{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NGVFA6O2SIU7M3U5MTLEFYGVWC","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":"f6759e5fb1d691c65b409c2624e9c91c3c6ac7b8cf645ddfeefbe48c211e520d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-29T02:52:00Z","title_canon_sha256":"c54a42a3e38c25054d13653b0814c19d6b642267ae3b4e2208a0cc7f585fcfa4"},"schema_version":"1.0","source":{"id":"2605.30766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30766","created_at":"2026-06-01T01:03:15Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30766v1","created_at":"2026-06-01T01:03:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30766","created_at":"2026-06-01T01:03:15Z"},{"alias_kind":"pith_short_12","alias_value":"NGVFA6O2SIU7","created_at":"2026-06-01T01:03:15Z"},{"alias_kind":"pith_short_16","alias_value":"NGVFA6O2SIU7M3U5","created_at":"2026-06-01T01:03:15Z"},{"alias_kind":"pith_short_8","alias_value":"NGVFA6O2","created_at":"2026-06-01T01:03:15Z"}],"graph_snapshots":[{"event_id":"sha256:9f881a063c0f9c3a969688223a85f8494c9afa52cb14265b1b8b589fdd7411db","target":"graph","created_at":"2026-06-01T01:03:15Z","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/2605.30766/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove an $L^2$ two-weight testing theorem for the Dunkl--Poisson semigroup. The difficulty is geometric. The Dunkl orbit distance has several reflected diagonals, so a single orbit-box test may mix different chamber components. We avoid this by working on one Weyl chamber and keeping the chamber indices. Under the wall-null assumption the full operator becomes a finite matrix of scalar positive Poisson-type operators. In each entry the orbit diagonal is just the ordinary diagonal in the chamber variables. The scalar proof is then a principal-cube stopping-time argument, with two Dunkl kerne","authors_text":"Brett D. Wick, Ji Li, Liangchuan Wu, Qingdong Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-29T02:52:00Z","title":"Two-weight inequalities for the Dunkl--Poisson integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30766","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":"sha256:85e6b508d179623e1a28b4d9b417da374ff39d9cac5bfbb7c5c0d31dea72639d","target":"record","created_at":"2026-06-01T01:03:15Z","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":"f6759e5fb1d691c65b409c2624e9c91c3c6ac7b8cf645ddfeefbe48c211e520d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-29T02:52:00Z","title_canon_sha256":"c54a42a3e38c25054d13653b0814c19d6b642267ae3b4e2208a0cc7f585fcfa4"},"schema_version":"1.0","source":{"id":"2605.30766","kind":"arxiv","version":1}},"canonical_sha256":"69aa5079da9229f66e9d64d642e0d5b0a46cb746155e683a2814a01f602bc157","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69aa5079da9229f66e9d64d642e0d5b0a46cb746155e683a2814a01f602bc157","first_computed_at":"2026-06-01T01:03:15.228060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:03:15.228060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k8QujtVYVB6oWCqrzu+npRgBoMP+mH7yU0YV2D3olq/0S7p8a5vcUqsoVU76DrXpBUtk/A+5bqgsG4kw7MQdDw==","signature_status":"signed_v1","signed_at":"2026-06-01T01:03:15.228949Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85e6b508d179623e1a28b4d9b417da374ff39d9cac5bfbb7c5c0d31dea72639d","sha256:9f881a063c0f9c3a969688223a85f8494c9afa52cb14265b1b8b589fdd7411db"],"state_sha256":"7dc674b68a7429c48c479fdab104aed41f2ed6a8adf601f7ef535d94417eb1dd"}