{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HFMC2LTABS4GA2SLUXQ3JR3DI5","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":"fd8c39ab2c254accf1c619adc20ccf9bcfbf9088c660e9aeea810c71ace8b784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-01T13:21:07Z","title_canon_sha256":"773bcc28a6bb4d855f90e78b5a3f0a6cd281dce5b1ad1852239e46deae6781fc"},"schema_version":"1.0","source":{"id":"1707.00155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00155","created_at":"2026-05-18T00:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00155v1","created_at":"2026-05-18T00:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00155","created_at":"2026-05-18T00:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"HFMC2LTABS4G","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HFMC2LTABS4GA2SL","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HFMC2LTA","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:b7dae491a709cbab4cb5c1f929f5a87485a718b11edb61fad8114eba56e9a48f","target":"graph","created_at":"2026-05-18T00:41:04Z","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 $\\vec{\\omega}=( \\omega_{1},...,\\omega_{m})$ be a multiple weight and $\\{\\Psi_{j}\\}^{m}_{j=1}$ be a sequence of Young functions. Let $\\mathcal{M}_{\\mathcal{R}}^{\\vec{\\Psi}}$ be the multilinear strong maximal function with Orlicz norms which is defined by $$\\mathcal{M}_{\\mathcal{R}}^{\\vec{\\Psi}}(\\vec{f})(x)=\\sup_{R\\in \\mathcal{R},R\\ni x}\\prod^{m}_{j=1}\\|f_{j}\\|_{\\Psi_{j},R}$$ where the supremum is taken over all rectangles with sides parallel to the coordinate axes. If $\\Psi_j(t)=t$, then $\\mathcal{M}_{\\mathcal{R}}^{\\vec{t}}$ coincides with the multilinear strong mximal function $\\mathcal{M}","authors_text":"Hiroki Saito, Juan Zhang, Qingying Xue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-01T13:21:07Z","title":"The Fefferman-Stein type inequalities for the multilinear strong maximal functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00155","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":"sha256:73bad6ab1436dbb84097f935dbad709a2f5f2e16087b24314b26efe838ecb323","target":"record","created_at":"2026-05-18T00:41:04Z","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":"fd8c39ab2c254accf1c619adc20ccf9bcfbf9088c660e9aeea810c71ace8b784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-01T13:21:07Z","title_canon_sha256":"773bcc28a6bb4d855f90e78b5a3f0a6cd281dce5b1ad1852239e46deae6781fc"},"schema_version":"1.0","source":{"id":"1707.00155","kind":"arxiv","version":1}},"canonical_sha256":"39582d2e600cb8606a4ba5e1b4c7634749aa5d4ca1eadc51a1cd0ad10dfd38a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39582d2e600cb8606a4ba5e1b4c7634749aa5d4ca1eadc51a1cd0ad10dfd38a2","first_computed_at":"2026-05-18T00:41:04.293906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:04.293906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tuaXSw1x1RdrM9pRWPIRcFfHDS3Mw2kLS/8UcX4MsirBZW4yunUW5RYWnetDv8EsqEP2JMP/Y11f44t+ZSy1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:04.294650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73bad6ab1436dbb84097f935dbad709a2f5f2e16087b24314b26efe838ecb323","sha256:b7dae491a709cbab4cb5c1f929f5a87485a718b11edb61fad8114eba56e9a48f"],"state_sha256":"05b744420c8f6e1bdb0775a37bdb99e481df5361ac9a38bef3490662a19482ef"}