{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:U4THKRABWKYSM34U3XLF5IIXLK","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":"7a4e38e7a60ee5e714cb3d0755ac645a9bc7ae0c6cb7d0370e27c7610c130077","cross_cats_sorted":["math.FA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-06-05T22:57:16Z","title_canon_sha256":"0a87acf6485be032aefec5981005ad8286a88dcc17e2c33bdf6864f23a661204"},"schema_version":"1.0","source":{"id":"2506.05624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05624","created_at":"2026-07-05T11:17:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05624v1","created_at":"2026-07-05T11:17:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05624","created_at":"2026-07-05T11:17:07Z"},{"alias_kind":"pith_short_12","alias_value":"U4THKRABWKYS","created_at":"2026-07-05T11:17:07Z"},{"alias_kind":"pith_short_16","alias_value":"U4THKRABWKYSM34U","created_at":"2026-07-05T11:17:07Z"},{"alias_kind":"pith_short_8","alias_value":"U4THKRAB","created_at":"2026-07-05T11:17:07Z"}],"graph_snapshots":[{"event_id":"sha256:3be2bdcdd230891e588c12e9f3f785809343dbfe7f44155fd858fbf8179efe67","target":"graph","created_at":"2026-07-05T11:17:07Z","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/2506.05624/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A Mizohata-Takeuchi type estimate is a type of weighted Fourier restriction estimate. Using tools from high dimensional probability, we construct a large class of weights that satisfy sharp estimates of Mizohata-Takeuchi type. One can interpret our result as saying that with high probability, a generic weight satisfies a sharp inequality of Mizohata-Takeuchi type (up to an epsilon-loss).","authors_text":"Siddharth Mulherkar","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-06-05T22:57:16Z","title":"Random Constructions for Sharp Estimates of Mizohata-Takeuchi Type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05624","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:c5dd4193dcab52940e97b0fd989e63f94cefad5629e6dbbec2ad6f0d71914f0a","target":"record","created_at":"2026-07-05T11:17:07Z","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":"7a4e38e7a60ee5e714cb3d0755ac645a9bc7ae0c6cb7d0370e27c7610c130077","cross_cats_sorted":["math.FA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-06-05T22:57:16Z","title_canon_sha256":"0a87acf6485be032aefec5981005ad8286a88dcc17e2c33bdf6864f23a661204"},"schema_version":"1.0","source":{"id":"2506.05624","kind":"arxiv","version":1}},"canonical_sha256":"a726754401b2b1266f94ddd65ea1175aac56152c93232339623d85e9fbc301a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a726754401b2b1266f94ddd65ea1175aac56152c93232339623d85e9fbc301a4","first_computed_at":"2026-07-05T11:17:07.026972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:07.026972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ZBIb2VrkS9V1sklgYkbJSIRRmRJQEzmcNx6q15xGCgLgvs9i6i8+da5EycxVFzozAQ7BaXF9rim4M8F9ZdHCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:07.027459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.05624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5dd4193dcab52940e97b0fd989e63f94cefad5629e6dbbec2ad6f0d71914f0a","sha256:3be2bdcdd230891e588c12e9f3f785809343dbfe7f44155fd858fbf8179efe67"],"state_sha256":"865290eccae7ad4fe777b4bae237531ffb524d2e0fbf95b08780c387008aae76"}