{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MHDQHYPKMT3YW75RPKMVK3RLOD","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":"6cc068707d8dfd432663fa532fddfe9468bb2049227e5e2fae61c881e53715fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-04-23T15:43:52Z","title_canon_sha256":"7abdb35638f50bab3ab317449d82c505a5b88d8adcec576bebf19623f4962b2a"},"schema_version":"1.0","source":{"id":"2504.16827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16827","created_at":"2026-07-05T10:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16827v1","created_at":"2026-07-05T10:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16827","created_at":"2026-07-05T10:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"MHDQHYPKMT3Y","created_at":"2026-07-05T10:53:05Z"},{"alias_kind":"pith_short_16","alias_value":"MHDQHYPKMT3YW75R","created_at":"2026-07-05T10:53:05Z"},{"alias_kind":"pith_short_8","alias_value":"MHDQHYPK","created_at":"2026-07-05T10:53:05Z"}],"graph_snapshots":[{"event_id":"sha256:d5982856c043e24650c3116269e60dc7d1d4538a58fab0f5d22ff885e56fce97","target":"graph","created_at":"2026-07-05T10:53:05Z","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/2504.16827/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $ \\mathcal{L} = -\\Delta + V $ be a Schr\\\"odinger operator acting on $ L^2(\\mathbb{R}^n) $, where the nonnegative potential $ V $ belongs to the reverse H\\\"older class $ RH_q $ for some $ q \\geq n/2 $. This article is primarily concerned with the study of endpoint boundedness for classical singular integral operators in the context of the space $ \\mathrm{CMO}_{\\mathcal{L}}(\\mathbb{R}^n) $, consisting of functions of vanishing mean oscillation associated with $ \\mathcal{L} $.\n  We establish the following main results: (i) the standard Hardy--Littlewood maximal operator is bounded on $\\mathrm","authors_text":"Ji Li, Liangchuan Wu, Xueting Han","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-04-23T15:43:52Z","title":"Endpoint boundedness of singular integrals: CMO space associated to Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16827","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:d8276cf267f9948d0b4cf7239786b96f3de4ff84277c841e415ae041fc6112d4","target":"record","created_at":"2026-07-05T10:53:05Z","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":"6cc068707d8dfd432663fa532fddfe9468bb2049227e5e2fae61c881e53715fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-04-23T15:43:52Z","title_canon_sha256":"7abdb35638f50bab3ab317449d82c505a5b88d8adcec576bebf19623f4962b2a"},"schema_version":"1.0","source":{"id":"2504.16827","kind":"arxiv","version":1}},"canonical_sha256":"61c703e1ea64f78b7fb17a99556e2b70d36b169d986d22c247e387d5712c4591","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61c703e1ea64f78b7fb17a99556e2b70d36b169d986d22c247e387d5712c4591","first_computed_at":"2026-07-05T10:53:05.021059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:53:05.021059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d7sJDehUaSieT+bVXd+aJkBIlfWxz+Qvh/WSVeVc7EW0dgX6HezRQqCm6m9s5641jov+GbIl80wPTzeFvNJbBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:53:05.021476Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.16827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8276cf267f9948d0b4cf7239786b96f3de4ff84277c841e415ae041fc6112d4","sha256:d5982856c043e24650c3116269e60dc7d1d4538a58fab0f5d22ff885e56fce97"],"state_sha256":"3d7b2ed148cffd905cee644e9b60c4bc69d80b106162e9ab1ea9a08ff4489d4f"}