{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GSYUAMWQFEU65KXU73GSKO3P7A","short_pith_number":"pith:GSYUAMWQ","schema_version":"1.0","canonical_sha256":"34b14032d02929eeaaf4fecd253b6ff82c50de67d054dccc2b706cd607a14d47","source":{"kind":"arxiv","id":"2601.19701","version":2},"attestation_state":"computed","paper":{"title":"High-energy eigenfunctions of point perturbations of the Laplacian on the spheres $\\mathbb{S}^{2}$ and $\\mathbb{S}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Santiago Verdasco","submitted_at":"2026-01-27T15:27:50Z","abstract_excerpt":"We study the set of Quantum Limits, and more generally, of semiclassical measures of sequences of eigenfunctions of perturbations of the Laplacian on the spheres $\\mathbb{S}^{2}$ and $\\mathbb{S}^{3}$ by point-scatterers. In the unperturbed case, it is known that the set of semiclassical measures coincides with the set of measures that are invariant under the geodesic flow; on the other hand, when the Laplacian is perturbed by a generic smooth potential, the set of semiclassical measures turns out to be strictly contained within that of invariant measures. In this article, we prove that the add"},"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":"2601.19701","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-01-27T15:27:50Z","cross_cats_sorted":[],"title_canon_sha256":"72164b17f867cc2114ef4e7e2d5e1560ebfdb8ccfb78e38d960c96414c7033c4","abstract_canon_sha256":"babdb3551c484f95f36490e5a017ce526d98bbf051142947cf200ec866894168"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:09:53.459817Z","signature_b64":"YVzeWkC07/4Wy8QD5da0qMgwcU66OaOQSabmh2qhYwKKXIcel6hzSoiWpAj2bYTJ00KAPE4FIOmXKqsAl74eBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34b14032d02929eeaaf4fecd253b6ff82c50de67d054dccc2b706cd607a14d47","last_reissued_at":"2026-06-10T01:09:53.458773Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:09:53.458773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High-energy eigenfunctions of point perturbations of the Laplacian on the spheres $\\mathbb{S}^{2}$ and $\\mathbb{S}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Santiago Verdasco","submitted_at":"2026-01-27T15:27:50Z","abstract_excerpt":"We study the set of Quantum Limits, and more generally, of semiclassical measures of sequences of eigenfunctions of perturbations of the Laplacian on the spheres $\\mathbb{S}^{2}$ and $\\mathbb{S}^{3}$ by point-scatterers. In the unperturbed case, it is known that the set of semiclassical measures coincides with the set of measures that are invariant under the geodesic flow; on the other hand, when the Laplacian is perturbed by a generic smooth potential, the set of semiclassical measures turns out to be strictly contained within that of invariant measures. In this article, we prove that the add"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.19701","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.19701/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2601.19701","created_at":"2026-06-10T01:09:53.458918+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.19701v2","created_at":"2026-06-10T01:09:53.458918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.19701","created_at":"2026-06-10T01:09:53.458918+00:00"},{"alias_kind":"pith_short_12","alias_value":"GSYUAMWQFEU6","created_at":"2026-06-10T01:09:53.458918+00:00"},{"alias_kind":"pith_short_16","alias_value":"GSYUAMWQFEU65KXU","created_at":"2026-06-10T01:09:53.458918+00:00"},{"alias_kind":"pith_short_8","alias_value":"GSYUAMWQ","created_at":"2026-06-10T01:09:53.458918+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.10847","citing_title":"Quantum Limits of the Laplacian perturbed along a geodesic on $\\mathbb{S}^{2}$","ref_index":36,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GSYUAMWQFEU65KXU73GSKO3P7A","json":"https://pith.science/pith/GSYUAMWQFEU65KXU73GSKO3P7A.json","graph_json":"https://pith.science/api/pith-number/GSYUAMWQFEU65KXU73GSKO3P7A/graph.json","events_json":"https://pith.science/api/pith-number/GSYUAMWQFEU65KXU73GSKO3P7A/events.json","paper":"https://pith.science/paper/GSYUAMWQ"},"agent_actions":{"view_html":"https://pith.science/pith/GSYUAMWQFEU65KXU73GSKO3P7A","download_json":"https://pith.science/pith/GSYUAMWQFEU65KXU73GSKO3P7A.json","view_paper":"https://pith.science/paper/GSYUAMWQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.19701&json=true","fetch_graph":"https://pith.science/api/pith-number/GSYUAMWQFEU65KXU73GSKO3P7A/graph.json","fetch_events":"https://pith.science/api/pith-number/GSYUAMWQFEU65KXU73GSKO3P7A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GSYUAMWQFEU65KXU73GSKO3P7A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GSYUAMWQFEU65KXU73GSKO3P7A/action/storage_attestation","attest_author":"https://pith.science/pith/GSYUAMWQFEU65KXU73GSKO3P7A/action/author_attestation","sign_citation":"https://pith.science/pith/GSYUAMWQFEU65KXU73GSKO3P7A/action/citation_signature","submit_replication":"https://pith.science/pith/GSYUAMWQFEU65KXU73GSKO3P7A/action/replication_record"}},"created_at":"2026-06-10T01:09:53.458918+00:00","updated_at":"2026-06-10T01:09:53.458918+00:00"}