{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:SMBOP2IAJYRJHZB32OIA2FAOJ6","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":"9ce1150b408d4f7d7a4cf1a88eb10cd3432c3f049f7cc3c69f170078e71c47c0","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2005-01-08T16:26:35Z","title_canon_sha256":"df1e5d8fcb4ed4460b4c39159d7b25ac6230ba357044d0d64983cea3dcb95781"},"schema_version":"1.0","source":{"id":"math/0501114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501114","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501114v1","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501114","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_12","alias_value":"SMBOP2IAJYRJ","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_16","alias_value":"SMBOP2IAJYRJHZB3","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_8","alias_value":"SMBOP2IA","created_at":"2026-07-04T17:23:15Z"}],"graph_snapshots":[{"event_id":"sha256:7ebb9673416a8e34f761a1404a2fa245e1820efb6b5fb369091b4f98a2831617","target":"graph","created_at":"2026-07-04T17:23:15Z","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/math/0501114/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given Mikhlin-H\\\"ormander multipliers $m_i$, $i=1,..., N$, with uniform estimates we prove an optimal $\\sqrt{\\log(N+1)}$ bound in $L^p$ for the maximal function $\\sup_i|\\cF^{-1}[m_i\\hat f]|$ and related bounds for maximal functions generated by dilations.","authors_text":"Andreas Seeger, Loukas Grafakos, Petr Honzik","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2005-01-08T16:26:35Z","title":"On maximal functions for Mikhlin-Hoermander multipliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501114","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":"sha256:3b47a298ae3d98f2238a7b5369eba05cd7c1df3aea5d085fa1d53e06bca76620","target":"record","created_at":"2026-07-04T17:23:15Z","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":"9ce1150b408d4f7d7a4cf1a88eb10cd3432c3f049f7cc3c69f170078e71c47c0","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2005-01-08T16:26:35Z","title_canon_sha256":"df1e5d8fcb4ed4460b4c39159d7b25ac6230ba357044d0d64983cea3dcb95781"},"schema_version":"1.0","source":{"id":"math/0501114","kind":"arxiv","version":1}},"canonical_sha256":"9302e7e9004e2293e43bd3900d140e4fb01cde56f6b6fd3ca7e2e5c13450e49a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9302e7e9004e2293e43bd3900d140e4fb01cde56f6b6fd3ca7e2e5c13450e49a","first_computed_at":"2026-07-04T17:23:15.300151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:23:15.300151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xCz31S26ITE7MitIsGInMS80dp+yBsXwLUDzTU70T10d3fI6WP2yiqmBRE/Gm8+RF7ZaymVzWYZ426C+KMB3AQ==","signature_status":"signed_v1","signed_at":"2026-07-04T17:23:15.300585Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b47a298ae3d98f2238a7b5369eba05cd7c1df3aea5d085fa1d53e06bca76620","sha256:7ebb9673416a8e34f761a1404a2fa245e1820efb6b5fb369091b4f98a2831617"],"state_sha256":"00f8afce8ecd29b250cf5252c8515329b7abe710bd00ea4209687c3bfbeb9a1b"}