{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UWTPG7TKV5GNBQXU3MHACRQX3Q","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":"9c855d5ad349e62b18500a494fe8cfad69d932cb43078e180e50238a0a8e8015","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-08-31T07:58:01Z","title_canon_sha256":"a90e4942859153d929029ccd9c48fd84c335b0adc15e6513ddfc7ab577f89443"},"schema_version":"1.0","source":{"id":"1808.10621","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10621","created_at":"2026-05-18T00:02:09Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10621v2","created_at":"2026-05-18T00:02:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10621","created_at":"2026-05-18T00:02:09Z"},{"alias_kind":"pith_short_12","alias_value":"UWTPG7TKV5GN","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UWTPG7TKV5GNBQXU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UWTPG7TK","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:9542cd6ffa7757928c18ca932cdaf84ecdd505855d2e00c16d1f2a7f14064408","target":"graph","created_at":"2026-05-18T00:02:09Z","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":"It is proved that if a bounded domain in three dimensions satisfies a certain concavity condition, then the Neumann-Poincar\\'e operator on the boundary of the domain or its inversion in a sphere has at least one negative eigenvalue. The concavity condition is quite simple, and is satisfied if there is a point on the boundary at which the Gaussian curvature is negative.","authors_text":"Hyeonbae Kang, Yong-Gwan Ji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-08-31T07:58:01Z","title":"A concavity condition for existence of a negative Neumann-Poincar\\'e eigenvalue in three dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10621","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":"sha256:30123909a39c5e71c2a8bfca86b2ef22efaa138c56dd4946271f39f30fa7a9db","target":"record","created_at":"2026-05-18T00:02:09Z","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":"9c855d5ad349e62b18500a494fe8cfad69d932cb43078e180e50238a0a8e8015","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-08-31T07:58:01Z","title_canon_sha256":"a90e4942859153d929029ccd9c48fd84c335b0adc15e6513ddfc7ab577f89443"},"schema_version":"1.0","source":{"id":"1808.10621","kind":"arxiv","version":2}},"canonical_sha256":"a5a6f37e6aaf4cd0c2f4db0e014617dc02c8254a8f3d25b5c436e3c0894b9676","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5a6f37e6aaf4cd0c2f4db0e014617dc02c8254a8f3d25b5c436e3c0894b9676","first_computed_at":"2026-05-18T00:02:09.153141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:09.153141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YfSZxLKOmA66jZkQBLUsMLLLHG/ygPJQqIcTyYp2j5Ss8ajTvXt5oKFFCzfmZptHCsZDb7nnnNgb0ihC02SaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:09.153811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.10621","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30123909a39c5e71c2a8bfca86b2ef22efaa138c56dd4946271f39f30fa7a9db","sha256:9542cd6ffa7757928c18ca932cdaf84ecdd505855d2e00c16d1f2a7f14064408"],"state_sha256":"18b5ba3bd45c8c96bf6397b932376856e1ea403f1e1c054133e705019a1279a9"}