{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WTMREO2XQI35PBSM4QJ5LX3JUK","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":"eebfcf19eaa740e690d6c6bb0c148db29154516481b3424a17e0bdff11b23d82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-25T19:57:58Z","title_canon_sha256":"04adc128a1c7c06b37abdc632325f388a0d6b61b9bf224de59178e03660b323b"},"schema_version":"1.0","source":{"id":"1409.7383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7383","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7383v1","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7383","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"WTMREO2XQI35","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WTMREO2XQI35PBSM","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WTMREO2X","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:5b621c1d1bcda60ab5efd21945e744d67855b4c5a25e1b164248a4b8f1a295b0","target":"graph","created_at":"2026-05-18T02:41:58Z","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 study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\\alpha$ with $-1<\\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates {assuming} that the exact solution is sufficiently regular. Thus, if for each time $t \\in [0,T]$ the approximations are taken to be piecewise polynomials of degree $k\\ge0$ on the spatial domain~$\\Omega$, the approximations to $u$ in the $L_\\infty\\bigr(0,T;L_2(\\Omega)\\bigr)$-norm and to $\\nabla u$ in the $L_\\infty\\bigr(0,T;{\\bf L}_2(\\Omega)\\bigr)$-norm are proven","authors_text":"Bernardo Cockburn, Kassem Mustapha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-25T19:57:58Z","title":"A hybridizable discontinuous Galerkin method for fractional diffusion problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7383","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":"sha256:294bec05b906ae8c978a5b2b88ad180ca57fcc97a0803f458efaf908b5c52179","target":"record","created_at":"2026-05-18T02:41:58Z","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":"eebfcf19eaa740e690d6c6bb0c148db29154516481b3424a17e0bdff11b23d82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-25T19:57:58Z","title_canon_sha256":"04adc128a1c7c06b37abdc632325f388a0d6b61b9bf224de59178e03660b323b"},"schema_version":"1.0","source":{"id":"1409.7383","kind":"arxiv","version":1}},"canonical_sha256":"b4d9123b578237d7864ce413d5df69a282805a3013044a31f964fd78870adbc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4d9123b578237d7864ce413d5df69a282805a3013044a31f964fd78870adbc7","first_computed_at":"2026-05-18T02:41:58.547082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:58.547082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RRw99ajsO4i9bYwc+Oh4DNAbMYPFlfjNA777oN9qTii5Y9FmY/sWTz40AKozsstnmyyJwf6swqErR5jWxW8MCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:58.547499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:294bec05b906ae8c978a5b2b88ad180ca57fcc97a0803f458efaf908b5c52179","sha256:5b621c1d1bcda60ab5efd21945e744d67855b4c5a25e1b164248a4b8f1a295b0"],"state_sha256":"267a0687c491dab670b323cfa3447d3c6748e20f3ec7bc5cbefc659c0cb2d97f"}