{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:72STCM5ZVQAYLHLLJ7YXKSDQZQ","short_pith_number":"pith:72STCM5Z","canonical_record":{"source":{"id":"1504.08140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-30T09:32:00Z","cross_cats_sorted":[],"title_canon_sha256":"a80565d132342881c475ac0435c120738b342438d53823d11a666e19362d6de6","abstract_canon_sha256":"5e265f2826d72f6416b67663c8113ff3cbad735564cfd5462bc94d9dfb3d47de"},"schema_version":"1.0"},"canonical_sha256":"fea53133b9ac01859d6b4ff1754870cc24f7b2b0819aa64e1303031fee2ad7d0","source":{"kind":"arxiv","id":"1504.08140","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.08140","created_at":"2026-05-18T02:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1504.08140v1","created_at":"2026-05-18T02:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08140","created_at":"2026-05-18T02:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"72STCM5ZVQAY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"72STCM5ZVQAYLHLL","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"72STCM5Z","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:72STCM5ZVQAYLHLLJ7YXKSDQZQ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.08140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-30T09:32:00Z","cross_cats_sorted":[],"title_canon_sha256":"a80565d132342881c475ac0435c120738b342438d53823d11a666e19362d6de6","abstract_canon_sha256":"5e265f2826d72f6416b67663c8113ff3cbad735564cfd5462bc94d9dfb3d47de"},"schema_version":"1.0"},"canonical_sha256":"fea53133b9ac01859d6b4ff1754870cc24f7b2b0819aa64e1303031fee2ad7d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:23.203550Z","signature_b64":"IbNGBGljSbbapEZeaoCU9Xe/CMoL4kdfP1VVgXcKsAPMBpwXioZI8nFZ3/mE1ChIcthk2SKuykgHIzBzbAn8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fea53133b9ac01859d6b4ff1754870cc24f7b2b0819aa64e1303031fee2ad7d0","last_reissued_at":"2026-05-18T02:17:23.202957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:23.202957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.08140","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":"2026-05-18T02:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zWIY8uco8gmeRI5fd1CrbtOnQnECP65ucGjS9KsYB+EJhd4NUP8P/fxEwC+bdCeRv7xTPIh5NLWO/utVm36BAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:17:25.742422Z"},"content_sha256":"b45724d497187b448922bec36bdb67f048a426e0e26670f41f80d40234ba638b","schema_version":"1.0","event_id":"sha256:b45724d497187b448922bec36bdb67f048a426e0e26670f41f80d40234ba638b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:72STCM5ZVQAYLHLLJ7YXKSDQZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiscale techniques for parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Anna Persson, Axel M{\\aa}lqvist","submitted_at":"2015-04-30T09:32:00Z","abstract_excerpt":"We use the local orthogonal decomposition technique to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale diffusion coefficient. We consider nonsmooth initial data and a backward Euler scheme for the temporal discretization. Optimal order convergence rate, depending only on the contrast, but not on the variations in the diffusion coefficient, is proven in the $L_\\infty(L_2)$-norm. We present numerical examples, which confirm our theoretical findings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08140","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":"2026-05-18T02:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nFnm3J0WHdXccOzS+hpFov/Dnpd/qlxvP1sjWrJ2oXPmH/LJi3gt8xWnOMD8Y4n7YtUHZjSWt3Bm5ElVFZ0YDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:17:25.743114Z"},"content_sha256":"0a6df9cdcf65627769dc46acb5a6443758a744f25671c205f301e7bce93f593e","schema_version":"1.0","event_id":"sha256:0a6df9cdcf65627769dc46acb5a6443758a744f25671c205f301e7bce93f593e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72STCM5ZVQAYLHLLJ7YXKSDQZQ/bundle.json","state_url":"https://pith.science/pith/72STCM5ZVQAYLHLLJ7YXKSDQZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72STCM5ZVQAYLHLLJ7YXKSDQZQ/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":"2026-05-27T12:17:25Z","links":{"resolver":"https://pith.science/pith/72STCM5ZVQAYLHLLJ7YXKSDQZQ","bundle":"https://pith.science/pith/72STCM5ZVQAYLHLLJ7YXKSDQZQ/bundle.json","state":"https://pith.science/pith/72STCM5ZVQAYLHLLJ7YXKSDQZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72STCM5ZVQAYLHLLJ7YXKSDQZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:72STCM5ZVQAYLHLLJ7YXKSDQZQ","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":"5e265f2826d72f6416b67663c8113ff3cbad735564cfd5462bc94d9dfb3d47de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-30T09:32:00Z","title_canon_sha256":"a80565d132342881c475ac0435c120738b342438d53823d11a666e19362d6de6"},"schema_version":"1.0","source":{"id":"1504.08140","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.08140","created_at":"2026-05-18T02:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1504.08140v1","created_at":"2026-05-18T02:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08140","created_at":"2026-05-18T02:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"72STCM5ZVQAY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"72STCM5ZVQAYLHLL","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"72STCM5Z","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:0a6df9cdcf65627769dc46acb5a6443758a744f25671c205f301e7bce93f593e","target":"graph","created_at":"2026-05-18T02:17:23Z","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 use the local orthogonal decomposition technique to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale diffusion coefficient. We consider nonsmooth initial data and a backward Euler scheme for the temporal discretization. Optimal order convergence rate, depending only on the contrast, but not on the variations in the diffusion coefficient, is proven in the $L_\\infty(L_2)$-norm. We present numerical examples, which confirm our theoretical findings.","authors_text":"Anna Persson, Axel M{\\aa}lqvist","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-30T09:32:00Z","title":"Multiscale techniques for parabolic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08140","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:b45724d497187b448922bec36bdb67f048a426e0e26670f41f80d40234ba638b","target":"record","created_at":"2026-05-18T02:17:23Z","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":"5e265f2826d72f6416b67663c8113ff3cbad735564cfd5462bc94d9dfb3d47de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-30T09:32:00Z","title_canon_sha256":"a80565d132342881c475ac0435c120738b342438d53823d11a666e19362d6de6"},"schema_version":"1.0","source":{"id":"1504.08140","kind":"arxiv","version":1}},"canonical_sha256":"fea53133b9ac01859d6b4ff1754870cc24f7b2b0819aa64e1303031fee2ad7d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fea53133b9ac01859d6b4ff1754870cc24f7b2b0819aa64e1303031fee2ad7d0","first_computed_at":"2026-05-18T02:17:23.202957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:23.202957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IbNGBGljSbbapEZeaoCU9Xe/CMoL4kdfP1VVgXcKsAPMBpwXioZI8nFZ3/mE1ChIcthk2SKuykgHIzBzbAn8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:23.203550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.08140","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b45724d497187b448922bec36bdb67f048a426e0e26670f41f80d40234ba638b","sha256:0a6df9cdcf65627769dc46acb5a6443758a744f25671c205f301e7bce93f593e"],"state_sha256":"062d7de020dd35d83c9996c93d7b9c9b4821db6d56cc8e6240b62f99ee5dbe15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6s0lhcUFyE9HClPVyaMBnsprIuLoNKkNZLJL8UTgCEXfZZMQrxIvUQKqp++Q25OXcM3wKK/ML5I6BVVAXqreAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:17:25.747060Z","bundle_sha256":"39dfc75d8df12c5aafab32fc6512de026aa518323b576f5d51615f04804e5e29"}}