{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IY6FBP35KNYM52KLUVT7FYC6Z2","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":"08fa1143b6f454b4754649b8b61caf68457c215f93d43f75abc002685f7e0de4","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-03T00:49:09Z","title_canon_sha256":"401701e2eb9fc56cb2c0b371431bfd13ec57ff56b306b16fa21386913bc64b92"},"schema_version":"1.0","source":{"id":"1307.0888","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0888","created_at":"2026-05-18T03:14:19Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0888v2","created_at":"2026-05-18T03:14:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0888","created_at":"2026-05-18T03:14:19Z"},{"alias_kind":"pith_short_12","alias_value":"IY6FBP35KNYM","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IY6FBP35KNYM52KL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IY6FBP35","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:a5d535a322673caf3c1cfc63f53ba5dbfbd6e27a188f203517f954781b931d92","target":"graph","created_at":"2026-05-18T03:14:19Z","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 present and study a novel numerical algorithm to approximate the action of $T^\\beta:=L^{-\\beta}$ where $L$ is a symmetric and positive definite unbounded operator on a Hilbert space $H_0$. The numerical method is based on a representation formula for $T^{-\\beta}$ in terms of Bochner integrals involving $(I+t^2L)^{-1}$ for $t\\in(0,\\infty)$.\n  To develop an approximation to $T^\\beta$, we introduce a finite element approximation $L_h$ to $L$ and base our approximation to $T^\\beta$ on $T_h^\\beta:= L_h^{-\\beta}$. The direct evaluation of $T_h^{\\beta}$ is extremely expensive as it involves expans","authors_text":"Andrea Bonito, Joseph E. Pasciak","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-03T00:49:09Z","title":"Numerical Approximation of Fractional Powers of Elliptic Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0888","kind":"arxiv","version":2},"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:ebd830adebbead779e3bb7920541a600f248876fd06fb3f8e123156eea99f3f7","target":"record","created_at":"2026-05-18T03:14:19Z","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":"08fa1143b6f454b4754649b8b61caf68457c215f93d43f75abc002685f7e0de4","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-03T00:49:09Z","title_canon_sha256":"401701e2eb9fc56cb2c0b371431bfd13ec57ff56b306b16fa21386913bc64b92"},"schema_version":"1.0","source":{"id":"1307.0888","kind":"arxiv","version":2}},"canonical_sha256":"463c50bf7d5370cee94ba567f2e05eceb3da1db4031c56a099f2833cd921d175","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"463c50bf7d5370cee94ba567f2e05eceb3da1db4031c56a099f2833cd921d175","first_computed_at":"2026-05-18T03:14:19.160712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:19.160712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EcvXcBQ9yH3B6pzkzcxd1ED3HNOoFFPMF5c97lZMRYLIisOGcUkko+mxhscwJAuTwlQQLFMbODq+Kj147eq2Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:19.161479Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0888","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebd830adebbead779e3bb7920541a600f248876fd06fb3f8e123156eea99f3f7","sha256:a5d535a322673caf3c1cfc63f53ba5dbfbd6e27a188f203517f954781b931d92"],"state_sha256":"0c1a61017a1e768f5c8de5a6fa3ac0a3dfe2cf549c8d553c409db591ae845d71"}