{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WXEVAWNHQ7QJQ4RZ7IFKNI2HP3","short_pith_number":"pith:WXEVAWNH","canonical_record":{"source":{"id":"2606.01130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-31T10:02:44Z","cross_cats_sorted":[],"title_canon_sha256":"6f9e832f7778320f16a885e1d337450cab32b8c7927b77a7a61ae67b93452df6","abstract_canon_sha256":"8923e4f917a29a41965e4c51437bda449d1c5fe3c5c919f6b56cf81324bbb84c"},"schema_version":"1.0"},"canonical_sha256":"b5c95059a787e0987239fa0aa6a3477ed871dfaa11e98aa3580853254bdac5d2","source":{"kind":"arxiv","id":"2606.01130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01130","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01130v1","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01130","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"WXEVAWNHQ7QJ","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"WXEVAWNHQ7QJQ4RZ","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"WXEVAWNH","created_at":"2026-06-02T02:04:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WXEVAWNHQ7QJQ4RZ7IFKNI2HP3","target":"record","payload":{"canonical_record":{"source":{"id":"2606.01130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-31T10:02:44Z","cross_cats_sorted":[],"title_canon_sha256":"6f9e832f7778320f16a885e1d337450cab32b8c7927b77a7a61ae67b93452df6","abstract_canon_sha256":"8923e4f917a29a41965e4c51437bda449d1c5fe3c5c919f6b56cf81324bbb84c"},"schema_version":"1.0"},"canonical_sha256":"b5c95059a787e0987239fa0aa6a3477ed871dfaa11e98aa3580853254bdac5d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:24.357533Z","signature_b64":"1jMOf0rYmdBCVYQkfQA4/EKWUeFuKdF5hPNXPgfkgLU4k29wK7lq3jUoBjT5TMGIQ1hPcMGvs39UXSs5zZcECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5c95059a787e0987239fa0aa6a3477ed871dfaa11e98aa3580853254bdac5d2","last_reissued_at":"2026-06-02T02:04:24.357060Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:24.357060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.01130","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T02:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZ7l6SGH+waNkElOtSzhl+XNLm+YiZMrXcazxZQPwt0LyP5pw1t+Y6HR/BwJMTvAMCnt+yWSi+5633j0YT2nBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:38:34.777627Z"},"content_sha256":"17d2c25fe35053ac51ba5ede6db0e30581fc5365e9011ad4159785b4760340a1","schema_version":"1.0","event_id":"sha256:17d2c25fe35053ac51ba5ede6db0e30581fc5365e9011ad4159785b4760340a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WXEVAWNHQ7QJQ4RZ7IFKNI2HP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chamber lifting and non-radial Dunkl multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Chaojie Wen, Der-Chen Chang, Ji Li, Liangchuan Wu","submitted_at":"2026-05-31T10:02:44Z","abstract_excerpt":"We study non-radial Dunkl multipliers via chamber lifting. For an arbitrary finite reflection group $G$, the chamber lifting records all reflected values of a function and conjugates a multiplier into a finite matrix-valued operator on the chamber. If the dyadic matrix entries admit off-diagonal kernels satisfying the chamber $L^2$ H\\\"ormander condition $\\operatorname{CH}^2_{s,\\eta}$ with $s>N_\\kappa/2$, then the original multiplier is bounded on $L^p(\\mathbb R^N,d\\omega)$ for every $1<p<\\infty$.\n  For the product reflection group $\\Sigma_N=A_1^N\\simeq\\mathbb Z_2^N$ this chamber condition foll"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01130","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/2606.01130/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T02:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8duH/6CubdDGkI1TcPKX/PzNH/n+bBAW88ngWbyhbAiMGrm8mdHalIwq1/DomJ8GAfNqm2qSrUoancVCV7pAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:38:34.778043Z"},"content_sha256":"3aa8cfb1343878f9678a7743c9322f04909a309c081f56cd2d3ee82eecebbcd3","schema_version":"1.0","event_id":"sha256:3aa8cfb1343878f9678a7743c9322f04909a309c081f56cd2d3ee82eecebbcd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WXEVAWNHQ7QJQ4RZ7IFKNI2HP3/bundle.json","state_url":"https://pith.science/pith/WXEVAWNHQ7QJQ4RZ7IFKNI2HP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WXEVAWNHQ7QJQ4RZ7IFKNI2HP3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T05:38:34Z","links":{"resolver":"https://pith.science/pith/WXEVAWNHQ7QJQ4RZ7IFKNI2HP3","bundle":"https://pith.science/pith/WXEVAWNHQ7QJQ4RZ7IFKNI2HP3/bundle.json","state":"https://pith.science/pith/WXEVAWNHQ7QJQ4RZ7IFKNI2HP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WXEVAWNHQ7QJQ4RZ7IFKNI2HP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WXEVAWNHQ7QJQ4RZ7IFKNI2HP3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8923e4f917a29a41965e4c51437bda449d1c5fe3c5c919f6b56cf81324bbb84c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-31T10:02:44Z","title_canon_sha256":"6f9e832f7778320f16a885e1d337450cab32b8c7927b77a7a61ae67b93452df6"},"schema_version":"1.0","source":{"id":"2606.01130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01130","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01130v1","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01130","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"WXEVAWNHQ7QJ","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"WXEVAWNHQ7QJQ4RZ","created_at":"2026-06-02T02:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"WXEVAWNH","created_at":"2026-06-02T02:04:24Z"}],"graph_snapshots":[{"event_id":"sha256:3aa8cfb1343878f9678a7743c9322f04909a309c081f56cd2d3ee82eecebbcd3","target":"graph","created_at":"2026-06-02T02:04:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.01130/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study non-radial Dunkl multipliers via chamber lifting. For an arbitrary finite reflection group $G$, the chamber lifting records all reflected values of a function and conjugates a multiplier into a finite matrix-valued operator on the chamber. If the dyadic matrix entries admit off-diagonal kernels satisfying the chamber $L^2$ H\\\"ormander condition $\\operatorname{CH}^2_{s,\\eta}$ with $s>N_\\kappa/2$, then the original multiplier is bounded on $L^p(\\mathbb R^N,d\\omega)$ for every $1<p<\\infty$.\n  For the product reflection group $\\Sigma_N=A_1^N\\simeq\\mathbb Z_2^N$ this chamber condition foll","authors_text":"Chaojie Wen, Der-Chen Chang, Ji Li, Liangchuan Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-31T10:02:44Z","title":"Chamber lifting and non-radial Dunkl multipliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01130","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":"sha256:17d2c25fe35053ac51ba5ede6db0e30581fc5365e9011ad4159785b4760340a1","target":"record","created_at":"2026-06-02T02:04:24Z","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":"8923e4f917a29a41965e4c51437bda449d1c5fe3c5c919f6b56cf81324bbb84c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-31T10:02:44Z","title_canon_sha256":"6f9e832f7778320f16a885e1d337450cab32b8c7927b77a7a61ae67b93452df6"},"schema_version":"1.0","source":{"id":"2606.01130","kind":"arxiv","version":1}},"canonical_sha256":"b5c95059a787e0987239fa0aa6a3477ed871dfaa11e98aa3580853254bdac5d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5c95059a787e0987239fa0aa6a3477ed871dfaa11e98aa3580853254bdac5d2","first_computed_at":"2026-06-02T02:04:24.357060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:24.357060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1jMOf0rYmdBCVYQkfQA4/EKWUeFuKdF5hPNXPgfkgLU4k29wK7lq3jUoBjT5TMGIQ1hPcMGvs39UXSs5zZcECg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:24.357533Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17d2c25fe35053ac51ba5ede6db0e30581fc5365e9011ad4159785b4760340a1","sha256:3aa8cfb1343878f9678a7743c9322f04909a309c081f56cd2d3ee82eecebbcd3"],"state_sha256":"2fc6db6d5f80c5a45a43314cd0d4b6c25a5c8a3a0bc363c0d6a768cffb3898a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b9WMp/yxVVXzzDpZQrYmgngUAMTve+9UxR2qK+iq7xmO9gECR/nHvyIVjQ80LiL5QxyyRpiMjOpp1yIKIQWCAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:38:34.780774Z","bundle_sha256":"233acc75a5811c5756d294f8a875a064e6d2e27acc51a1aff10088a6105410a8"}}