{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BPZYHCDYKUSXEP7RT35YQUIMFR","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":"6710384b89835cde38771c00beb30c19574679222eb52e016e95b8a25a8930f6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-09T13:29:04Z","title_canon_sha256":"4e79601179a2de36e5f37ba6fe847b75f590b720b8182c555de80adad9fee4a8"},"schema_version":"1.0","source":{"id":"2606.10847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10847","created_at":"2026-06-10T01:10:43Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10847v1","created_at":"2026-06-10T01:10:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10847","created_at":"2026-06-10T01:10:43Z"},{"alias_kind":"pith_short_12","alias_value":"BPZYHCDYKUSX","created_at":"2026-06-10T01:10:43Z"},{"alias_kind":"pith_short_16","alias_value":"BPZYHCDYKUSXEP7R","created_at":"2026-06-10T01:10:43Z"},{"alias_kind":"pith_short_8","alias_value":"BPZYHCDY","created_at":"2026-06-10T01:10:43Z"}],"graph_snapshots":[{"event_id":"sha256:0f235156f6a255609fd204726f76ea31565d3acd1542c4b19235471be4ec7ef5","target":"graph","created_at":"2026-06-10T01:10:43Z","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/2606.10847/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article studies the high-frequency behavior of eigenstates of perturbations of the Laplace-Beltrami operator on the two-sphere $\\mathbb{S}^{2}$ by a measure supported on an equator. We are interested in understanding to what extent this behavior can be described in terms of the geodesic flow of the sphere. This is done by analyzing quantum limits and semiclassical measures of sequences of high-frequency eigenfunctions, which describe how their $L^2$-masses concentrate in phase space. When the Laplacian on $\\mathbb{S}^{2}$ is perturbed by a bounded potential, it is known that the family of","authors_text":"Santiago Verdasco","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-09T13:29:04Z","title":"Quantum Limits of the Laplacian perturbed along a geodesic on $\\mathbb{S}^{2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10847","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":"sha256:21e30e5820f2570cbc5950ce66b8a5f042a8a20ab8c3f1d4c0249b29fc4d7015","target":"record","created_at":"2026-06-10T01:10:43Z","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":"6710384b89835cde38771c00beb30c19574679222eb52e016e95b8a25a8930f6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-09T13:29:04Z","title_canon_sha256":"4e79601179a2de36e5f37ba6fe847b75f590b720b8182c555de80adad9fee4a8"},"schema_version":"1.0","source":{"id":"2606.10847","kind":"arxiv","version":1}},"canonical_sha256":"0bf38388785525723ff19efb88510c2c48a77524d8a3c5d0f8cbdf8e0ee2f931","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bf38388785525723ff19efb88510c2c48a77524d8a3c5d0f8cbdf8e0ee2f931","first_computed_at":"2026-06-10T01:10:43.742700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:10:43.742700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yEpVtres3uxB6jAq2/1N0Mq5n/oZba7LdRZmDqxV2TgY0cRCfAJTLwa1ZAAuousB1VwacI6d8nLM3Kpl2QOYCw==","signature_status":"signed_v1","signed_at":"2026-06-10T01:10:43.743574Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.10847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21e30e5820f2570cbc5950ce66b8a5f042a8a20ab8c3f1d4c0249b29fc4d7015","sha256:0f235156f6a255609fd204726f76ea31565d3acd1542c4b19235471be4ec7ef5"],"state_sha256":"2f4e24b50cbb5e52afd2e525f6ce97da44ad15e505f4ff2b769f4b2d2c3a17e6"}