{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WIB5ZYGVQ23S6VJ5KRTZWLK6YM","short_pith_number":"pith:WIB5ZYGV","schema_version":"1.0","canonical_sha256":"b203dce0d586b72f553d54679b2d5ec33a9b7efc5ebff21289a7d529f07e0d0f","source":{"kind":"arxiv","id":"2605.18705","version":1},"attestation_state":"computed","paper":{"title":"Nested nodal loops for sums of Laplace eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Robert Koirala","submitted_at":"2026-05-18T17:38:22Z","abstract_excerpt":"We study nested loops in zero sets of sums of Laplace eigenfunctions on closed surfaces. In the real-analytic category, answering a question of Logunov, we prove a uniform bound for the number of rooted double nests in terms of the surface, the root, and the spectral cutoff. We show that this analyticity hypothesis is sharp: on a smooth sphere, a linear combination of eigenfunctions with eigenvalues \\(0\\) and \\(2\\) can have infinitely many rooted double nests. We also answer a question of Logunov and Nadirashvili by constructing a planar biharmonic function whose nodal set contains a double ne"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.18705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-18T17:38:22Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"f5a545fd431c27c9cad86604f68746af028dc7ea8a15e2210c5c27e8b382cfbc","abstract_canon_sha256":"b5db85d3cb1cda8a7231d2beb9c13cfd5a304fbc3d26149b0c2e05f7bbf7327f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:06:16.086097Z","signature_b64":"3yhQ+CiXBgGRDCtcX/u1mz4p2EEOV9HMgnI1yrZeqKy/nYMcdd3zWV5tDTfgENGhn7gIZUkGo8+LUf5afdMfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b203dce0d586b72f553d54679b2d5ec33a9b7efc5ebff21289a7d529f07e0d0f","last_reissued_at":"2026-05-20T00:06:16.085217Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:06:16.085217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nested nodal loops for sums of Laplace eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Robert Koirala","submitted_at":"2026-05-18T17:38:22Z","abstract_excerpt":"We study nested loops in zero sets of sums of Laplace eigenfunctions on closed surfaces. In the real-analytic category, answering a question of Logunov, we prove a uniform bound for the number of rooted double nests in terms of the surface, the root, and the spectral cutoff. We show that this analyticity hypothesis is sharp: on a smooth sphere, a linear combination of eigenfunctions with eigenvalues \\(0\\) and \\(2\\) can have infinitely many rooted double nests. We also answer a question of Logunov and Nadirashvili by constructing a planar biharmonic function whose nodal set contains a double ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18705","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18705/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.069909Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b7a1a9362e445460f9d4d1239d1cf9c7a032ff073f6cb9383c769cbff9af868f"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.18705","created_at":"2026-05-20T00:06:16.085373+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.18705v1","created_at":"2026-05-20T00:06:16.085373+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18705","created_at":"2026-05-20T00:06:16.085373+00:00"},{"alias_kind":"pith_short_12","alias_value":"WIB5ZYGVQ23S","created_at":"2026-05-20T00:06:16.085373+00:00"},{"alias_kind":"pith_short_16","alias_value":"WIB5ZYGVQ23S6VJ5","created_at":"2026-05-20T00:06:16.085373+00:00"},{"alias_kind":"pith_short_8","alias_value":"WIB5ZYGV","created_at":"2026-05-20T00:06:16.085373+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WIB5ZYGVQ23S6VJ5KRTZWLK6YM","json":"https://pith.science/pith/WIB5ZYGVQ23S6VJ5KRTZWLK6YM.json","graph_json":"https://pith.science/api/pith-number/WIB5ZYGVQ23S6VJ5KRTZWLK6YM/graph.json","events_json":"https://pith.science/api/pith-number/WIB5ZYGVQ23S6VJ5KRTZWLK6YM/events.json","paper":"https://pith.science/paper/WIB5ZYGV"},"agent_actions":{"view_html":"https://pith.science/pith/WIB5ZYGVQ23S6VJ5KRTZWLK6YM","download_json":"https://pith.science/pith/WIB5ZYGVQ23S6VJ5KRTZWLK6YM.json","view_paper":"https://pith.science/paper/WIB5ZYGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.18705&json=true","fetch_graph":"https://pith.science/api/pith-number/WIB5ZYGVQ23S6VJ5KRTZWLK6YM/graph.json","fetch_events":"https://pith.science/api/pith-number/WIB5ZYGVQ23S6VJ5KRTZWLK6YM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WIB5ZYGVQ23S6VJ5KRTZWLK6YM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WIB5ZYGVQ23S6VJ5KRTZWLK6YM/action/storage_attestation","attest_author":"https://pith.science/pith/WIB5ZYGVQ23S6VJ5KRTZWLK6YM/action/author_attestation","sign_citation":"https://pith.science/pith/WIB5ZYGVQ23S6VJ5KRTZWLK6YM/action/citation_signature","submit_replication":"https://pith.science/pith/WIB5ZYGVQ23S6VJ5KRTZWLK6YM/action/replication_record"}},"created_at":"2026-05-20T00:06:16.085373+00:00","updated_at":"2026-05-20T00:06:16.085373+00:00"}