{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:S4X273BTHCFYGVBJYNTH3BL3LP","short_pith_number":"pith:S4X273BT","canonical_record":{"source":{"id":"1511.04648","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-15T03:17:45Z","cross_cats_sorted":[],"title_canon_sha256":"9446e9da801764a67cc8c95a573b206fb32d2a104ffea90df8e4aac31589cb68","abstract_canon_sha256":"5294724fb64b74e92bc7f3b9c16d161a0509a8aa51760a482cd2c3e4c5984db2"},"schema_version":"1.0"},"canonical_sha256":"972fafec33388b835429c3667d857b5bc8b7039b348a9fc987ba081e91dff37f","source":{"kind":"arxiv","id":"1511.04648","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04648","created_at":"2026-05-18T00:50:42Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04648v2","created_at":"2026-05-18T00:50:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04648","created_at":"2026-05-18T00:50:42Z"},{"alias_kind":"pith_short_12","alias_value":"S4X273BTHCFY","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S4X273BTHCFYGVBJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S4X273BT","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:S4X273BTHCFYGVBJYNTH3BL3LP","target":"record","payload":{"canonical_record":{"source":{"id":"1511.04648","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-15T03:17:45Z","cross_cats_sorted":[],"title_canon_sha256":"9446e9da801764a67cc8c95a573b206fb32d2a104ffea90df8e4aac31589cb68","abstract_canon_sha256":"5294724fb64b74e92bc7f3b9c16d161a0509a8aa51760a482cd2c3e4c5984db2"},"schema_version":"1.0"},"canonical_sha256":"972fafec33388b835429c3667d857b5bc8b7039b348a9fc987ba081e91dff37f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:42.932163Z","signature_b64":"Bo9HJbSK/tUjficBoItmhSabEtEbCMyN+3hwJj5jlw8nrsp8uNKF5R31D67oX2w71qLTsq2nyemq8qkz6bqTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"972fafec33388b835429c3667d857b5bc8b7039b348a9fc987ba081e91dff37f","last_reissued_at":"2026-05-18T00:50:42.931639Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:42.931639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.04648","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b8inIzWBKuUkYJjEUHjgE70lZAg40zbbEz4xgW7btuadOrRaD60JiUD19dP6Wa3McAkkH3OGCtUeSOd0HBp5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:41:07.313306Z"},"content_sha256":"5696716dc34359e946fbf1e8aa8a79367ce183c5bad54b95480d50f24901701f","schema_version":"1.0","event_id":"sha256:5696716dc34359e946fbf1e8aa8a79367ce183c5bad54b95480d50f24901701f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:S4X273BTHCFYGVBJYNTH3BL3LP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Superconvergence of Immersed Finite Element Methods for Interface Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Waixiang Cao, Xu Zhang, Zhimin Zhang","submitted_at":"2015-11-15T03:17:45Z","abstract_excerpt":"In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite element methods disappears unless the discontinuity of the coefficient is resolved by partition. We show that immersed finite element solutions inherit all desired superconvergence properties from standard finite element methods without requiring the mesh to be aligned with the interface. In particular, on interface elements, superconvergence occurs at roots of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04648","kind":"arxiv","version":2},"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":"2026-05-18T00:50:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7t5bgo53a5FEgFxWQjdhZ1lHtStXdbFE6i53IKAR7VYG4JscT28jKjCm9+/RwgskjGmbzJX3puHNZ6WPH030Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:41:07.314056Z"},"content_sha256":"5c1c5ff399849687e54f5c2d4969fe9d538d2fdad71772e9c55a84c0b3ae0b24","schema_version":"1.0","event_id":"sha256:5c1c5ff399849687e54f5c2d4969fe9d538d2fdad71772e9c55a84c0b3ae0b24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S4X273BTHCFYGVBJYNTH3BL3LP/bundle.json","state_url":"https://pith.science/pith/S4X273BTHCFYGVBJYNTH3BL3LP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S4X273BTHCFYGVBJYNTH3BL3LP/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":"2026-06-07T22:41:07Z","links":{"resolver":"https://pith.science/pith/S4X273BTHCFYGVBJYNTH3BL3LP","bundle":"https://pith.science/pith/S4X273BTHCFYGVBJYNTH3BL3LP/bundle.json","state":"https://pith.science/pith/S4X273BTHCFYGVBJYNTH3BL3LP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S4X273BTHCFYGVBJYNTH3BL3LP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S4X273BTHCFYGVBJYNTH3BL3LP","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":"5294724fb64b74e92bc7f3b9c16d161a0509a8aa51760a482cd2c3e4c5984db2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-15T03:17:45Z","title_canon_sha256":"9446e9da801764a67cc8c95a573b206fb32d2a104ffea90df8e4aac31589cb68"},"schema_version":"1.0","source":{"id":"1511.04648","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04648","created_at":"2026-05-18T00:50:42Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04648v2","created_at":"2026-05-18T00:50:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04648","created_at":"2026-05-18T00:50:42Z"},{"alias_kind":"pith_short_12","alias_value":"S4X273BTHCFY","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S4X273BTHCFYGVBJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S4X273BT","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:5c1c5ff399849687e54f5c2d4969fe9d538d2fdad71772e9c55a84c0b3ae0b24","target":"graph","created_at":"2026-05-18T00:50:42Z","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 article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite element methods disappears unless the discontinuity of the coefficient is resolved by partition. We show that immersed finite element solutions inherit all desired superconvergence properties from standard finite element methods without requiring the mesh to be aligned with the interface. In particular, on interface elements, superconvergence occurs at roots of ","authors_text":"Waixiang Cao, Xu Zhang, Zhimin Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-15T03:17:45Z","title":"Superconvergence of Immersed Finite Element Methods for Interface Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04648","kind":"arxiv","version":2},"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":"sha256:5696716dc34359e946fbf1e8aa8a79367ce183c5bad54b95480d50f24901701f","target":"record","created_at":"2026-05-18T00:50:42Z","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":"5294724fb64b74e92bc7f3b9c16d161a0509a8aa51760a482cd2c3e4c5984db2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-15T03:17:45Z","title_canon_sha256":"9446e9da801764a67cc8c95a573b206fb32d2a104ffea90df8e4aac31589cb68"},"schema_version":"1.0","source":{"id":"1511.04648","kind":"arxiv","version":2}},"canonical_sha256":"972fafec33388b835429c3667d857b5bc8b7039b348a9fc987ba081e91dff37f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"972fafec33388b835429c3667d857b5bc8b7039b348a9fc987ba081e91dff37f","first_computed_at":"2026-05-18T00:50:42.931639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:42.931639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bo9HJbSK/tUjficBoItmhSabEtEbCMyN+3hwJj5jlw8nrsp8uNKF5R31D67oX2w71qLTsq2nyemq8qkz6bqTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:42.932163Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04648","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5696716dc34359e946fbf1e8aa8a79367ce183c5bad54b95480d50f24901701f","sha256:5c1c5ff399849687e54f5c2d4969fe9d538d2fdad71772e9c55a84c0b3ae0b24"],"state_sha256":"85c0a3bfdac77386459da7603a0052bda9968429a41f96a9bc80b7f3fd50e7db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K/fk8jC9hv/Uvf5RAmdWPtHEctteR+C7fKUAzxaYimwe7UTrO8yMkkg2mg3k7zn8ditxnFTckT+NNCU5Y7E5Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:41:07.317883Z","bundle_sha256":"ca71295a59a98fdda2e2923770dc34579abf93f989c97b821d52c1d89d434667"}}