{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QPH7FXJHLQ554YLYQOTT2X75J3","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":"242256446b59516bd3767a1e09bc9613ad412cd4771c5ad76f1ff15468690475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2019-04-05T13:33:13Z","title_canon_sha256":"c4ef5337d492de0cd60389a50be756444f2ee1983d38f62473e84e5a52710745"},"schema_version":"1.0","source":{"id":"1904.03057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03057","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03057v1","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03057","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"QPH7FXJHLQ55","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QPH7FXJHLQ554YLY","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QPH7FXJH","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:dc82b4fdec11c9016cfbddbb7489be095db1bbc2faf6733e49e32de3678c8feb","target":"graph","created_at":"2026-05-17T23:49:18Z","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":"Tensor B-spline methods are a high-performance alternative to solve partial differential equations (PDEs). This paper gives an overview on the principles of Tensor B-spline methodology, shows their use and analyzes their performance in application examples, and discusses its merits. Tensors preserve the dimensional structure of a discretized PDE, which makes it possible to develop highly efficient computational solvers. B-splines provide high-quality approximations, lead to a sparse structure of the system operator represented by shift-invariant separable kernels in the domain, and are mesh-fr","authors_text":"Dmytro Shulga, Felix Friedrich, Oleksii Morozov, Patrick Hunziker, Volker Roth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2019-04-05T13:33:13Z","title":"Tensor B-Spline Numerical Methods for PDEs: a High-Performance Alternative to FEM"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03057","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:ee927a03e5265cb4778ad87fbaf6782703691e9f9f2c0aa7ac95f24db0506726","target":"record","created_at":"2026-05-17T23:49:18Z","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":"242256446b59516bd3767a1e09bc9613ad412cd4771c5ad76f1ff15468690475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2019-04-05T13:33:13Z","title_canon_sha256":"c4ef5337d492de0cd60389a50be756444f2ee1983d38f62473e84e5a52710745"},"schema_version":"1.0","source":{"id":"1904.03057","kind":"arxiv","version":1}},"canonical_sha256":"83cff2dd275c3bde617883a73d5ffd4eddd474034c36c30c9d81b650580f130f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83cff2dd275c3bde617883a73d5ffd4eddd474034c36c30c9d81b650580f130f","first_computed_at":"2026-05-17T23:49:18.743341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:18.743341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OXxtmsPEIIthwq+a4F//DVXmL2cgT9nDNZbn5rf7Rpvw+vRRjDOZ49zcf6iiykUICIaYUBBEbpUtNePOhkuLCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:18.743821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee927a03e5265cb4778ad87fbaf6782703691e9f9f2c0aa7ac95f24db0506726","sha256:dc82b4fdec11c9016cfbddbb7489be095db1bbc2faf6733e49e32de3678c8feb"],"state_sha256":"d79ce0d0a604544794e829b49a2c1caa975f4eba2de0e47fa3dce0818559fff8"}