{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PSSZG2MOMY4CRRK4Z5KEXND5I6","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":"16d93d6f5c824e0f0e401ea1b6285e051c452b3ce473e59b1e6c7b4d9a601187","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-08T19:05:20Z","title_canon_sha256":"5d97a4eae388f3708675be6926432f2e4d3ddbb789601cfe8d78cd1175ce14f6"},"schema_version":"1.0","source":{"id":"1409.2466","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2466","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2466v1","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2466","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"pith_short_12","alias_value":"PSSZG2MOMY4C","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PSSZG2MOMY4CRRK4","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PSSZG2MO","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:08a434e7c003cca188526a40e6e76b4e2d2075903723a94c5e6633ed7755987a","target":"graph","created_at":"2026-05-18T02:43:16Z","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 presents a simple and effective new numerical scheme for the computation of electrostatic fields exterior to a collection of close-to-touching discs. The method is presented in detail for the two-cylinder case. The key idea is to represent the required complex potential using a hybrid set of basis functions comprising the usual Fourier-Laurent expansion about each circle centre comple- mented by a subsidiary expansion in a variable associated with conformal mapping of the physical domain to a concentric annulus domain. We also rigorously prove that there is a representation of the s","authors_text":"D.G. Crowdy, S. Tanveer, T. Delillo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-08T19:05:20Z","title":"Hybrid Basis Scheme for computing Electrostatic fields exterior to close-to-touching discs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2466","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":"sha256:202f8bd66d050ed3c4e33180fbf0ebd14a0727a502f2cdc6a75e7a9c037c5b7e","target":"record","created_at":"2026-05-18T02:43:16Z","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":"16d93d6f5c824e0f0e401ea1b6285e051c452b3ce473e59b1e6c7b4d9a601187","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-08T19:05:20Z","title_canon_sha256":"5d97a4eae388f3708675be6926432f2e4d3ddbb789601cfe8d78cd1175ce14f6"},"schema_version":"1.0","source":{"id":"1409.2466","kind":"arxiv","version":1}},"canonical_sha256":"7ca593698e663828c55ccf544bb47d47a525cc758fbcf4156f1daddb3daa847d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ca593698e663828c55ccf544bb47d47a525cc758fbcf4156f1daddb3daa847d","first_computed_at":"2026-05-18T02:43:16.943820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:16.943820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AmNbTrDFamaNa/3riyU7q/42l0z+bswM9Dvcs706G39mnMZDAQW1W0aS4Dn30uTmXOY5ogg1vJAuSg3R3TrMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:16.944413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2466","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:202f8bd66d050ed3c4e33180fbf0ebd14a0727a502f2cdc6a75e7a9c037c5b7e","sha256:08a434e7c003cca188526a40e6e76b4e2d2075903723a94c5e6633ed7755987a"],"state_sha256":"da419acff3fba182164cb8f23ccceee86607caadb5ba2e150a5de612bb9c8e24"}