{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EKWGOAFDMLH4ZLS5Y3QSGBHIEG","short_pith_number":"pith:EKWGOAFD","canonical_record":{"source":{"id":"1805.11441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-29T13:31:15Z","cross_cats_sorted":[],"title_canon_sha256":"d2a5fef965b03199eb9d503c5f0c7a5f04f7d4b4f5b68823bdd2f220b62fc8f1","abstract_canon_sha256":"32e40c5b50a1e132ed5eda55dcafbf92a85e43bdf30106873efe525d031a64b4"},"schema_version":"1.0"},"canonical_sha256":"22ac6700a362cfccae5dc6e12304e8218df75645bb6d137484263cdbf3db91d8","source":{"kind":"arxiv","id":"1805.11441","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11441","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11441v1","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11441","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"pith_short_12","alias_value":"EKWGOAFDMLH4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EKWGOAFDMLH4ZLS5","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EKWGOAFD","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EKWGOAFDMLH4ZLS5Y3QSGBHIEG","target":"record","payload":{"canonical_record":{"source":{"id":"1805.11441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-29T13:31:15Z","cross_cats_sorted":[],"title_canon_sha256":"d2a5fef965b03199eb9d503c5f0c7a5f04f7d4b4f5b68823bdd2f220b62fc8f1","abstract_canon_sha256":"32e40c5b50a1e132ed5eda55dcafbf92a85e43bdf30106873efe525d031a64b4"},"schema_version":"1.0"},"canonical_sha256":"22ac6700a362cfccae5dc6e12304e8218df75645bb6d137484263cdbf3db91d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:42.552986Z","signature_b64":"FGLMFX9q/VbwFgj5WLd/3vLOOrntkPXnA6OGV5WVxCU4YRFvDQq4uIIVteTX6iI/avx9eqTE1ll7KEteE3qvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22ac6700a362cfccae5dc6e12304e8218df75645bb6d137484263cdbf3db91d8","last_reissued_at":"2026-05-18T00:14:42.552368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:42.552368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.11441","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":"2026-05-18T00:14:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9A3Y6YxmobOzMv45e+kympRLnMW44SS/2ipQ8NLiU3M8MJ9Du40mcZZlv1erPSbGWtHgMj2PTUZ5SVPDdTWUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:37:56.325525Z"},"content_sha256":"604576b871e73925838a764fba8fbea06452983effc6432bbc1d9fc2536c1f21","schema_version":"1.0","event_id":"sha256:604576b871e73925838a764fba8fbea06452983effc6432bbc1d9fc2536c1f21"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EKWGOAFDMLH4ZLS5Y3QSGBHIEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reliable computer simulation methods for electrostatic biomolecular models based on the Poisson-Boltzmann equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Johannes Kraus, Sergey Repin, Svetoslav Nakov","submitted_at":"2018-05-29T13:31:15Z","abstract_excerpt":"In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can serve as a basis for a reliable adaptive finite element algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11441","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":"2026-05-18T00:14:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ajnjNYOVY5LkRYcgqBrbdTS6C9IUo5A+5zV9wgbD8I63+3Wpr0lrkg09XrWdsDTPKiBZPIhNgyAXxwEMbtCNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:37:56.325926Z"},"content_sha256":"667151de2a0d068d9f6f11e28addd84b5bd1c78c92cb77dbaf4586618f9310e4","schema_version":"1.0","event_id":"sha256:667151de2a0d068d9f6f11e28addd84b5bd1c78c92cb77dbaf4586618f9310e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKWGOAFDMLH4ZLS5Y3QSGBHIEG/bundle.json","state_url":"https://pith.science/pith/EKWGOAFDMLH4ZLS5Y3QSGBHIEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKWGOAFDMLH4ZLS5Y3QSGBHIEG/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":"2026-05-26T21:37:56Z","links":{"resolver":"https://pith.science/pith/EKWGOAFDMLH4ZLS5Y3QSGBHIEG","bundle":"https://pith.science/pith/EKWGOAFDMLH4ZLS5Y3QSGBHIEG/bundle.json","state":"https://pith.science/pith/EKWGOAFDMLH4ZLS5Y3QSGBHIEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKWGOAFDMLH4ZLS5Y3QSGBHIEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EKWGOAFDMLH4ZLS5Y3QSGBHIEG","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":"32e40c5b50a1e132ed5eda55dcafbf92a85e43bdf30106873efe525d031a64b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-29T13:31:15Z","title_canon_sha256":"d2a5fef965b03199eb9d503c5f0c7a5f04f7d4b4f5b68823bdd2f220b62fc8f1"},"schema_version":"1.0","source":{"id":"1805.11441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11441","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11441v1","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11441","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"pith_short_12","alias_value":"EKWGOAFDMLH4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EKWGOAFDMLH4ZLS5","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EKWGOAFD","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:667151de2a0d068d9f6f11e28addd84b5bd1c78c92cb77dbaf4586618f9310e4","target":"graph","created_at":"2026-05-18T00:14:42Z","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 paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can serve as a basis for a reliable adaptive finite element algorithm.","authors_text":"Johannes Kraus, Sergey Repin, Svetoslav Nakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-29T13:31:15Z","title":"Reliable computer simulation methods for electrostatic biomolecular models based on the Poisson-Boltzmann equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11441","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":"sha256:604576b871e73925838a764fba8fbea06452983effc6432bbc1d9fc2536c1f21","target":"record","created_at":"2026-05-18T00:14:42Z","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":"32e40c5b50a1e132ed5eda55dcafbf92a85e43bdf30106873efe525d031a64b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-29T13:31:15Z","title_canon_sha256":"d2a5fef965b03199eb9d503c5f0c7a5f04f7d4b4f5b68823bdd2f220b62fc8f1"},"schema_version":"1.0","source":{"id":"1805.11441","kind":"arxiv","version":1}},"canonical_sha256":"22ac6700a362cfccae5dc6e12304e8218df75645bb6d137484263cdbf3db91d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22ac6700a362cfccae5dc6e12304e8218df75645bb6d137484263cdbf3db91d8","first_computed_at":"2026-05-18T00:14:42.552368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:42.552368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FGLMFX9q/VbwFgj5WLd/3vLOOrntkPXnA6OGV5WVxCU4YRFvDQq4uIIVteTX6iI/avx9eqTE1ll7KEteE3qvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:42.552986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:604576b871e73925838a764fba8fbea06452983effc6432bbc1d9fc2536c1f21","sha256:667151de2a0d068d9f6f11e28addd84b5bd1c78c92cb77dbaf4586618f9310e4"],"state_sha256":"36acb39ca89e8cf1f49983da0c36a2af3ecaa2d2e1f95594b93b92eb5cb91bf7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/MnQsyCHOhsIGXOr6XO6wUh4ggLcZhNZLmChDPhEOjMNea9cqZgbm8BNjg8c94ycvVACzGebUjXDP2ZXj4zrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:37:56.328508Z","bundle_sha256":"b4b274fba3417966f15883be42a0f68ea167fe6549658ef0981a9a6196e8e356"}}