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These bounds are formulated in terms of the L^p-norms of the corresponding potentials.","weakest_assumption":"The adaptation of Cuenin-Sogge methods to the fractional Laplacian on compact manifolds works without extra restrictions on the potential or the geometry beyond those already present in the cited works."}},"verdict_id":"eff11438-bc14-4bb0-8c29-dc2826865244"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:112fa9ae31dfa6ca1fcf9ab35daa6e9eb49179faa7bf2510b1c31181e5f70783","target":"record","created_at":"2026-05-20T00:02:29Z","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":"8acca9acc16e64ef9aaaf74fa10deb120efb263057c84c75474b056bcc2b8ebc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2026-05-15T19:16:22Z","title_canon_sha256":"36e079deb151ed8bbb2f600a0c068862ff7de90b415012c0c42f87b11c7db220"},"schema_version":"1.0","source":{"id":"2605.16569","kind":"arxiv","version":1}},"canonical_sha256":"e1a1ca09fba49633fef3c18e8b42bb8578dd854464a3d50d07c3c5dce599953b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1a1ca09fba49633fef3c18e8b42bb8578dd854464a3d50d07c3c5dce599953b","first_computed_at":"2026-05-20T00:02:29.652989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:29.652989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eOXgJJqCTpH+7X+T0c6kc9nfAuslpuCIf3jkBcOOk6I8A1vTQBld/scbSSm2N4xHs+/y3kbhEZ2dN1n2yOzcCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:29.653828Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:112fa9ae31dfa6ca1fcf9ab35daa6e9eb49179faa7bf2510b1c31181e5f70783","sha256:4b10a6cdb8fc9ff0028be2c9dd700c3e6c019aa6cc9ae0bc9f3cfe85ae3cd736"],"state_sha256":"0bc876c753200698c31319e6b2070763723cbfb0c1a14715b9e9ee57792c77fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z6qsrREM6KesmgKltePu1wsBESFjGqSNytb83PrnV+xmtCMDZWcsGxsA/iSRts+rbogLvr2fldw8cYA/3I6MBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:39:29.832408Z","bundle_sha256":"5615ebad611f88ab21b8045f906393cedb3673c6e0ced895161c282ee262ed9c"}}