{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:7WLA6WHCIGHEJ4ZJX3LS2EZPF4","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":"61c494aef1bf20094d173f74ec67cc8049c61efed6e8dcac810523559d1029eb","cross_cats_sorted":[],"license":"","primary_cat":"math.NA","submitted_at":"2005-04-22T12:56:36Z","title_canon_sha256":"26fea0a93f8eac6dfc60509e62f90b5073b03ac9e572e1e61116c47042e51d02"},"schema_version":"1.0","source":{"id":"math/0504461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504461","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504461v1","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504461","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"7WLA6WHCIGHE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7WLA6WHCIGHEJ4ZJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7WLA6WHC","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:73bcd7994bb61cfba0e0314e210127b7d9259a83073e0446e103f96b5016267d","target":"graph","created_at":"2026-05-18T04:08:35Z","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 give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N \\log N)$ multiplications and $O(\\log N)$ active memory. The method does not require evaluations of the convolution kernel, but instead $O(\\log N)$ evaluations of its Laplace transform, which is assumed sectorial.\n  The algorithm can be used for the stable numerical solution with quasi-optimal complexity of linear and nonlinear integral and integro-differential equations of convolution type. In a numerical example we apply it to solve a subdiffusion equation w","authors_text":"Achim Sch\\\"adle, Christian Lubich, Mar\\'ia L\\'opez-Fern\\'andez","cross_cats":[],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2005-04-22T12:56:36Z","title":"Fast and oblivious convolution quadrature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504461","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":"sha256:36070c4c80d358a650ec691e4abfa33e03da403d7b0bad618523ec9e11bc11fa","target":"record","created_at":"2026-05-18T04:08:35Z","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":"61c494aef1bf20094d173f74ec67cc8049c61efed6e8dcac810523559d1029eb","cross_cats_sorted":[],"license":"","primary_cat":"math.NA","submitted_at":"2005-04-22T12:56:36Z","title_canon_sha256":"26fea0a93f8eac6dfc60509e62f90b5073b03ac9e572e1e61116c47042e51d02"},"schema_version":"1.0","source":{"id":"math/0504461","kind":"arxiv","version":1}},"canonical_sha256":"fd960f58e2418e44f329bed72d132f2f22fb1cf26819782b545630fcbd3b3d3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd960f58e2418e44f329bed72d132f2f22fb1cf26819782b545630fcbd3b3d3b","first_computed_at":"2026-05-18T04:08:35.714888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:35.714888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cfM32unj4ALi0v/XKRZVYBGfW2rL/ljcX6MIqTNMq0ccMKnKZZcvhftPNMvx/6rkBxR+wXQQyPxcGchCkspDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:35.715417Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36070c4c80d358a650ec691e4abfa33e03da403d7b0bad618523ec9e11bc11fa","sha256:73bcd7994bb61cfba0e0314e210127b7d9259a83073e0446e103f96b5016267d"],"state_sha256":"a745464b46a3bd7daec995d722570d146fd879997e9b9c181af005151bc7abb1"}