{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IIENI3HXXKLGW2B2Z6GU7LXJNC","short_pith_number":"pith:IIENI3HX","canonical_record":{"source":{"id":"1806.00950","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-06-04T04:44:25Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"8259cd41b8aa90876c83b419677cc7833e399a4deaa417804eeb2d75a5ba18e8","abstract_canon_sha256":"ab766de9d3616921c3f6419b16c3c88e3b6e65420869522cc800b8e55aca5801"},"schema_version":"1.0"},"canonical_sha256":"4208d46cf7ba966b683acf8d4faee968af8f94f8020ca66b120da76e702e561e","source":{"kind":"arxiv","id":"1806.00950","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00950","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00950v4","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00950","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"IIENI3HXXKLG","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IIENI3HXXKLGW2B2","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IIENI3HX","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IIENI3HXXKLGW2B2Z6GU7LXJNC","target":"record","payload":{"canonical_record":{"source":{"id":"1806.00950","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-06-04T04:44:25Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"8259cd41b8aa90876c83b419677cc7833e399a4deaa417804eeb2d75a5ba18e8","abstract_canon_sha256":"ab766de9d3616921c3f6419b16c3c88e3b6e65420869522cc800b8e55aca5801"},"schema_version":"1.0"},"canonical_sha256":"4208d46cf7ba966b683acf8d4faee968af8f94f8020ca66b120da76e702e561e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:18.272190Z","signature_b64":"838vR7JIlElUtPrTiweampNQuvWHQlPo3etakCsMGyJi6b3FyTBjOlPF78caGdU4r7yZfTGT1GE5AZR+xyL4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4208d46cf7ba966b683acf8d4faee968af8f94f8020ca66b120da76e702e561e","last_reissued_at":"2026-05-17T23:52:18.271379Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:18.271379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.00950","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7BX3BSIZmVormtpbqvdnajIXmx1pDydhAbK6CSLbVueKOSQ5kBmtPJnIc7lRZYrxxmvNHVzX1m5MAC4IL+9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:08:04.149117Z"},"content_sha256":"699e61d8bc5a937e4def32dd70909cd20da1f10e2e8388fb3781a4768f574a89","schema_version":"1.0","event_id":"sha256:699e61d8bc5a937e4def32dd70909cd20da1f10e2e8388fb3781a4768f574a89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IIENI3HXXKLGW2B2Z6GU7LXJNC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embedded eigenvalues for the Neumann-Poincar\\'e operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.SP","authors_text":"Stephen P. Shipman, Wei Li","submitted_at":"2018-06-04T04:44:25Z","abstract_excerpt":"The Neumann-Poincar\\'e operator is a boundary-integral operator associated with harmonic layer potentials. This article proves the existence of eigenvalues within the essential spectrum for the Neumann-Poincar\\'e operator for certain Lipschitz curves in the plane with reflectional symmetry, when considered in the functional space in which it is self-adjoint. The proof combines the compactness of the Neumann-Poincar\\'e operator for curves of class $C^{2,\\alpha}$ with the essential spectrum generated by a corner. Eigenvalues corresponding to even (odd) eigenfunctions are proved to lie within the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00950","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":""},"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":"2026-05-17T23:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AV00yw448fZBkj9zKcDZ28RNbT3GJwaCsQt6157jXnBXVDlRWFO5USqSCtqXEodG1nh5An0KFs1UyI0k5JMJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:08:04.149479Z"},"content_sha256":"a6f0c7f908120ab5cc1cab5db4f0948b1f82c0dab116ff1a1b0df30d0041dcc2","schema_version":"1.0","event_id":"sha256:a6f0c7f908120ab5cc1cab5db4f0948b1f82c0dab116ff1a1b0df30d0041dcc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IIENI3HXXKLGW2B2Z6GU7LXJNC/bundle.json","state_url":"https://pith.science/pith/IIENI3HXXKLGW2B2Z6GU7LXJNC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IIENI3HXXKLGW2B2Z6GU7LXJNC/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":"2026-06-04T23:08:04Z","links":{"resolver":"https://pith.science/pith/IIENI3HXXKLGW2B2Z6GU7LXJNC","bundle":"https://pith.science/pith/IIENI3HXXKLGW2B2Z6GU7LXJNC/bundle.json","state":"https://pith.science/pith/IIENI3HXXKLGW2B2Z6GU7LXJNC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IIENI3HXXKLGW2B2Z6GU7LXJNC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IIENI3HXXKLGW2B2Z6GU7LXJNC","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":"ab766de9d3616921c3f6419b16c3c88e3b6e65420869522cc800b8e55aca5801","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-06-04T04:44:25Z","title_canon_sha256":"8259cd41b8aa90876c83b419677cc7833e399a4deaa417804eeb2d75a5ba18e8"},"schema_version":"1.0","source":{"id":"1806.00950","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00950","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00950v4","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00950","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"IIENI3HXXKLG","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IIENI3HXXKLGW2B2","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IIENI3HX","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:a6f0c7f908120ab5cc1cab5db4f0948b1f82c0dab116ff1a1b0df30d0041dcc2","target":"graph","created_at":"2026-05-17T23:52:18Z","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":"The Neumann-Poincar\\'e operator is a boundary-integral operator associated with harmonic layer potentials. This article proves the existence of eigenvalues within the essential spectrum for the Neumann-Poincar\\'e operator for certain Lipschitz curves in the plane with reflectional symmetry, when considered in the functional space in which it is self-adjoint. The proof combines the compactness of the Neumann-Poincar\\'e operator for curves of class $C^{2,\\alpha}$ with the essential spectrum generated by a corner. Eigenvalues corresponding to even (odd) eigenfunctions are proved to lie within the","authors_text":"Stephen P. Shipman, Wei Li","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-06-04T04:44:25Z","title":"Embedded eigenvalues for the Neumann-Poincar\\'e operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00950","kind":"arxiv","version":4},"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":"sha256:699e61d8bc5a937e4def32dd70909cd20da1f10e2e8388fb3781a4768f574a89","target":"record","created_at":"2026-05-17T23:52:18Z","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":"ab766de9d3616921c3f6419b16c3c88e3b6e65420869522cc800b8e55aca5801","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-06-04T04:44:25Z","title_canon_sha256":"8259cd41b8aa90876c83b419677cc7833e399a4deaa417804eeb2d75a5ba18e8"},"schema_version":"1.0","source":{"id":"1806.00950","kind":"arxiv","version":4}},"canonical_sha256":"4208d46cf7ba966b683acf8d4faee968af8f94f8020ca66b120da76e702e561e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4208d46cf7ba966b683acf8d4faee968af8f94f8020ca66b120da76e702e561e","first_computed_at":"2026-05-17T23:52:18.271379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:18.271379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"838vR7JIlElUtPrTiweampNQuvWHQlPo3etakCsMGyJi6b3FyTBjOlPF78caGdU4r7yZfTGT1GE5AZR+xyL4Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:18.272190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00950","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:699e61d8bc5a937e4def32dd70909cd20da1f10e2e8388fb3781a4768f574a89","sha256:a6f0c7f908120ab5cc1cab5db4f0948b1f82c0dab116ff1a1b0df30d0041dcc2"],"state_sha256":"624d88f0599ef0aee6910178b5dc59003bf439bfdf14a36f7a791543d63a0ddb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUrW1Wh4oRM/eGsDcKn3cXQw1UV4kBZoFQVrsrejwy5yqLrA6w4yZA+obKzhsmyqRnOCooT0aXFwN9gudIO4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:08:04.151552Z","bundle_sha256":"ad14256d22fc57151b258cee1342155007676ea94f036c7724771e66893418d5"}}