{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4WMLQ4SDBFQML5DRPPNNAS4VTA","short_pith_number":"pith:4WMLQ4SD","canonical_record":{"source":{"id":"1605.04364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-14T01:53:48Z","cross_cats_sorted":[],"title_canon_sha256":"098c57f1b4e1de7261c2668417923b21dae5b538837825fa2c1b5e302d3fbc2c","abstract_canon_sha256":"a53d5b8e3260e1b0fbdb44683b17b0aa36beb0f0382cfaa505df44790cf8e927"},"schema_version":"1.0"},"canonical_sha256":"e598b872430960c5f4717bdad04b95982f9f741dd82412f6454cfdbfca54c35f","source":{"kind":"arxiv","id":"1605.04364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04364","created_at":"2026-05-18T01:14:51Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04364v1","created_at":"2026-05-18T01:14:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04364","created_at":"2026-05-18T01:14:51Z"},{"alias_kind":"pith_short_12","alias_value":"4WMLQ4SDBFQM","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4WMLQ4SDBFQML5DR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4WMLQ4SD","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4WMLQ4SDBFQML5DRPPNNAS4VTA","target":"record","payload":{"canonical_record":{"source":{"id":"1605.04364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-14T01:53:48Z","cross_cats_sorted":[],"title_canon_sha256":"098c57f1b4e1de7261c2668417923b21dae5b538837825fa2c1b5e302d3fbc2c","abstract_canon_sha256":"a53d5b8e3260e1b0fbdb44683b17b0aa36beb0f0382cfaa505df44790cf8e927"},"schema_version":"1.0"},"canonical_sha256":"e598b872430960c5f4717bdad04b95982f9f741dd82412f6454cfdbfca54c35f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:51.908597Z","signature_b64":"c6QaYDIUYW4LYRl2yF+jx6Az/QhNycGY7vqQzOqJVgcpGpnQQPaZA8gxX9ut+EEeoBRiWOLmNo20LuhWAlK8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e598b872430960c5f4717bdad04b95982f9f741dd82412f6454cfdbfca54c35f","last_reissued_at":"2026-05-18T01:14:51.908158Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:51.908158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.04364","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":"2026-05-18T01:14:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3K/7YlhK+m8tDivdSegE3qpbgauJcUgEn7XDHmgpq9Jwk0gnOLECnzsi9Aob2s2TNVIDu4vhQzMbewcrnAOZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:05:36.142568Z"},"content_sha256":"52689037dd9833e60987d0bf51d1e0173a0ea07c2e0b1114c4c35d72e87cc06f","schema_version":"1.0","event_id":"sha256:52689037dd9833e60987d0bf51d1e0173a0ea07c2e0b1114c4c35d72e87cc06f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4WMLQ4SDBFQML5DRPPNNAS4VTA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interior Penalty Discontinuous Galerkin Methods for Second Order Linear Non-Divergence Form Elliptic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Michael Neilan, Stefan Schnake, Xiaobing Feng","submitted_at":"2016-05-14T01:53:48Z","abstract_excerpt":"This paper develops interior penalty discontinuous Galerkin (IP-DG) methods to approximate $W^{2,p}$ strong solutions of second order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients. The proposed IP-DG methods are closely related to the IP-DG methods for advection-diffusion equations, and they are easy to implement on existing standard IP-DG software platforms. It is proved that the proposed IP-DG methods have unique solutions and converge with optimal rate to the $W^{2,p}$ strong solution in a discrete $W^{2,p}$-norm. The crux of the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04364","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":"2026-05-18T01:14:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rcc6TtyqWOv0u2i9nLlY1AcrIMnkcPQ+uhmJ/lOoYq5PLfUFUEJUYp4VN6o6urwPz4Na83SrWiHsydx/ZE4PBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:05:36.143250Z"},"content_sha256":"57afff16457e97b97a7ecd8bbddf970ec73f267ce749c4894629afc6712d9240","schema_version":"1.0","event_id":"sha256:57afff16457e97b97a7ecd8bbddf970ec73f267ce749c4894629afc6712d9240"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WMLQ4SDBFQML5DRPPNNAS4VTA/bundle.json","state_url":"https://pith.science/pith/4WMLQ4SDBFQML5DRPPNNAS4VTA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WMLQ4SDBFQML5DRPPNNAS4VTA/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":"2026-05-28T19:05:36Z","links":{"resolver":"https://pith.science/pith/4WMLQ4SDBFQML5DRPPNNAS4VTA","bundle":"https://pith.science/pith/4WMLQ4SDBFQML5DRPPNNAS4VTA/bundle.json","state":"https://pith.science/pith/4WMLQ4SDBFQML5DRPPNNAS4VTA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WMLQ4SDBFQML5DRPPNNAS4VTA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4WMLQ4SDBFQML5DRPPNNAS4VTA","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":"a53d5b8e3260e1b0fbdb44683b17b0aa36beb0f0382cfaa505df44790cf8e927","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-14T01:53:48Z","title_canon_sha256":"098c57f1b4e1de7261c2668417923b21dae5b538837825fa2c1b5e302d3fbc2c"},"schema_version":"1.0","source":{"id":"1605.04364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04364","created_at":"2026-05-18T01:14:51Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04364v1","created_at":"2026-05-18T01:14:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04364","created_at":"2026-05-18T01:14:51Z"},{"alias_kind":"pith_short_12","alias_value":"4WMLQ4SDBFQM","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4WMLQ4SDBFQML5DR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4WMLQ4SD","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:57afff16457e97b97a7ecd8bbddf970ec73f267ce749c4894629afc6712d9240","target":"graph","created_at":"2026-05-18T01:14:51Z","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":"This paper develops interior penalty discontinuous Galerkin (IP-DG) methods to approximate $W^{2,p}$ strong solutions of second order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients. The proposed IP-DG methods are closely related to the IP-DG methods for advection-diffusion equations, and they are easy to implement on existing standard IP-DG software platforms. It is proved that the proposed IP-DG methods have unique solutions and converge with optimal rate to the $W^{2,p}$ strong solution in a discrete $W^{2,p}$-norm. The crux of the a","authors_text":"Michael Neilan, Stefan Schnake, Xiaobing Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-14T01:53:48Z","title":"Interior Penalty Discontinuous Galerkin Methods for Second Order Linear Non-Divergence Form Elliptic PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04364","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":"sha256:52689037dd9833e60987d0bf51d1e0173a0ea07c2e0b1114c4c35d72e87cc06f","target":"record","created_at":"2026-05-18T01:14:51Z","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":"a53d5b8e3260e1b0fbdb44683b17b0aa36beb0f0382cfaa505df44790cf8e927","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-14T01:53:48Z","title_canon_sha256":"098c57f1b4e1de7261c2668417923b21dae5b538837825fa2c1b5e302d3fbc2c"},"schema_version":"1.0","source":{"id":"1605.04364","kind":"arxiv","version":1}},"canonical_sha256":"e598b872430960c5f4717bdad04b95982f9f741dd82412f6454cfdbfca54c35f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e598b872430960c5f4717bdad04b95982f9f741dd82412f6454cfdbfca54c35f","first_computed_at":"2026-05-18T01:14:51.908158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:51.908158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c6QaYDIUYW4LYRl2yF+jx6Az/QhNycGY7vqQzOqJVgcpGpnQQPaZA8gxX9ut+EEeoBRiWOLmNo20LuhWAlK8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:51.908597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52689037dd9833e60987d0bf51d1e0173a0ea07c2e0b1114c4c35d72e87cc06f","sha256:57afff16457e97b97a7ecd8bbddf970ec73f267ce749c4894629afc6712d9240"],"state_sha256":"8977f80f82be674e2f1aebdba2b7a560cccb5b8d4dd576adac2873458ca6d613"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3d+kBx4NhcRvmPhCEA5oFUwgIRVRxBmUynKL106agwO63wJfuQV887MTDkKGW2+oCn9Nf4849tbnoIMZoXy6Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:05:36.147115Z","bundle_sha256":"582a42f46d60868a4e1521c5e5937613fad5432caeaa8ce328f778c890ac9ddd"}}