{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GSYUAMWQFEU65KXU73GSKO3P7A","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":"babdb3551c484f95f36490e5a017ce526d98bbf051142947cf200ec866894168","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-01-27T15:27:50Z","title_canon_sha256":"72164b17f867cc2114ef4e7e2d5e1560ebfdb8ccfb78e38d960c96414c7033c4"},"schema_version":"1.0","source":{"id":"2601.19701","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.19701","created_at":"2026-06-10T01:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"2601.19701v2","created_at":"2026-06-10T01:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.19701","created_at":"2026-06-10T01:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"GSYUAMWQFEU6","created_at":"2026-06-10T01:09:53Z"},{"alias_kind":"pith_short_16","alias_value":"GSYUAMWQFEU65KXU","created_at":"2026-06-10T01:09:53Z"},{"alias_kind":"pith_short_8","alias_value":"GSYUAMWQ","created_at":"2026-06-10T01:09:53Z"}],"graph_snapshots":[{"event_id":"sha256:ac1fe3dd41a22c924ba19fe550a260927faf3790cd102ac668ba5bfc23c328ca","target":"graph","created_at":"2026-06-10T01:09:53Z","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/2601.19701/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Santiago Verdasco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-01-27T15:27:50Z","title":"High-energy eigenfunctions of point perturbations of the Laplacian on the spheres $\\mathbb{S}^{2}$ and $\\mathbb{S}^{3}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.19701","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":"sha256:96dcd638afefbc25432e68a73e4cc42df230e91dbbd8ead273907698eb0d3548","target":"record","created_at":"2026-06-10T01:09:53Z","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":"babdb3551c484f95f36490e5a017ce526d98bbf051142947cf200ec866894168","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-01-27T15:27:50Z","title_canon_sha256":"72164b17f867cc2114ef4e7e2d5e1560ebfdb8ccfb78e38d960c96414c7033c4"},"schema_version":"1.0","source":{"id":"2601.19701","kind":"arxiv","version":2}},"canonical_sha256":"34b14032d02929eeaaf4fecd253b6ff82c50de67d054dccc2b706cd607a14d47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34b14032d02929eeaaf4fecd253b6ff82c50de67d054dccc2b706cd607a14d47","first_computed_at":"2026-06-10T01:09:53.458773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:09:53.458773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YVzeWkC07/4Wy8QD5da0qMgwcU66OaOQSabmh2qhYwKKXIcel6hzSoiWpAj2bYTJ00KAPE4FIOmXKqsAl74eBg==","signature_status":"signed_v1","signed_at":"2026-06-10T01:09:53.459817Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.19701","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96dcd638afefbc25432e68a73e4cc42df230e91dbbd8ead273907698eb0d3548","sha256:ac1fe3dd41a22c924ba19fe550a260927faf3790cd102ac668ba5bfc23c328ca"],"state_sha256":"62605f1621fedacc796911f3922aec7b7ee4dbeaa18c7caa28ab8485a7eaf0a1"}