{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JY4SHXHLPFUWHH7MPZZFYUNGCV","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":"de3a62df30e82cb2d905e409bda29c677809543a0eaef9ac1d2a8ab5b39ffbfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-05-07T09:38:27Z","title_canon_sha256":"ce4e338e4cba67495cbd8973f19d021321f312009cf13efdf53d9cd15ba6d2cb"},"schema_version":"1.0","source":{"id":"1805.02414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02414","created_at":"2026-05-18T00:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02414v1","created_at":"2026-05-18T00:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02414","created_at":"2026-05-18T00:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"JY4SHXHLPFUW","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"JY4SHXHLPFUWHH7M","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"JY4SHXHL","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:a96bd6efb617f00b64b88b4173f2e156c2506960b0c050edc45c2a2815ee130e","target":"graph","created_at":"2026-05-18T00:16:40Z","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 on the sphere has $\\frac{1}{2(2k+1)}$, $k=0,1,2,\\ldots$, as its eigenvalues and the corresponding multiplicity is $2k+1$. We consider the bifurcation of eigenvalues under deformation of domains, and show that Frech\\'et derivative of the sum of the bifurcations is zero. We then discuss the connection of this result with some conjectures regarding the Neumann-Poincar\\'e operator.","authors_text":"Erika Ushikoshi, Hyeonbae Kang, Kazunori Ando, Yoshihisa Miyanishi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-05-07T09:38:27Z","title":"The first Hadamard variation of Neumann-Poincar\\'e eigenvalues on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02414","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":"sha256:47f1b3d2e1ba2cf616efccc2c8c0a5c4323d1100c2f932ee859ac66efea8d25f","target":"record","created_at":"2026-05-18T00:16:40Z","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":"de3a62df30e82cb2d905e409bda29c677809543a0eaef9ac1d2a8ab5b39ffbfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-05-07T09:38:27Z","title_canon_sha256":"ce4e338e4cba67495cbd8973f19d021321f312009cf13efdf53d9cd15ba6d2cb"},"schema_version":"1.0","source":{"id":"1805.02414","kind":"arxiv","version":1}},"canonical_sha256":"4e3923dceb7969639fec7e725c51a6155884dd4bd725cb7ff091330d84a8d235","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e3923dceb7969639fec7e725c51a6155884dd4bd725cb7ff091330d84a8d235","first_computed_at":"2026-05-18T00:16:40.021704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:40.021704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"clRwTnB41PNYQRihzGOjqKrlFOjmn474LA3D0gtqQhMHQu/jShDW3k1HYDb2GHdxNPjAkIAWsP+O5DSRF6N5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:40.022211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47f1b3d2e1ba2cf616efccc2c8c0a5c4323d1100c2f932ee859ac66efea8d25f","sha256:a96bd6efb617f00b64b88b4173f2e156c2506960b0c050edc45c2a2815ee130e"],"state_sha256":"cbb70e96eff43230881f57691200ecaede47c6591fed283eb080f2570526e5af"}