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We assume that $P_1$ is quantum completely integrable in the sense that there exist functionally independent pseuodifferential operators $P_2,\\dots P_n$ with $[P_i,P_j]=0$, $i,j=1,\\dots ,n$. We study the pointwise bounds for the joint eigenfunctions, $u_h$ of the system $\\{P_i\\}_{i=1}^n$ with $P_1u_h=E_1u_h+o(1)$. We first give polynomial improvements over the standard H\\\"ormander bounds for typical points in $M$. In two and three dimensions, these estimates agree with the Hardy expon"},"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":"1810.04232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T20:17:55Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"434b40986414aa655edd82dbfde0c10f81c01a1972da8e0bab2be7011ad9ead8","abstract_canon_sha256":"1ed073816550a8a3f599a064b41e486e7427f06c0198823c72075881232e0530"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:40.758416Z","signature_b64":"4sZiJ940XObedwyEvmsea0wsjOB1ccPe/60ncZxcIGcfqEGiVIBGDmPCnk6mH+DY1a081lWwwYH87ldtBVPCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a24b0090941e1d121b1f2648da9fd63f659335bacbb933e6f85fb54177ce9af","last_reissued_at":"2026-05-18T00:03:40.757815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:40.757815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pointwise bounds for joint eigenfunctions of quantum completely integrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Jeffrey Galkowski, John A. 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