{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TE46A46NMNJM4HDIHSWLS2A3XE","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":"67d1f9f2a5f57a8e8554d5cf699e122f50aee62bc7db206951bd96823e931a0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2024-03-12T07:29:46Z","title_canon_sha256":"c214944d595a46af587b008e0cd45d56793404f7e6c5917a7b7fe7ca74e520ad"},"schema_version":"1.0","source":{"id":"2403.07377","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.07377","created_at":"2026-07-05T08:45:50Z"},{"alias_kind":"arxiv_version","alias_value":"2403.07377v2","created_at":"2026-07-05T08:45:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.07377","created_at":"2026-07-05T08:45:50Z"},{"alias_kind":"pith_short_12","alias_value":"TE46A46NMNJM","created_at":"2026-07-05T08:45:50Z"},{"alias_kind":"pith_short_16","alias_value":"TE46A46NMNJM4HDI","created_at":"2026-07-05T08:45:50Z"},{"alias_kind":"pith_short_8","alias_value":"TE46A46N","created_at":"2026-07-05T08:45:50Z"}],"graph_snapshots":[{"event_id":"sha256:81eada409aba137457b5aafec61d263c0dce479e33d7628f0819755fe8bd90c5","target":"graph","created_at":"2026-07-05T08:45:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.07377/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the Laplace spectrum of the generic ellipse is simple, both with Neumann and Dirichlet boundary condition. We rely on the known multiplicities in the spectrum of the disk (Bourget's hypothesis) and on a refined version of our method of asymptotic separation of variables.\n  In v1, the statement of prop. 2.1 is correct but the proof is not.","authors_text":"Chris M. Judge, Luc Hillairet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2024-03-12T07:29:46Z","title":"Generic simplicity of ellipses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.07377","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":"sha256:0f17066355b91eaaf7428318c650732eb78a3c3276a304454eb9afdb09db0ddf","target":"record","created_at":"2026-07-05T08:45:50Z","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":"67d1f9f2a5f57a8e8554d5cf699e122f50aee62bc7db206951bd96823e931a0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2024-03-12T07:29:46Z","title_canon_sha256":"c214944d595a46af587b008e0cd45d56793404f7e6c5917a7b7fe7ca74e520ad"},"schema_version":"1.0","source":{"id":"2403.07377","kind":"arxiv","version":2}},"canonical_sha256":"9939e073cd6352ce1c683cacb9681bb93e424bc3265cabaddce4b2033103d363","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9939e073cd6352ce1c683cacb9681bb93e424bc3265cabaddce4b2033103d363","first_computed_at":"2026-07-05T08:45:50.262970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:45:50.262970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t/QAmrQ5CFTLcq3K1s1kmrQNC4HsBEhugrI8QAVv0OkUvN/FMtbenT7s9OfpeSldE3tDK/7YNL8Ap7ZQou1VDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:45:50.263399Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.07377","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f17066355b91eaaf7428318c650732eb78a3c3276a304454eb9afdb09db0ddf","sha256:81eada409aba137457b5aafec61d263c0dce479e33d7628f0819755fe8bd90c5"],"state_sha256":"235376d96dbfab8dd8cc9a0f822a7f1358ada5c675ca8a3c65170e18e93657c4"}