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We prove the sharp log-free endpoint estimate $||\\Pi_\\lambda||_{L^2(\\mathbb R^2)\\to L^{10/3}(\\mathbb R^2)}\\lesssim\\lambda^{-1/10}$. The proof uses a spectral decomposition in polar coordinates and combines Koch-Tataru localized spectral projection bounds with a Liouville-Green representation, van der Corput estimates for exponential sums, and a weighted $TT^*$ argument across radial scales."},"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":"2608.08423","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-09T02:43:57Z","cross_cats_sorted":["math.CA","math.SP"],"title_canon_sha256":"bc474bd95f9cf26227579300f034b35a849da417e7ba6e977c8c15ad047711d6","abstract_canon_sha256":"66555222b1e5c70456fac8b862bf9da7d1a4a68a1d1b620335d8ba689cb257fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:22:36.071624Z","signature_b64":"7D5mM94/XAb8TAOz6bU00pvLbUbbhO/b9k/BvpYwbB5yUYgKlMZLsOqAQy4xShLThWYFApDVz+bcLMbrnRjXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a70248de3f9fcab5c5024158bd25c70afe1e6025309b17fe9d9222cbd773a91f","last_reissued_at":"2026-08-11T01:22:36.069311Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:22:36.069311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Endpoint Eigenfunction Estimates for the Two-Dimensional Hermite Operator","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.SP"],"primary_cat":"math.AP","authors_text":"Cheng Zhang, Guiyu Xie","submitted_at":"2026-08-09T02:43:57Z","abstract_excerpt":"Let $\\mathcal H=-\\Delta+|x|^2$ be the Hermite operator on $\\mathbb R^2$, and let $\\Pi_\\lambda$ denote the spectral projection corresponding to $\\lambda=2N+2$. We prove the sharp log-free endpoint estimate $||\\Pi_\\lambda||_{L^2(\\mathbb R^2)\\to L^{10/3}(\\mathbb R^2)}\\lesssim\\lambda^{-1/10}$. 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