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When X is compact, this implies the law of large numbers and central limit theorem for the corresponding empirical measures.","weakest_assumption":"The non-degeneracy of the curvature form of L together with the bounded-geometry assumption on the Riemannian manifold X; these are invoked to guarantee that the local Landau levels remain separated and that the spectrum of H_p asymptotically coincides with their union Σ."}},"verdict_id":"47971f3e-b0dd-4c83-b980-dcc0f75527e6"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2729313d8165f570701348a4091becdb0c0211ba51a3d08af8b9c4e2baf18836","target":"record","created_at":"2026-05-18T02:44:23Z","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":"9972a394bd146afd05d2490733cab92e2f767f8aed6ed08f5557c2f089300a1d","cross_cats_sorted":["math-ph","math.MP","math.PR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-13T14:10:23Z","title_canon_sha256":"1c40fc355adf0f94aacb20823d6d1129ab311947d41d6bfc5362fb7838f13e44"},"schema_version":"1.0","source":{"id":"2605.13575","kind":"arxiv","version":1}},"canonical_sha256":"37975f9453ced4e13400e5b8b3bde969c114e42fb5497fb3dd76ca65c9ec69c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37975f9453ced4e13400e5b8b3bde969c114e42fb5497fb3dd76ca65c9ec69c8","first_computed_at":"2026-05-18T02:44:23.300546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:23.300546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t//Z4yjC1zIQzTAHtuIjpg7+X3Y9GJAhoKsmGlHOUbMLXBwISth0VpJpCPyeNFkKLtI8rbJOUYm2ByFR0QVlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:23.300988Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13575","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2729313d8165f570701348a4091becdb0c0211ba51a3d08af8b9c4e2baf18836","sha256:bd0e7e9e5af427069780418d2eab9eb7d394ba6a4d8012313e96a536836dd214"],"state_sha256":"956b7ec6dca3afff5cb698e26ee50e11748d1044a1314393d69d20b4c29a7875"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VLPYFrf1unLHSbvMQr640WKcjQ1OjULl7blEyuh2eGArPEx7LM4g1pwGqfQrgaVcbibf10BWiHK3ARJoCnjRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:45:13.022497Z","bundle_sha256":"b533e1b4ed87f93eb9708d3c9c85b786e3ba18974d43d84564d451c35ad1a155"}}