{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PXAAB3QK6CPDXJW6BTHSUN47QK","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":"856a4085b20217398d0d69a43165ac9472da55edcd30658aaa3fc6995f810a61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-28T14:29:33Z","title_canon_sha256":"6a632f43b9bd660dd80a0aa14271689fb501477e2e17ec3a8604b87b19266a92"},"schema_version":"1.0","source":{"id":"1811.11588","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11588","created_at":"2026-05-17T23:59:40Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11588v1","created_at":"2026-05-17T23:59:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11588","created_at":"2026-05-17T23:59:40Z"},{"alias_kind":"pith_short_12","alias_value":"PXAAB3QK6CPD","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PXAAB3QK6CPDXJW6","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PXAAB3QK","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:b6739643182ef431195d90cabbe0b4fbfc8d59470fc6ab9af8e8a4fdc255282a","target":"graph","created_at":"2026-05-17T23:59:40Z","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"},"paper":{"abstract_excerpt":"For a prime number $p,$ let $\\mathbb{Q}_p$ be the field of $p$-adic numbers. In this paper, we established the boundedness of a class of $p$-adic singular integral operators on the $p$-adic generalized Morrey spaces. The corresponding boundedness for the commutators generalized by the $p$-adic singular integral operators and $p$-adic Lipschitz functions or $p$-adic generalized Campanato functions is also considered.","authors_text":"Huixia Mo, Liu Yang, Zhe Han","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-28T14:29:33Z","title":"$p$-adic singular integral and their commutator in generalized Morrey space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11588","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":"sha256:109c95a029e8622d9e054dca23237ad1423c132227371f2457964ca1174be0b0","target":"record","created_at":"2026-05-17T23:59:40Z","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":"856a4085b20217398d0d69a43165ac9472da55edcd30658aaa3fc6995f810a61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-28T14:29:33Z","title_canon_sha256":"6a632f43b9bd660dd80a0aa14271689fb501477e2e17ec3a8604b87b19266a92"},"schema_version":"1.0","source":{"id":"1811.11588","kind":"arxiv","version":1}},"canonical_sha256":"7dc000ee0af09e3ba6de0ccf2a379f828ffe29d9d47d90a631888470f4d3159f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dc000ee0af09e3ba6de0ccf2a379f828ffe29d9d47d90a631888470f4d3159f","first_computed_at":"2026-05-17T23:59:40.613519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:40.613519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FYtYUHAO8o3G49KYZmPLkTNquGo0PXZzoNGbwtM2HIk2xUmTup2ye4A4SS3KszlqjnTn0tp0qtGBfhJpaoTbDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:40.614278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.11588","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:109c95a029e8622d9e054dca23237ad1423c132227371f2457964ca1174be0b0","sha256:b6739643182ef431195d90cabbe0b4fbfc8d59470fc6ab9af8e8a4fdc255282a"],"state_sha256":"9ca7ca750eaebd3a0ac317c2bce96d86a3bac0f1c3e9894e63af5c1892841f4f"}