{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:WLSA5R2DQCLFUXNYZ3K4AUO6V2","short_pith_number":"pith:WLSA5R2D","schema_version":"1.0","canonical_sha256":"b2e40ec74380965a5db8ced5c051deae8bd700ace6faccd6bacc377b55c42ffb","source":{"kind":"arxiv","id":"2309.06862","version":2},"attestation_state":"computed","paper":{"title":"Domain Decomposition Method for Poisson--Boltzmann Equations based on Solvent Excluded Surface","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NT"],"primary_cat":"math.NA","authors_text":"Abhinav Jha, Benjamin Stamm","submitted_at":"2023-09-13T10:17:43Z","abstract_excerpt":"In this paper, we develop a domain decomposition method for the nonlinear Poisson-Boltzmann equation based on a solvent-excluded surface widely used in computational chemistry. The model relies on a nonlinear equation defined in $\\mathbb{R}^3$ with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for steric effects. Potential theory arguments transform the nonlinear equation into two coupled equations defined in a bounded domain. Then, the Schwarz decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2309.06862","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-09-13T10:17:43Z","cross_cats_sorted":["cs.NA","math.NT"],"title_canon_sha256":"d4af5488a7ef00c1efdd96e03b98496db1083c1e74c3dfb4cef3d981cde032a5","abstract_canon_sha256":"98c5f31995b8a38dbab87b395091ba0d798e8de94b5a13e0154e23f01561a9c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:04:33.553752Z","signature_b64":"cHInme54egKVZ6LH/drVOZeY1xm5aDMvmzJC/GOUw29TUC8s1ie+ra8Ol+B9X0dX4GnyIhaCQVqwzC2WPYC5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2e40ec74380965a5db8ced5c051deae8bd700ace6faccd6bacc377b55c42ffb","last_reissued_at":"2026-07-05T08:04:33.553234Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:04:33.553234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Domain Decomposition Method for Poisson--Boltzmann Equations based on Solvent Excluded Surface","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NT"],"primary_cat":"math.NA","authors_text":"Abhinav Jha, Benjamin Stamm","submitted_at":"2023-09-13T10:17:43Z","abstract_excerpt":"In this paper, we develop a domain decomposition method for the nonlinear Poisson-Boltzmann equation based on a solvent-excluded surface widely used in computational chemistry. The model relies on a nonlinear equation defined in $\\mathbb{R}^3$ with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for steric effects. Potential theory arguments transform the nonlinear equation into two coupled equations defined in a bounded domain. Then, the Schwarz decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.06862","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.06862/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2309.06862","created_at":"2026-07-05T08:04:33.553298+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.06862v2","created_at":"2026-07-05T08:04:33.553298+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.06862","created_at":"2026-07-05T08:04:33.553298+00:00"},{"alias_kind":"pith_short_12","alias_value":"WLSA5R2DQCLF","created_at":"2026-07-05T08:04:33.553298+00:00"},{"alias_kind":"pith_short_16","alias_value":"WLSA5R2DQCLFUXNY","created_at":"2026-07-05T08:04:33.553298+00:00"},{"alias_kind":"pith_short_8","alias_value":"WLSA5R2D","created_at":"2026-07-05T08:04:33.553298+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2408.14500","citing_title":"Some challenges of diffused interfaces in implicit-solvent models","ref_index":42,"is_internal_anchor":false},{"citing_arxiv_id":"2511.21713","citing_title":"A Self-Adjusting FEM-BEM Coupling Scheme for the Nonlinear Poisson-Boltzmann Equation","ref_index":24,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WLSA5R2DQCLFUXNYZ3K4AUO6V2","json":"https://pith.science/pith/WLSA5R2DQCLFUXNYZ3K4AUO6V2.json","graph_json":"https://pith.science/api/pith-number/WLSA5R2DQCLFUXNYZ3K4AUO6V2/graph.json","events_json":"https://pith.science/api/pith-number/WLSA5R2DQCLFUXNYZ3K4AUO6V2/events.json","paper":"https://pith.science/paper/WLSA5R2D"},"agent_actions":{"view_html":"https://pith.science/pith/WLSA5R2DQCLFUXNYZ3K4AUO6V2","download_json":"https://pith.science/pith/WLSA5R2DQCLFUXNYZ3K4AUO6V2.json","view_paper":"https://pith.science/paper/WLSA5R2D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.06862&json=true","fetch_graph":"https://pith.science/api/pith-number/WLSA5R2DQCLFUXNYZ3K4AUO6V2/graph.json","fetch_events":"https://pith.science/api/pith-number/WLSA5R2DQCLFUXNYZ3K4AUO6V2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WLSA5R2DQCLFUXNYZ3K4AUO6V2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WLSA5R2DQCLFUXNYZ3K4AUO6V2/action/storage_attestation","attest_author":"https://pith.science/pith/WLSA5R2DQCLFUXNYZ3K4AUO6V2/action/author_attestation","sign_citation":"https://pith.science/pith/WLSA5R2DQCLFUXNYZ3K4AUO6V2/action/citation_signature","submit_replication":"https://pith.science/pith/WLSA5R2DQCLFUXNYZ3K4AUO6V2/action/replication_record"}},"created_at":"2026-07-05T08:04:33.553298+00:00","updated_at":"2026-07-05T08:04:33.553298+00:00"}