.416532+00:00"},{"alias_kind":"pith_short_12","alias_value":"GKZ2PTVDV2TF","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GKZ2PTVDV2TFLHA6","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GKZ2PTVD","created_at":"2026-05-18T12:29:22.688609+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/GKZ2PTVDV2TFLHA6CG46O6C62Q","json":"https://pith.science/pith/GKZ2PTVDV2TFLHA6CG46O6C62Q.json","graph_json":"https://pith.science/api/pith-number/GKZ2PTVDV2TFLHA6CG46O6C62Q/graph.json","events_json":"https://pith.science/api/pith-number/GKZ2PTVDV2TFLHA6CG46O6C62Q/events.json","paper":"https://pith.science/paper/GKZ2PTVD"},"agent_actions":{"view_html":"https://pith.science/pith/GKZ2PTVDV2TFLHA6CG46O6C62Q","download_json":"https://pith.science/pith/GKZ2PTVDV2TFLHA6CG46O6C62Q.json","view_paper":"https://pith.science/paper/GKZ2PTVD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.06527&json=true","fetch_graph":"https://pith.science/api/pith-number/GKZ2PTVDV2TFLHA6CG46O6C62Q/graph.json","fetch_events":"https://pith.science/api/pith-number/GKZ2PTVDV2TFLHA6CG46O6C62Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GKZ2PTVDV2TFLHA6CG46O6C62Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GKZ2PTVDV2TFLHA6CG46O6C62Q/action/storage_attestation","attest_author":"https://pith.science/pith/GKZ2PTVDV2TFLHA6CG46O6C62Q/action/author_attestation","sign_citation":"https://pith.science/pith/GKZ2PTVDV2TFLHA6CG46O6C62Q/action/citation_signature","submit_replication":"https://pith.science/pith/GKZ2PTVDV2TFLHA6CG46O6C62Q/action/replication_record"}},"created_at":"2026-05-18T00:52:29.416532+00:00","updated_at":"2026-05-18T00:52:29.416532+00:00"}