{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PDUQFWJMWBNJ4677OTDRTCX62P","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":"08910eff7dd653ff94b6bf4e6e73f47ff2005f0f9b662c1798b84d65281ad2b7","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-09T04:30:05Z","title_canon_sha256":"7eb8affee708046fb95908d8e8e0065b7c1854fb639d6a2ac2c73e4827d8f8a1"},"schema_version":"1.0","source":{"id":"1908.03307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03307","created_at":"2026-07-04T23:52:38Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03307v1","created_at":"2026-07-04T23:52:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03307","created_at":"2026-07-04T23:52:38Z"},{"alias_kind":"pith_short_12","alias_value":"PDUQFWJMWBNJ","created_at":"2026-07-04T23:52:38Z"},{"alias_kind":"pith_short_16","alias_value":"PDUQFWJMWBNJ4677","created_at":"2026-07-04T23:52:38Z"},{"alias_kind":"pith_short_8","alias_value":"PDUQFWJM","created_at":"2026-07-04T23:52:38Z"}],"graph_snapshots":[{"event_id":"sha256:5c4a228b0f07897b8603138ccf8a1932cf9fbc7e47c3c2b7dcbed4ff18d54efb","target":"graph","created_at":"2026-07-04T23:52:38Z","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/1908.03307/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article concerns the asymptotic geometric character of the nodal set of the eigenfunctions of the Steklov eigenvalue problem $$ -\\Delta \\phi_{\\sigma_j}=0,\\quad\\text{ on }\\Omega,\\qquad\\qquad \\partial_\\nu \\phi_{\\sigma_j}=\\sigma_j \\phi_{\\sigma_j}\\quad \\text{ on }\\partial\\Omega $$ in two-dimensional domains $\\Omega$. In particular, this paper presents a dense family $\\mathcal{A}$ of simply-connected two-dimensional domains with analytic boundaries such that, for each $\\Omega\\in \\mathcal{A}$, the nodal set of the eigenfunction $\\phi_{\\sigma_j}$ \"is $not$ dense at scale $\\sigma_j^{-1}$\". This r","authors_text":"Jeffrey Galkowski, Oscar Bruno","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-09T04:30:05Z","title":"Domains without dense Steklov nodal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03307","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:cf812be3005a2eb32134091b2dc961164ce9ffbec6dd8528c6dbd81574375748","target":"record","created_at":"2026-07-04T23:52:38Z","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":"08910eff7dd653ff94b6bf4e6e73f47ff2005f0f9b662c1798b84d65281ad2b7","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-09T04:30:05Z","title_canon_sha256":"7eb8affee708046fb95908d8e8e0065b7c1854fb639d6a2ac2c73e4827d8f8a1"},"schema_version":"1.0","source":{"id":"1908.03307","kind":"arxiv","version":1}},"canonical_sha256":"78e902d92cb05a9e7bff74c7198afed3e50e52b319f14cb0dd7b44aa473fb792","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78e902d92cb05a9e7bff74c7198afed3e50e52b319f14cb0dd7b44aa473fb792","first_computed_at":"2026-07-04T23:52:38.722622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:38.722622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tlm3OMWeIovq/EC90JwjqpRwyBXZLCimNLVARC4vbwCFwlOfCPeIzU19uDw0Y9o1wHCL5KRFrHTeUPzGfrMbCA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:38.723083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf812be3005a2eb32134091b2dc961164ce9ffbec6dd8528c6dbd81574375748","sha256:5c4a228b0f07897b8603138ccf8a1932cf9fbc7e47c3c2b7dcbed4ff18d54efb"],"state_sha256":"bcd640a2a898f839d5d1bd636ce74cb347784cdb5b60af5ba116a62251bbd2bb"}