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If $b$ belongs to the orbit Lipschitz class $\\operatorname{Lip}_d$, then for every $1<p<\\infty$ we prove $$\\|[M_b,T_i\\mathcal R_j]f\\|_{L^p(\\mathbb{R}^N,d\\omega)}\\le C_p\\|b\\|_{\\operatorname{Lip}_d}\\|f\\|_{L^p(\\mathbb{R}^N,d\\omega)}.$$ No $G$-invariance is imposed on the input function $f$.\n  The key is a chamber lifting: fix a closed Weyl chamber $\\mathcal C$ and set $Uf(x)=(f(\\sigma_1x),\\dots,f(\\sigma_{|G|}x))$ for $x\\in\\mathcal C$. This identifies $L^p(\\mathbb{R}^N,d\\o","authors_text":"Eric Sawyer, Ji Li, Liangchuan Wu, Ming-Yi Lee, Yongsheng Han","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-25T13:01:43Z","title":"Calderon-type commutators and chamber lifting in the Dunkl setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25808","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7a04a2c448af2c1db107acb0005e3e5a3c80cb985a6cd40677d77680eb245ccc","target":"record","created_at":"2026-05-26T02:05:12Z","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":"b1c00567072304215293af9af46dea934f4e4371b01f48902d73728a1ec8220a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-25T13:01:43Z","title_canon_sha256":"4d02991347ee2643c1e5ca34a4e48b3c7f4203c4c828dbeb9ea964f98160726d"},"schema_version":"1.0","source":{"id":"2605.25808","kind":"arxiv","version":1}},"canonical_sha256":"e4a1024d72521bae33598ec2d0b0d8dd613acbfaf5a34f742a55ed96b454722f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4a1024d72521bae33598ec2d0b0d8dd613acbfaf5a34f742a55ed96b454722f","first_computed_at":"2026-05-26T02:05:12.756768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:05:12.756768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VS+MCydXWkImN1idljk6wfIo/PeF5PvVpOTtDNsKnxw1tdsxDmtfCEHxPUC7C8zoZOCOp6V0IYmip1Fi0eDhCA==","signature_status":"signed_v1","signed_at":"2026-05-26T02:05:12.757544Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a04a2c448af2c1db107acb0005e3e5a3c80cb985a6cd40677d77680eb245ccc","sha256:df97144d77a6c82f2b333cd89fe0846d8e391af9a723438f81a5037e654fc35e"],"state_sha256":"b67da0833ad93f9663f53c152ec73e6ae132ba3467cba67712e0c25d25d6db89"}