{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WR2LQD3G6AZGROEDZWNT536DSH","short_pith_number":"pith:WR2LQD3G","schema_version":"1.0","canonical_sha256":"b474b80f66f03268b883cd9b3eefc391f8dae4644da0fbcdf94590b26df2ec2b","source":{"kind":"arxiv","id":"1902.01315","version":4},"attestation_state":"computed","paper":{"title":"An Integral Equation Formulation of the $N$-Body Dielectric Spheres Problem. Part I: Numerical Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Benjamin Stamm, Muhammad Hassan","submitted_at":"2019-02-04T17:12:57Z","abstract_excerpt":"In this article, we analyse an integral equation of the second kind that represents the solution of $N$ interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the stability constants -- and thus the approximation error -- with respect to the number $N$ of involved dielectric spheres. We develop a new a priori error analysis that demonstrates $N$-independent stability of the continuous and discrete formulations of the integral equation. Consequently, we obtain convergence rates that are independent of $N$."},"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":"1902.01315","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-04T17:12:57Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2c354f8e008afd6727e37f8ac0b1fe910a091fd073fee84491f2a12f2a985084","abstract_canon_sha256":"5e907b526393c1292d16288640f8183e4d2eb3d58ad1cad5be472e768de7c551"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:17:56.155137Z","signature_b64":"gPEbY6TrcLfH6uAwGF3q0fD5Z3+hLifFUkGc3jeT/oMbW+41dAWRPtxLrznnVC/hRA0wR/Ih6JUArNd0H3ReCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b474b80f66f03268b883cd9b3eefc391f8dae4644da0fbcdf94590b26df2ec2b","last_reissued_at":"2026-07-05T01:17:56.154733Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:17:56.154733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Integral Equation Formulation of the $N$-Body Dielectric Spheres Problem. Part I: Numerical Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Benjamin Stamm, Muhammad Hassan","submitted_at":"2019-02-04T17:12:57Z","abstract_excerpt":"In this article, we analyse an integral equation of the second kind that represents the solution of $N$ interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the stability constants -- and thus the approximation error -- with respect to the number $N$ of involved dielectric spheres. We develop a new a priori error analysis that demonstrates $N$-independent stability of the continuous and discrete formulations of the integral equation. Consequently, we obtain convergence rates that are independent of $N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01315","kind":"arxiv","version":4},"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/1902.01315/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":"1902.01315","created_at":"2026-07-05T01:17:56.154792+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.01315v4","created_at":"2026-07-05T01:17:56.154792+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01315","created_at":"2026-07-05T01:17:56.154792+00:00"},{"alias_kind":"pith_short_12","alias_value":"WR2LQD3G6AZG","created_at":"2026-07-05T01:17:56.154792+00:00"},{"alias_kind":"pith_short_16","alias_value":"WR2LQD3G6AZGROED","created_at":"2026-07-05T01:17:56.154792+00:00"},{"alias_kind":"pith_short_8","alias_value":"WR2LQD3G","created_at":"2026-07-05T01:17:56.154792+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WR2LQD3G6AZGROEDZWNT536DSH","json":"https://pith.science/pith/WR2LQD3G6AZGROEDZWNT536DSH.json","graph_json":"https://pith.science/api/pith-number/WR2LQD3G6AZGROEDZWNT536DSH/graph.json","events_json":"https://pith.science/api/pith-number/WR2LQD3G6AZGROEDZWNT536DSH/events.json","paper":"https://pith.science/paper/WR2LQD3G"},"agent_actions":{"view_html":"https://pith.science/pith/WR2LQD3G6AZGROEDZWNT536DSH","download_json":"https://pith.science/pith/WR2LQD3G6AZGROEDZWNT536DSH.json","view_paper":"https://pith.science/paper/WR2LQD3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.01315&json=true","fetch_graph":"https://pith.science/api/pith-number/WR2LQD3G6AZGROEDZWNT536DSH/graph.json","fetch_events":"https://pith.science/api/pith-number/WR2LQD3G6AZGROEDZWNT536DSH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WR2LQD3G6AZGROEDZWNT536DSH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WR2LQD3G6AZGROEDZWNT536DSH/action/storage_attestation","attest_author":"https://pith.science/pith/WR2LQD3G6AZGROEDZWNT536DSH/action/author_attestation","sign_citation":"https://pith.science/pith/WR2LQD3G6AZGROEDZWNT536DSH/action/citation_signature","submit_replication":"https://pith.science/pith/WR2LQD3G6AZGROEDZWNT536DSH/action/replication_record"}},"created_at":"2026-07-05T01:17:56.154792+00:00","updated_at":"2026-07-05T01:17:56.154792+00:00"}