{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XE6YLXZZPSA7JT6VHMBM4LK5AG","short_pith_number":"pith:XE6YLXZZ","canonical_record":{"source":{"id":"1811.05070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-11-13T02:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"a279329a8986efcef10f8a80e5fa6adbfa00365eced89c6da048d89235841279","abstract_canon_sha256":"f3ffd23331f5b72f0d1ba123b5287c2388d906844ebcd6e75d3ef57e12dca2e4"},"schema_version":"1.0"},"canonical_sha256":"b93d85df397c81f4cfd53b02ce2d5d01b0af5422ed92cc072dfe14b6a0b435f6","source":{"kind":"arxiv","id":"1811.05070","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05070","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05070v2","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05070","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"pith_short_12","alias_value":"XE6YLXZZPSA7","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XE6YLXZZPSA7JT6V","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XE6YLXZZ","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XE6YLXZZPSA7JT6VHMBM4LK5AG","target":"record","payload":{"canonical_record":{"source":{"id":"1811.05070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-11-13T02:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"a279329a8986efcef10f8a80e5fa6adbfa00365eced89c6da048d89235841279","abstract_canon_sha256":"f3ffd23331f5b72f0d1ba123b5287c2388d906844ebcd6e75d3ef57e12dca2e4"},"schema_version":"1.0"},"canonical_sha256":"b93d85df397c81f4cfd53b02ce2d5d01b0af5422ed92cc072dfe14b6a0b435f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:18.811494Z","signature_b64":"uejCaGh1g/T3NDoTSwgSkEcIzFUUL+KCSMEGPNHp3MGnDVPmJ2+zbNKOulp3ntTVKLQjQvLaj8cuDfK0jvCSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b93d85df397c81f4cfd53b02ce2d5d01b0af5422ed92cc072dfe14b6a0b435f6","last_reissued_at":"2026-05-17T23:58:18.811002Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:18.811002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.05070","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":"2026-05-17T23:58:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rkZXyvPwaK+nZnawSv6z4T3oBZC1FGGishfyvAdilgqbj6pWAMghtAxmvX96khUmXl1PAfvKCxQX+/F+IgFUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:15:38.069282Z"},"content_sha256":"b831c317fe337e9c31cfa138365baf9449f357b13b6c3f99a0183117cf5596c3","schema_version":"1.0","event_id":"sha256:b831c317fe337e9c31cfa138365baf9449f357b13b6c3f99a0183117cf5596c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XE6YLXZZPSA7JT6VHMBM4LK5AG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A decay estimate for the eigenvalues of the Neumann-Poincar\\'{e} operator in two dimensions using the Grunsky coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Mikyoung Lim, Younghoon Jung","submitted_at":"2018-11-13T02:09:12Z","abstract_excerpt":"We investigate the decay property of the eigenvalues of the Neumann-Poincar\\'{e} operator in two dimensions. As is well-known, this operator admits only a sequence of eigenvalues that accumulates to zero as its spectrum for a bounded domain having $C^{1,\\alpha}$ boundary with $\\alpha\\in (0,1)$. In this paper, we show that the eigenvalue $\\lambda_k$'s of the Neumann-Poincar\\'{e} operator ordered by size satisfy that $|\\lambda_k| = O(k^{-p-\\alpha+1/2})$ for an arbitrary simply connected domain having $C^{1+p,\\alpha}$ boundary with $p\\geq 0,~ \\alpha\\in(0,1)$ and $p+\\alpha>\\frac{1}{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05070","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":"2026-05-17T23:58:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DkSs6HksFHXYvzX5NCMXDgRRe92P3K8+kWSLoI6836sVkDcTT3HWYiM+jJtbIDZC9cMu+jt2lBcv26g0K+ToBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:15:38.069643Z"},"content_sha256":"b608b35e8074f0d5e512eb48ec3730a3315dba9d0aa0695560b78b9cb6c4c3d1","schema_version":"1.0","event_id":"sha256:b608b35e8074f0d5e512eb48ec3730a3315dba9d0aa0695560b78b9cb6c4c3d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XE6YLXZZPSA7JT6VHMBM4LK5AG/bundle.json","state_url":"https://pith.science/pith/XE6YLXZZPSA7JT6VHMBM4LK5AG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XE6YLXZZPSA7JT6VHMBM4LK5AG/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":"2026-06-25T13:15:38Z","links":{"resolver":"https://pith.science/pith/XE6YLXZZPSA7JT6VHMBM4LK5AG","bundle":"https://pith.science/pith/XE6YLXZZPSA7JT6VHMBM4LK5AG/bundle.json","state":"https://pith.science/pith/XE6YLXZZPSA7JT6VHMBM4LK5AG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XE6YLXZZPSA7JT6VHMBM4LK5AG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XE6YLXZZPSA7JT6VHMBM4LK5AG","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":"f3ffd23331f5b72f0d1ba123b5287c2388d906844ebcd6e75d3ef57e12dca2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-11-13T02:09:12Z","title_canon_sha256":"a279329a8986efcef10f8a80e5fa6adbfa00365eced89c6da048d89235841279"},"schema_version":"1.0","source":{"id":"1811.05070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05070","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05070v2","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05070","created_at":"2026-05-17T23:58:18Z"},{"alias_kind":"pith_short_12","alias_value":"XE6YLXZZPSA7","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XE6YLXZZPSA7JT6V","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XE6YLXZZ","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:b608b35e8074f0d5e512eb48ec3730a3315dba9d0aa0695560b78b9cb6c4c3d1","target":"graph","created_at":"2026-05-17T23:58:18Z","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":"We investigate the decay property of the eigenvalues of the Neumann-Poincar\\'{e} operator in two dimensions. As is well-known, this operator admits only a sequence of eigenvalues that accumulates to zero as its spectrum for a bounded domain having $C^{1,\\alpha}$ boundary with $\\alpha\\in (0,1)$. In this paper, we show that the eigenvalue $\\lambda_k$'s of the Neumann-Poincar\\'{e} operator ordered by size satisfy that $|\\lambda_k| = O(k^{-p-\\alpha+1/2})$ for an arbitrary simply connected domain having $C^{1+p,\\alpha}$ boundary with $p\\geq 0,~ \\alpha\\in(0,1)$ and $p+\\alpha>\\frac{1}{2}$.","authors_text":"Mikyoung Lim, Younghoon Jung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-11-13T02:09:12Z","title":"A decay estimate for the eigenvalues of the Neumann-Poincar\\'{e} operator in two dimensions using the Grunsky coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05070","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:b831c317fe337e9c31cfa138365baf9449f357b13b6c3f99a0183117cf5596c3","target":"record","created_at":"2026-05-17T23:58:18Z","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":"f3ffd23331f5b72f0d1ba123b5287c2388d906844ebcd6e75d3ef57e12dca2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-11-13T02:09:12Z","title_canon_sha256":"a279329a8986efcef10f8a80e5fa6adbfa00365eced89c6da048d89235841279"},"schema_version":"1.0","source":{"id":"1811.05070","kind":"arxiv","version":2}},"canonical_sha256":"b93d85df397c81f4cfd53b02ce2d5d01b0af5422ed92cc072dfe14b6a0b435f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b93d85df397c81f4cfd53b02ce2d5d01b0af5422ed92cc072dfe14b6a0b435f6","first_computed_at":"2026-05-17T23:58:18.811002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:18.811002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uejCaGh1g/T3NDoTSwgSkEcIzFUUL+KCSMEGPNHp3MGnDVPmJ2+zbNKOulp3ntTVKLQjQvLaj8cuDfK0jvCSDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:18.811494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b831c317fe337e9c31cfa138365baf9449f357b13b6c3f99a0183117cf5596c3","sha256:b608b35e8074f0d5e512eb48ec3730a3315dba9d0aa0695560b78b9cb6c4c3d1"],"state_sha256":"540644d3c4c3f8e111816a0f665f0845d45487a5873c96e921b3445e2c5d387d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"asCAOz1k7afAWHSvEqSLBOWcbXLRI9UJyv87oBpkXrnmHDUS1bL3iv24QLhQE1RNtlkmBu+3YwIRa0whkWdvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:15:38.071712Z","bundle_sha256":"3d618cc342d23c3eb8e8195d8626566542425b3845e8fbd6c154bdcd63b5dbb4"}}