{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FY6Z37QWBOSSWOLGE7D4IVHLET","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":"9ca183249b693dacc4969482b8a8c4413765d9e3077fa33e6f133fc79e298345","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-08-20T14:55:36Z","title_canon_sha256":"07c974d6933857c2f4ff06e4407718972c59a9423a0bb856a74358b5381a8110"},"schema_version":"1.0","source":{"id":"2408.10911","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.10911","created_at":"2026-07-05T10:50:30Z"},{"alias_kind":"arxiv_version","alias_value":"2408.10911v2","created_at":"2026-07-05T10:50:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.10911","created_at":"2026-07-05T10:50:30Z"},{"alias_kind":"pith_short_12","alias_value":"FY6Z37QWBOSS","created_at":"2026-07-05T10:50:30Z"},{"alias_kind":"pith_short_16","alias_value":"FY6Z37QWBOSSWOLG","created_at":"2026-07-05T10:50:30Z"},{"alias_kind":"pith_short_8","alias_value":"FY6Z37QW","created_at":"2026-07-05T10:50:30Z"}],"graph_snapshots":[{"event_id":"sha256:1514a8dd555a29509beff50824e10e6ab1e80b583564e1a6f3fb24155fe96f37","target":"graph","created_at":"2026-07-05T10:50:30Z","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/2408.10911/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the generic multiplicative approximation rate on a hypersurface. There are four regimes, according to convergence or divergence and curved or flat, and we address all of them. Using geometry and arithmetic in Fourier space, we develop a general framework of moment transference principles, which convert Lebesgue data into data for some other measure.","authors_text":"Han Yu, Sam Chow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-08-20T14:55:36Z","title":"Moment transference principles and multiplicative diophantine approximation on hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.10911","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:a008367f9ef446d094aa94b3b54d69423b99ee6ee3b4c6bd18fb33d01da440d3","target":"record","created_at":"2026-07-05T10:50:30Z","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":"9ca183249b693dacc4969482b8a8c4413765d9e3077fa33e6f133fc79e298345","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-08-20T14:55:36Z","title_canon_sha256":"07c974d6933857c2f4ff06e4407718972c59a9423a0bb856a74358b5381a8110"},"schema_version":"1.0","source":{"id":"2408.10911","kind":"arxiv","version":2}},"canonical_sha256":"2e3d9dfe160ba52b396627c7c454eb24fadab9b6c94474c213fd7b26f9152a8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e3d9dfe160ba52b396627c7c454eb24fadab9b6c94474c213fd7b26f9152a8f","first_computed_at":"2026-07-05T10:50:30.542228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:50:30.542228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TeHWltVBMvfQhZ+z6GwcVhTl985pqi4gyvtpjXAWpkClxP9yndKKlXvUNdzQQRjv1iKwF0zCXU9ZWK942JC+Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:50:30.542811Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.10911","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a008367f9ef446d094aa94b3b54d69423b99ee6ee3b4c6bd18fb33d01da440d3","sha256:1514a8dd555a29509beff50824e10e6ab1e80b583564e1a6f3fb24155fe96f37"],"state_sha256":"d862ca5c347f84cf80847e6bb885b12965fbfa5462c13238a5eaacfa4384d848"}