{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:77EHPB2B4KGHOZXIIXOOHSAJJP","short_pith_number":"pith:77EHPB2B","schema_version":"1.0","canonical_sha256":"ffc8778741e28c7766e845dce3c8094bce4ec93ced27df0f2ced0da10294cdd0","source":{"kind":"arxiv","id":"1409.1634","version":2},"attestation_state":"computed","paper":{"title":"Decouplings for curves and hypersurfaces with nonzero Gaussian curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NT"],"primary_cat":"math.CA","authors_text":"Ciprian Demeter, Jean Bourgain","submitted_at":"2014-09-05T00:52:10Z","abstract_excerpt":"We prove two types of results. First we develop the decoupling theory for hypersurfaces with nonzero Gaussian curvature, which extends our earlier work from \\cite{BD3}. As a consequence of this we obtain sharp (up to $\\epsilon$ losses) Strichartz estimates for the hyperbolic Schr\\\"odinger equation on the torus.\n  Our second main result is an $l^2$ decoupling for non degenerate curves which has implications for Vinogradov's mean value theorem."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.1634","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-05T00:52:10Z","cross_cats_sorted":["math.AP","math.NT"],"title_canon_sha256":"0f2c31eab819025a958fc080c4c82f01457bfcf58a0c33f504e986f866e347ff","abstract_canon_sha256":"c40fa32fd8de74c45274c7f2af6b1ca85d188e594e4b39e7b672a5be8076c62e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:05.565938Z","signature_b64":"bb1nl5zUyuu/N4dgjOG5OMeodfK2c62lnxrzRbatm6YCrKOw6WnJQ+gOrbJLD6t0T4yOLA/PA6buTaoo3dLeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffc8778741e28c7766e845dce3c8094bce4ec93ced27df0f2ced0da10294cdd0","last_reissued_at":"2026-05-18T01:34:05.565430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:05.565430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decouplings for curves and hypersurfaces with nonzero Gaussian curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NT"],"primary_cat":"math.CA","authors_text":"Ciprian Demeter, Jean Bourgain","submitted_at":"2014-09-05T00:52:10Z","abstract_excerpt":"We prove two types of results. First we develop the decoupling theory for hypersurfaces with nonzero Gaussian curvature, which extends our earlier work from \\cite{BD3}. As a consequence of this we obtain sharp (up to $\\epsilon$ losses) Strichartz estimates for the hyperbolic Schr\\\"odinger equation on the torus.\n  Our second main result is an $l^2$ decoupling for non degenerate curves which has implications for Vinogradov's mean value theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1634","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.1634","created_at":"2026-05-18T01:34:05.565514+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1634v2","created_at":"2026-05-18T01:34:05.565514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1634","created_at":"2026-05-18T01:34:05.565514+00:00"},{"alias_kind":"pith_short_12","alias_value":"77EHPB2B4KGH","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"77EHPB2B4KGHOZXI","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"77EHPB2B","created_at":"2026-05-18T12:28:16.859392+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/77EHPB2B4KGHOZXIIXOOHSAJJP","json":"https://pith.science/pith/77EHPB2B4KGHOZXIIXOOHSAJJP.json","graph_json":"https://pith.science/api/pith-number/77EHPB2B4KGHOZXIIXOOHSAJJP/graph.json","events_json":"https://pith.science/api/pith-number/77EHPB2B4KGHOZXIIXOOHSAJJP/events.json","paper":"https://pith.science/paper/77EHPB2B"},"agent_actions":{"view_html":"https://pith.science/pith/77EHPB2B4KGHOZXIIXOOHSAJJP","download_json":"https://pith.science/pith/77EHPB2B4KGHOZXIIXOOHSAJJP.json","view_paper":"https://pith.science/paper/77EHPB2B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1634&json=true","fetch_graph":"https://pith.science/api/pith-number/77EHPB2B4KGHOZXIIXOOHSAJJP/graph.json","fetch_events":"https://pith.science/api/pith-number/77EHPB2B4KGHOZXIIXOOHSAJJP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/77EHPB2B4KGHOZXIIXOOHSAJJP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/77EHPB2B4KGHOZXIIXOOHSAJJP/action/storage_attestation","attest_author":"https://pith.science/pith/77EHPB2B4KGHOZXIIXOOHSAJJP/action/author_attestation","sign_citation":"https://pith.science/pith/77EHPB2B4KGHOZXIIXOOHSAJJP/action/citation_signature","submit_replication":"https://pith.science/pith/77EHPB2B4KGHOZXIIXOOHSAJJP/action/replication_record"}},"created_at":"2026-05-18T01:34:05.565514+00:00","updated_at":"2026-05-18T01:34:05.565514+00:00"}