{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4SQQETLSKIN24M2ZR3BNBMGY3V","short_pith_number":"pith:4SQQETLS","schema_version":"1.0","canonical_sha256":"e4a1024d72521bae33598ec2d0b0d8dd613acbfaf5a34f742a55ed96b454722f","source":{"kind":"arxiv","id":"2605.25808","version":1},"attestation_state":"computed","paper":{"title":"Calderon-type commutators and chamber lifting in the Dunkl setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eric Sawyer, Ji Li, Liangchuan Wu, Ming-Yi Lee, Yongsheng Han","submitted_at":"2026-05-25T13:01:43Z","abstract_excerpt":"We study Calder\\'on-type commutators $[M_b,T_i\\mathcal R_j]$ in the rational Dunkl setting with a finite reflection group $G$. 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"},"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":"2605.25808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-25T13:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"4d02991347ee2643c1e5ca34a4e48b3c7f4203c4c828dbeb9ea964f98160726d","abstract_canon_sha256":"b1c00567072304215293af9af46dea934f4e4371b01f48902d73728a1ec8220a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:12.757544Z","signature_b64":"VS+MCydXWkImN1idljk6wfIo/PeF5PvVpOTtDNsKnxw1tdsxDmtfCEHxPUC7C8zoZOCOp6V0IYmip1Fi0eDhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4a1024d72521bae33598ec2d0b0d8dd613acbfaf5a34f742a55ed96b454722f","last_reissued_at":"2026-05-26T02:05:12.756768Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:12.756768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Calderon-type commutators and chamber lifting in the Dunkl setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eric Sawyer, Ji Li, Liangchuan Wu, Ming-Yi Lee, Yongsheng Han","submitted_at":"2026-05-25T13:01:43Z","abstract_excerpt":"We study Calder\\'on-type commutators $[M_b,T_i\\mathcal R_j]$ in the rational Dunkl setting with a finite reflection group $G$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25808","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25808/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.25808","created_at":"2026-05-26T02:05:12.756904+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25808v1","created_at":"2026-05-26T02:05:12.756904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25808","created_at":"2026-05-26T02:05:12.756904+00:00"},{"alias_kind":"pith_short_12","alias_value":"4SQQETLSKIN2","created_at":"2026-05-26T02:05:12.756904+00:00"},{"alias_kind":"pith_short_16","alias_value":"4SQQETLSKIN24M2Z","created_at":"2026-05-26T02:05:12.756904+00:00"},{"alias_kind":"pith_short_8","alias_value":"4SQQETLS","created_at":"2026-05-26T02:05:12.756904+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4SQQETLSKIN24M2ZR3BNBMGY3V","json":"https://pith.science/pith/4SQQETLSKIN24M2ZR3BNBMGY3V.json","graph_json":"https://pith.science/api/pith-number/4SQQETLSKIN24M2ZR3BNBMGY3V/graph.json","events_json":"https://pith.science/api/pith-number/4SQQETLSKIN24M2ZR3BNBMGY3V/events.json","paper":"https://pith.science/paper/4SQQETLS"},"agent_actions":{"view_html":"https://pith.science/pith/4SQQETLSKIN24M2ZR3BNBMGY3V","download_json":"https://pith.science/pith/4SQQETLSKIN24M2ZR3BNBMGY3V.json","view_paper":"https://pith.science/paper/4SQQETLS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25808&json=true","fetch_graph":"https://pith.science/api/pith-number/4SQQETLSKIN24M2ZR3BNBMGY3V/graph.json","fetch_events":"https://pith.science/api/pith-number/4SQQETLSKIN24M2ZR3BNBMGY3V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4SQQETLSKIN24M2ZR3BNBMGY3V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4SQQETLSKIN24M2ZR3BNBMGY3V/action/storage_attestation","attest_author":"https://pith.science/pith/4SQQETLSKIN24M2ZR3BNBMGY3V/action/author_attestation","sign_citation":"https://pith.science/pith/4SQQETLSKIN24M2ZR3BNBMGY3V/action/citation_signature","submit_replication":"https://pith.science/pith/4SQQETLSKIN24M2ZR3BNBMGY3V/action/replication_record"}},"created_at":"2026-05-26T02:05:12.756904+00:00","updated_at":"2026-05-26T02:05:12.756904+00:00"}