{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:B3OPXXUFQ6IV6UCLD4ARWQ657U","short_pith_number":"pith:B3OPXXUF","canonical_record":{"source":{"id":"1212.0537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-02T23:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"ac0c71b601813d8cd85581d4edf0fa0dfb6552402f499eed53eb11fb17a8263f","abstract_canon_sha256":"b7f6c5030926f1ac0e0b5b95082b1b41e5615f7bb1606965f4011e9799903d23"},"schema_version":"1.0"},"canonical_sha256":"0edcfbde8587915f504b1f011b43ddfd186716bfe3344a85c2ce7205a09c181c","source":{"kind":"arxiv","id":"1212.0537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0537","created_at":"2026-05-18T03:39:15Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0537v1","created_at":"2026-05-18T03:39:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0537","created_at":"2026-05-18T03:39:15Z"},{"alias_kind":"pith_short_12","alias_value":"B3OPXXUFQ6IV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B3OPXXUFQ6IV6UCL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B3OPXXUF","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:B3OPXXUFQ6IV6UCLD4ARWQ657U","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-02T23:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"ac0c71b601813d8cd85581d4edf0fa0dfb6552402f499eed53eb11fb17a8263f","abstract_canon_sha256":"b7f6c5030926f1ac0e0b5b95082b1b41e5615f7bb1606965f4011e9799903d23"},"schema_version":"1.0"},"canonical_sha256":"0edcfbde8587915f504b1f011b43ddfd186716bfe3344a85c2ce7205a09c181c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:15.801663Z","signature_b64":"BKU3EYNAbQ9FpPSYP8NXqlmDpD+6JF7OSks8Eo/Xl+aAFDCZs7NuYfHHE/crdiSgCF3jO57l7O7AI9KRHuAXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0edcfbde8587915f504b1f011b43ddfd186716bfe3344a85c2ce7205a09c181c","last_reissued_at":"2026-05-18T03:39:15.801044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:15.801044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0537","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":"2026-05-18T03:39:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W8Fwqbqr0mUxpEc6a4o1M1Fsm44nX273vhwSB1DFBawbd7hHl8zpvuOKFIWLkwBr5NypcgOiaCJo9F4a57hADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:11:21.202606Z"},"content_sha256":"af865d1b85675ff0d6cf35355487944df1d8cc320290f2ebcdb11cb5772d7d7c","schema_version":"1.0","event_id":"sha256:af865d1b85675ff0d6cf35355487944df1d8cc320290f2ebcdb11cb5772d7d7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:B3OPXXUFQ6IV6UCLD4ARWQ657U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local discontinuous Galerkin methods for one-dimensional second order fully nonlinear elliptic and parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Thomas Lewis, Xiaobing Feng","submitted_at":"2012-12-02T23:58:52Z","abstract_excerpt":"This paper is concerned with developing accurate and efficient discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary goal of the paper to develop a general framework for constructing high order local discontinuous Galerkin (LDG) methods for approximating viscosity solutions of these fully nonlinear PDEs which are merely continuous functions by definition. In order to capture discontinuities of the first order derivative $u_x$ of the solution $u$, two independent functions $q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0537","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":"2026-05-18T03:39:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LwvU/HP+b7t6UPxRxz8POoAjZjvLVsXgo7wLbVK3KUyVWKXge/nERZ0rOUWg/jX+yLQ/TI4gphrjUEjGnX9UDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:11:21.203171Z"},"content_sha256":"35926d401c7a66183193ca5b9fbd3d7854b4bb2a6ea557945ec8a6e597c9c674","schema_version":"1.0","event_id":"sha256:35926d401c7a66183193ca5b9fbd3d7854b4bb2a6ea557945ec8a6e597c9c674"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3OPXXUFQ6IV6UCLD4ARWQ657U/bundle.json","state_url":"https://pith.science/pith/B3OPXXUFQ6IV6UCLD4ARWQ657U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3OPXXUFQ6IV6UCLD4ARWQ657U/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":"2026-06-04T10:11:21Z","links":{"resolver":"https://pith.science/pith/B3OPXXUFQ6IV6UCLD4ARWQ657U","bundle":"https://pith.science/pith/B3OPXXUFQ6IV6UCLD4ARWQ657U/bundle.json","state":"https://pith.science/pith/B3OPXXUFQ6IV6UCLD4ARWQ657U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3OPXXUFQ6IV6UCLD4ARWQ657U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B3OPXXUFQ6IV6UCLD4ARWQ657U","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":"b7f6c5030926f1ac0e0b5b95082b1b41e5615f7bb1606965f4011e9799903d23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-02T23:58:52Z","title_canon_sha256":"ac0c71b601813d8cd85581d4edf0fa0dfb6552402f499eed53eb11fb17a8263f"},"schema_version":"1.0","source":{"id":"1212.0537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0537","created_at":"2026-05-18T03:39:15Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0537v1","created_at":"2026-05-18T03:39:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0537","created_at":"2026-05-18T03:39:15Z"},{"alias_kind":"pith_short_12","alias_value":"B3OPXXUFQ6IV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B3OPXXUFQ6IV6UCL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B3OPXXUF","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:35926d401c7a66183193ca5b9fbd3d7854b4bb2a6ea557945ec8a6e597c9c674","target":"graph","created_at":"2026-05-18T03:39:15Z","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 is concerned with developing accurate and efficient discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary goal of the paper to develop a general framework for constructing high order local discontinuous Galerkin (LDG) methods for approximating viscosity solutions of these fully nonlinear PDEs which are merely continuous functions by definition. In order to capture discontinuities of the first order derivative $u_x$ of the solution $u$, two independent functions $q","authors_text":"Thomas Lewis, Xiaobing Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-02T23:58:52Z","title":"Local discontinuous Galerkin methods for one-dimensional second order fully nonlinear elliptic and parabolic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0537","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:af865d1b85675ff0d6cf35355487944df1d8cc320290f2ebcdb11cb5772d7d7c","target":"record","created_at":"2026-05-18T03:39:15Z","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":"b7f6c5030926f1ac0e0b5b95082b1b41e5615f7bb1606965f4011e9799903d23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-02T23:58:52Z","title_canon_sha256":"ac0c71b601813d8cd85581d4edf0fa0dfb6552402f499eed53eb11fb17a8263f"},"schema_version":"1.0","source":{"id":"1212.0537","kind":"arxiv","version":1}},"canonical_sha256":"0edcfbde8587915f504b1f011b43ddfd186716bfe3344a85c2ce7205a09c181c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0edcfbde8587915f504b1f011b43ddfd186716bfe3344a85c2ce7205a09c181c","first_computed_at":"2026-05-18T03:39:15.801044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:15.801044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BKU3EYNAbQ9FpPSYP8NXqlmDpD+6JF7OSks8Eo/Xl+aAFDCZs7NuYfHHE/crdiSgCF3jO57l7O7AI9KRHuAXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:15.801663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af865d1b85675ff0d6cf35355487944df1d8cc320290f2ebcdb11cb5772d7d7c","sha256:35926d401c7a66183193ca5b9fbd3d7854b4bb2a6ea557945ec8a6e597c9c674"],"state_sha256":"1f2572a7bafbffff2f09c3b143ea87f089a948f498606772708ce6c86251500d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QC2gLIuLA4kLhR7pjw68M9tS/acRXwW/8u4Xrz6FXm5qOjrwiR/8W3qcJqhOisGr1gchA736tr9Syv0TvMD+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:11:21.205199Z","bundle_sha256":"3d9a175136c9d97f37c431f8147f8c64799bf280fd7399e1fe9ac4e53088f222"}}