{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ULDRLIDGSPQ75HUGOZT53K6VPZ","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":"f35e75b90bf3fcc4c122e136b839dd0ec5526dc17b27c49309102652f4bfd337","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-30T02:35:39Z","title_canon_sha256":"e12e8684e4413ea28e207054add23b1107bc47a673a421e19480cb0ce705d4da"},"schema_version":"1.0","source":{"id":"1801.09828","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09828","created_at":"2026-05-18T00:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09828v2","created_at":"2026-05-18T00:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09828","created_at":"2026-05-18T00:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"ULDRLIDGSPQ7","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"ULDRLIDGSPQ75HUG","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"ULDRLIDG","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:bdfb0dc6ae3f9c4bb70dd4241c7a4519847caf9e116dfdb6ce9d37467d1e8b76","target":"graph","created_at":"2026-05-18T00:24:41Z","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":"Let $m\\ge 1$, in this paper, our object of investigation is the regularity and and continuity properties of the following multilinear strong maximal operator $${\\mathscr{M}}_{\\mathcal{R}}(\\vec{f})(x)=\\sup_{\\substack{R \\ni x R\\in\\mathcal{R}}}\\prod\\limits_{i=1}^m\\frac{1}{|R|}\\int_{R}|f_i(y)|dy,$$ where $x\\in\\mathbb{R}^d$ and $\\mathcal{R}$ denotes the family of all rectangles in $\\mathbb{R}^d$ with sides parallel to the axes. When $m=1$, denote $\\mathscr{M}_{\\mathcal{R}}$ by $\\mathcal {M}_{\\mathcal{R}}$.Then, $\\mathcal {M}_{\\mathcal{R}}$ coincides with the classical strong maximal function initia","authors_text":"Feng Liu, Kozo Yabuta, Qingying Xue","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-30T02:35:39Z","title":"Regularity and continuity of the multilinear strong maximal operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09828","kind":"arxiv","version":2},"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":"sha256:9b6759af7cabf8fd549c6fb5c805e248f5e0ab2b309c8384918c2c9f0325cd82","target":"record","created_at":"2026-05-18T00:24:41Z","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":"f35e75b90bf3fcc4c122e136b839dd0ec5526dc17b27c49309102652f4bfd337","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-30T02:35:39Z","title_canon_sha256":"e12e8684e4413ea28e207054add23b1107bc47a673a421e19480cb0ce705d4da"},"schema_version":"1.0","source":{"id":"1801.09828","kind":"arxiv","version":2}},"canonical_sha256":"a2c715a06693e1fe9e867667ddabd57e57226c31a2afb842b314cfa3f6507fe4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2c715a06693e1fe9e867667ddabd57e57226c31a2afb842b314cfa3f6507fe4","first_computed_at":"2026-05-18T00:24:41.598392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:41.598392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RC9khbRI64HtgEaUWAGCymC/V7/uI6MYIeGXTaPi1UFutR0OReMGuIgMTfk4dVwiQDc6Y1k/3vH/yJKwq+UGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:41.599042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09828","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b6759af7cabf8fd549c6fb5c805e248f5e0ab2b309c8384918c2c9f0325cd82","sha256:bdfb0dc6ae3f9c4bb70dd4241c7a4519847caf9e116dfdb6ce9d37467d1e8b76"],"state_sha256":"3037f33233e1b7aab5fbe8de84496c9681d6637231047bc7774a95a9b845d3a7"}