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It has been proved by Raich \\cite{R10} that on a CR manifold of dimension $2n-1$ which is compact pseudoconvex of hypersurface type embedded in $\\C^n$ and orientable, the property named \"$(CR-P_q)$\" for $1\\leq q\\leq \\frac{n-1}2$, a generalization of the one introduced by Catlin in \\cite{C84}, implies compactness est"},"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":"1101.0017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-29T22:33:56Z","cross_cats_sorted":[],"title_canon_sha256":"4f251f42ab3e83c9870d274d9984283558784d642549562bb06350d6cf69c8b7","abstract_canon_sha256":"121be5287df5351220cb1ea83275d0ced182178a200d99ebf88ca0c6bab4c2da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:11.204608Z","signature_b64":"IXuQ5QGKSnrBXP/5lUE8jX8f5gJjvzZM469Y2rjTPGrDNPq139nx0xxFbHb8x1OrWdOZqOjbdfESHMt/+uUGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f10e3bfcd436b5ce57ad1d78358ea1a20e13b360c44ab62ae13eff40b159bc7e","last_reissued_at":"2026-05-18T04:32:11.203903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:11.203903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compactness of $\\Box_b$ in a CR manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Giuseppe Zampieri, Stefano Pinton, Tran Vu Khanh","submitted_at":"2010-12-29T22:33:56Z","abstract_excerpt":"This note is aimed at simplifying current literature about compactness estimates for the Kohn-Laplacian on CR manifolds. 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