{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4ABOMQUILOBUK3FLPDT5AQH3WA","short_pith_number":"pith:4ABOMQUI","canonical_record":{"source":{"id":"1412.2098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T18:42:23Z","cross_cats_sorted":[],"title_canon_sha256":"84e60395fb7605fceb3c2dccc787857aa9d31824e95282b777679e24ec4e25cb","abstract_canon_sha256":"7185f8d99bbee2ad7ccdd86ade0457c18a938a5d59a175d9879ee7553fa1be47"},"schema_version":"1.0"},"canonical_sha256":"e002e642885b83456cab78e7d040fbb00d4640e61c684cf78d971edf1a7bef27","source":{"kind":"arxiv","id":"1412.2098","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2098","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2098v1","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2098","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"4ABOMQUILOBU","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4ABOMQUILOBUK3FL","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4ABOMQUI","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4ABOMQUILOBUK3FLPDT5AQH3WA","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T18:42:23Z","cross_cats_sorted":[],"title_canon_sha256":"84e60395fb7605fceb3c2dccc787857aa9d31824e95282b777679e24ec4e25cb","abstract_canon_sha256":"7185f8d99bbee2ad7ccdd86ade0457c18a938a5d59a175d9879ee7553fa1be47"},"schema_version":"1.0"},"canonical_sha256":"e002e642885b83456cab78e7d040fbb00d4640e61c684cf78d971edf1a7bef27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:05.381803Z","signature_b64":"YmtDNCpgXRNla/XwjsGvpvQPF+aFcbUGFssxzw7SP71jb8+agZvAK1zo2X7YdgHA+X4bNGR/1dheKpqI4Y/VBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e002e642885b83456cab78e7d040fbb00d4640e61c684cf78d971edf1a7bef27","last_reissued_at":"2026-05-18T02:32:05.381444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:05.381444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2098","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UgudApODITLsUE0Ao215fmqofMu/IkSdn+HJGVZ477GEzQIDGOIBUaBNGtBoXpOOAuuSfUP48x6kOvajnWMTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:42:12.120825Z"},"content_sha256":"33f53c32f22c5d66355aa8c6f85c2a4437aa9831a1b8cebeaa4ad1176b2b73c9","schema_version":"1.0","event_id":"sha256:33f53c32f22c5d66355aa8c6f85c2a4437aa9831a1b8cebeaa4ad1176b2b73c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4ABOMQUILOBUK3FLPDT5AQH3WA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bernardo Cockburn, Kassem Mustapha, Maher Nour","submitted_at":"2014-12-05T18:42:23Z","abstract_excerpt":"We study the hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order $0<\\alpha<1$. For each time $t \\in [0,T]$, the HDG approximations are taken to be piecewise polynomials of degree $k\\ge0$ on the spatial domain~$\\Omega$, the approximations to the exact solution $u$ 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 to converge with the rate $h^{k+1}$ provided that $u$ is sufficiently regular, where $h$ is the maximum d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2098","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hQOhcwGdl0oFL9c94RGCtHB9CHEkurOBheVgisTffeBF0L2gFx563+BBgktlpACwTJEPREAKanU3RZrLoqEvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:42:12.121197Z"},"content_sha256":"c71d9fbd04590f6075d590d61365597b0d47c8fe912ad0b1923d37031160c372","schema_version":"1.0","event_id":"sha256:c71d9fbd04590f6075d590d61365597b0d47c8fe912ad0b1923d37031160c372"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ABOMQUILOBUK3FLPDT5AQH3WA/bundle.json","state_url":"https://pith.science/pith/4ABOMQUILOBUK3FLPDT5AQH3WA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ABOMQUILOBUK3FLPDT5AQH3WA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T04:42:12Z","links":{"resolver":"https://pith.science/pith/4ABOMQUILOBUK3FLPDT5AQH3WA","bundle":"https://pith.science/pith/4ABOMQUILOBUK3FLPDT5AQH3WA/bundle.json","state":"https://pith.science/pith/4ABOMQUILOBUK3FLPDT5AQH3WA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ABOMQUILOBUK3FLPDT5AQH3WA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4ABOMQUILOBUK3FLPDT5AQH3WA","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":"7185f8d99bbee2ad7ccdd86ade0457c18a938a5d59a175d9879ee7553fa1be47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T18:42:23Z","title_canon_sha256":"84e60395fb7605fceb3c2dccc787857aa9d31824e95282b777679e24ec4e25cb"},"schema_version":"1.0","source":{"id":"1412.2098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2098","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2098v1","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2098","created_at":"2026-05-18T02:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"4ABOMQUILOBU","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4ABOMQUILOBUK3FL","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4ABOMQUI","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:c71d9fbd04590f6075d590d61365597b0d47c8fe912ad0b1923d37031160c372","target":"graph","created_at":"2026-05-18T02:32:05Z","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 hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order $0<\\alpha<1$. For each time $t \\in [0,T]$, the HDG approximations are taken to be piecewise polynomials of degree $k\\ge0$ on the spatial domain~$\\Omega$, the approximations to the exact solution $u$ 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 to converge with the rate $h^{k+1}$ provided that $u$ is sufficiently regular, where $h$ is the maximum d","authors_text":"Bernardo Cockburn, Kassem Mustapha, Maher Nour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T18:42:23Z","title":"Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2098","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":"sha256:33f53c32f22c5d66355aa8c6f85c2a4437aa9831a1b8cebeaa4ad1176b2b73c9","target":"record","created_at":"2026-05-18T02:32:05Z","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":"7185f8d99bbee2ad7ccdd86ade0457c18a938a5d59a175d9879ee7553fa1be47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T18:42:23Z","title_canon_sha256":"84e60395fb7605fceb3c2dccc787857aa9d31824e95282b777679e24ec4e25cb"},"schema_version":"1.0","source":{"id":"1412.2098","kind":"arxiv","version":1}},"canonical_sha256":"e002e642885b83456cab78e7d040fbb00d4640e61c684cf78d971edf1a7bef27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e002e642885b83456cab78e7d040fbb00d4640e61c684cf78d971edf1a7bef27","first_computed_at":"2026-05-18T02:32:05.381444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:05.381444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YmtDNCpgXRNla/XwjsGvpvQPF+aFcbUGFssxzw7SP71jb8+agZvAK1zo2X7YdgHA+X4bNGR/1dheKpqI4Y/VBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:05.381803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33f53c32f22c5d66355aa8c6f85c2a4437aa9831a1b8cebeaa4ad1176b2b73c9","sha256:c71d9fbd04590f6075d590d61365597b0d47c8fe912ad0b1923d37031160c372"],"state_sha256":"29d394201663429e37a9478989496ce4de204cf97e5f65f6581e8ce2f5e7a4fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aiUsU1xgnrWuk3f3gR+S1ZbqzuIbl9f6rX56qDvnSmJn7aUBJM2ZuLQjK3WFXK1ABm3yZ2wVycOBx68XB/qnCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:42:12.123286Z","bundle_sha256":"899d6fbcc5326a6d4430b4d19208597b4ce6210398176dec56bd2442e89ea025"}}