{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OEPWUYLV2NXDTVVLOB2YQA3VJL","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":"5bb32c33a21528ff00893f6657d1cf74f93f719438b9cbbc8601f4e47a372b36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-07-05T20:10:21Z","title_canon_sha256":"e1794a0e275e26857edb7699332fb843cd2e82c02f4db3baf5a075b96326fa32"},"schema_version":"1.0","source":{"id":"1707.01566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01566","created_at":"2026-05-17T23:54:56Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01566v1","created_at":"2026-05-17T23:54:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01566","created_at":"2026-05-17T23:54:56Z"},{"alias_kind":"pith_short_12","alias_value":"OEPWUYLV2NXD","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OEPWUYLV2NXDTVVL","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OEPWUYLV","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:2371f9c5762105449c35478413b07118d8ff48df73bfcc2a4dd13f0cd70b53d2","target":"graph","created_at":"2026-05-17T23:54:56Z","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 three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the extension to one higher dimension. The second method is the integral formulation and deals with singular non-integrable kernels. The third method is a discretization of the Dunford-Taylor formula. We discuss pros and cons of each method, error estimates, and document their performance with a few numerical experiments.","authors_text":"Abner J. Salgado, Andrea Bonito, Enrique Otarola, Juan Pablo Borthagaray, Ricardo H. Nochetto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-07-05T20:10:21Z","title":"Numerical Methods for Fractional Diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01566","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":"sha256:93206237bd979a09d0e583213539ec01612634a9d9f1d5885fb66bb8f05259d1","target":"record","created_at":"2026-05-17T23:54:56Z","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":"5bb32c33a21528ff00893f6657d1cf74f93f719438b9cbbc8601f4e47a372b36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-07-05T20:10:21Z","title_canon_sha256":"e1794a0e275e26857edb7699332fb843cd2e82c02f4db3baf5a075b96326fa32"},"schema_version":"1.0","source":{"id":"1707.01566","kind":"arxiv","version":1}},"canonical_sha256":"711f6a6175d36e39d6ab70758803754afd5dc5abc19ace3b1650144b7b0b384b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"711f6a6175d36e39d6ab70758803754afd5dc5abc19ace3b1650144b7b0b384b","first_computed_at":"2026-05-17T23:54:56.818448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:56.818448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wNpY1yaS45uZGuRadFTALyF+G9uNd5VotzxIrqlnxPR16ApQimRKBmiq/4k466PU7/fHOBeUF1z0tVNewqxoCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:56.819016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93206237bd979a09d0e583213539ec01612634a9d9f1d5885fb66bb8f05259d1","sha256:2371f9c5762105449c35478413b07118d8ff48df73bfcc2a4dd13f0cd70b53d2"],"state_sha256":"127596826aca5b32dc805dfd554b58f64dcdcdbf3a2e15219c6b0c3152543a28"}