{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YYRLAHW5LQPKG4BG2THE7MI535","short_pith_number":"pith:YYRLAHW5","canonical_record":{"source":{"id":"1208.3866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-08-19T16:56:04Z","cross_cats_sorted":["cs.MS","cs.NA"],"title_canon_sha256":"2f817946514b0de0503d8047e750589a45734c363094fbc346fe23f08e6258a9","abstract_canon_sha256":"2cd10cd1eb9895217069e19a6228c75fbc38cb0bf809a3326eabd8a0b54b7fc3"},"schema_version":"1.0"},"canonical_sha256":"c622b01edd5c1ea37026d4ce4fb11ddf6b21a1c151d9ceff9d5c2532ab64fae9","source":{"kind":"arxiv","id":"1208.3866","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3866","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3866v2","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3866","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"YYRLAHW5LQPK","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YYRLAHW5LQPKG4BG","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YYRLAHW5","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YYRLAHW5LQPKG4BG2THE7MI535","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-08-19T16:56:04Z","cross_cats_sorted":["cs.MS","cs.NA"],"title_canon_sha256":"2f817946514b0de0503d8047e750589a45734c363094fbc346fe23f08e6258a9","abstract_canon_sha256":"2cd10cd1eb9895217069e19a6228c75fbc38cb0bf809a3326eabd8a0b54b7fc3"},"schema_version":"1.0"},"canonical_sha256":"c622b01edd5c1ea37026d4ce4fb11ddf6b21a1c151d9ceff9d5c2532ab64fae9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:24.994848Z","signature_b64":"0ckKHwXPWMpxlpvjOhj1fhDVxXgN7D/y4XorqV4Iqn1ceVFKJaUbJtlsihPYOWPnxQjZekRqwpS4F4PIqQBWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c622b01edd5c1ea37026d4ce4fb11ddf6b21a1c151d9ceff9d5c2532ab64fae9","last_reissued_at":"2026-05-18T03:48:24.994207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:24.994207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3866","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":"2026-05-18T03:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+BvRANOwPbk/ynI0i1aD4qD1XX4VnOT3LKVSbhcpm8geeYhVxq/jHUrthTrL4zwWLzDWIcRqx+vAMeSlHSkAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:52:45.108577Z"},"content_sha256":"93999d3815e9c0e64e685cb21f07c090986e9ede44d4a901cc82b43d49f677fd","schema_version":"1.0","event_id":"sha256:93999d3815e9c0e64e685cb21f07c090986e9ede44d4a901cc82b43d49f677fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YYRLAHW5LQPKG4BG2THE7MI535","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical Nonlocal Electrostatics Using Eigenfunction Expansions of Boundary-Integral Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS","cs.NA"],"primary_cat":"physics.chem-ph","authors_text":"Jaydeep P. Bardhan, Matthew G. Knepley, Peter R. Brune","submitted_at":"2012-08-19T16:56:04Z","abstract_excerpt":"In this paper, we present an analytical solution to nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for analytical calculations in separable geometries, we rederive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion layer and then a dilu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3866","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":"2026-05-18T03:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CNE9+E2nBybtvzqIte+dDUolRLrzYe56nRU7nrVhlLdXDnK3YVDVywv9AI7aTXKY0IOYT8rzkP1vwRSnJG0BCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:52:45.109286Z"},"content_sha256":"5075ff5ae1333b81af1c8f960a33fc7227329ca92bf28a1bacb2a61ba47c879e","schema_version":"1.0","event_id":"sha256:5075ff5ae1333b81af1c8f960a33fc7227329ca92bf28a1bacb2a61ba47c879e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYRLAHW5LQPKG4BG2THE7MI535/bundle.json","state_url":"https://pith.science/pith/YYRLAHW5LQPKG4BG2THE7MI535/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYRLAHW5LQPKG4BG2THE7MI535/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":"2026-05-31T17:52:45Z","links":{"resolver":"https://pith.science/pith/YYRLAHW5LQPKG4BG2THE7MI535","bundle":"https://pith.science/pith/YYRLAHW5LQPKG4BG2THE7MI535/bundle.json","state":"https://pith.science/pith/YYRLAHW5LQPKG4BG2THE7MI535/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYRLAHW5LQPKG4BG2THE7MI535/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YYRLAHW5LQPKG4BG2THE7MI535","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":"2cd10cd1eb9895217069e19a6228c75fbc38cb0bf809a3326eabd8a0b54b7fc3","cross_cats_sorted":["cs.MS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-08-19T16:56:04Z","title_canon_sha256":"2f817946514b0de0503d8047e750589a45734c363094fbc346fe23f08e6258a9"},"schema_version":"1.0","source":{"id":"1208.3866","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3866","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3866v2","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3866","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"YYRLAHW5LQPK","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YYRLAHW5LQPKG4BG","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YYRLAHW5","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:5075ff5ae1333b81af1c8f960a33fc7227329ca92bf28a1bacb2a61ba47c879e","target":"graph","created_at":"2026-05-18T03:48:24Z","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 present an analytical solution to nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for analytical calculations in separable geometries, we rederive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion layer and then a dilu","authors_text":"Jaydeep P. Bardhan, Matthew G. Knepley, Peter R. Brune","cross_cats":["cs.MS","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-08-19T16:56:04Z","title":"Analytical Nonlocal Electrostatics Using Eigenfunction Expansions of Boundary-Integral Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3866","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":"sha256:93999d3815e9c0e64e685cb21f07c090986e9ede44d4a901cc82b43d49f677fd","target":"record","created_at":"2026-05-18T03:48:24Z","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":"2cd10cd1eb9895217069e19a6228c75fbc38cb0bf809a3326eabd8a0b54b7fc3","cross_cats_sorted":["cs.MS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-08-19T16:56:04Z","title_canon_sha256":"2f817946514b0de0503d8047e750589a45734c363094fbc346fe23f08e6258a9"},"schema_version":"1.0","source":{"id":"1208.3866","kind":"arxiv","version":2}},"canonical_sha256":"c622b01edd5c1ea37026d4ce4fb11ddf6b21a1c151d9ceff9d5c2532ab64fae9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c622b01edd5c1ea37026d4ce4fb11ddf6b21a1c151d9ceff9d5c2532ab64fae9","first_computed_at":"2026-05-18T03:48:24.994207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:24.994207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0ckKHwXPWMpxlpvjOhj1fhDVxXgN7D/y4XorqV4Iqn1ceVFKJaUbJtlsihPYOWPnxQjZekRqwpS4F4PIqQBWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:24.994848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3866","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93999d3815e9c0e64e685cb21f07c090986e9ede44d4a901cc82b43d49f677fd","sha256:5075ff5ae1333b81af1c8f960a33fc7227329ca92bf28a1bacb2a61ba47c879e"],"state_sha256":"e49d08798f93b3fa100f3350a695924968ea5bc51a9d141c190670117beaf59b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kEtbRfclE1fn3xwi4YpXh2p5wVXkGJjlYb9sCt8mqDP15A1nholonLYdnNC1HkaENejFSw2uO8u14MbcjtieBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:52:45.113240Z","bundle_sha256":"7221195ae65cda48e49435625564d5fd617eda37e4acf909e3dce3afa2ea1cb1"}}