{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GMI4NHAUPLSDMEBKSBQGTDSRQC","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":"20c07ac99294713ccf62cb99495fa4f4dcecd0e5f9afd8da04c4fad655105ee4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-07T09:27:32Z","title_canon_sha256":"581ffbac608fabbe6a5396fa1eedeaafb16e864359333d809e578cb1213ded9e"},"schema_version":"1.0","source":{"id":"1504.01529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01529","created_at":"2026-05-18T02:19:26Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01529v1","created_at":"2026-05-18T02:19:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01529","created_at":"2026-05-18T02:19:26Z"},{"alias_kind":"pith_short_12","alias_value":"GMI4NHAUPLSD","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GMI4NHAUPLSDMEBK","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GMI4NHAU","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:be8293897df48ed4b4449cf760ad005351572e877de1e010dc326382baac21f0","target":"graph","created_at":"2026-05-18T02:19:26Z","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":"In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in some physical problems, whose solution decays only logarithmically as the time $t$ tends to infinity. We develop a space semidiscrete scheme based on the standard Galerkin finite element method, and establish error estimates optimal with respect to data regularity in $L^2(D)$ and $H^1(D)$ norms for both smooth and nonsmooth initial data. Further, we propose ","authors_text":"Bangti Jin, Dongwoo Sheen, Raytcho Lazarov, Zhi Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-07T09:27:32Z","title":"Error Estimates for Approximations of Distributed Order Time Fractional Diffusion with Nonsmooth Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01529","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":"sha256:9489426bdd62cd2a1afe1108a9a8a3c59afc5d82973560294840af4d7299f0d4","target":"record","created_at":"2026-05-18T02:19:26Z","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":"20c07ac99294713ccf62cb99495fa4f4dcecd0e5f9afd8da04c4fad655105ee4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-07T09:27:32Z","title_canon_sha256":"581ffbac608fabbe6a5396fa1eedeaafb16e864359333d809e578cb1213ded9e"},"schema_version":"1.0","source":{"id":"1504.01529","kind":"arxiv","version":1}},"canonical_sha256":"3311c69c147ae436102a9060698e5180884eac29331feb1578cb1d0dddc2244b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3311c69c147ae436102a9060698e5180884eac29331feb1578cb1d0dddc2244b","first_computed_at":"2026-05-18T02:19:26.856606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:26.856606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oi6Y5xnxAS786EpkbysaYRxU7rWZAys+Sw3wcue+svsMEylszQQiaLdnIW6hecdWlYfz1zWHe2Ypz+ZjMsI7Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:26.857154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9489426bdd62cd2a1afe1108a9a8a3c59afc5d82973560294840af4d7299f0d4","sha256:be8293897df48ed4b4449cf760ad005351572e877de1e010dc326382baac21f0"],"state_sha256":"5a6a43c08cfe91d816774643ca1a5bb361297dae0c761b4ae6790b9e3611088c"}