{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4ZJ4Y67JLL7LYDVM74UG7N2HRX","short_pith_number":"pith:4ZJ4Y67J","schema_version":"1.0","canonical_sha256":"e653cc7be95afebc0eacff286fb7478dca57f54182cac027f6f6eef89191e23e","source":{"kind":"arxiv","id":"1612.08460","version":3},"attestation_state":"computed","paper":{"title":"On a bilinear Strichartz estimate on irrational tori and some application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bobby Wilson, Chenjie Fan, Gigliola Staffilani, Hong Wang","submitted_at":"2016-12-26T23:40:32Z","abstract_excerpt":"We prove a bilinear Strichartz type estimate for irrational tori via a decoupling type argument, \\cite{bourgain2014proof}, recovering and generalizing the result of \\cite{de2006global}. As a corollary, we derive a global well-posedness result for the cubic defocusing NLS on two dimensional irrational tori with data of infinite energy."},"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":"1612.08460","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-26T23:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"3c9614247a5ce5e681a942ee1d8da6c8919b79b9dbe0803976bbbaba10d958e0","abstract_canon_sha256":"5178b8765bfde6ef1211aa48da2400734fae74d43067d231a5df96f2544fb505"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:31.647823Z","signature_b64":"0zbh0CaiWIk98jeROt1WXvP0btCDxhZzeenIpIG2/v3Z2J1wLgQj6pzHnZ8jy907flSUbZ4MsS0SZfAnAZhOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e653cc7be95afebc0eacff286fb7478dca57f54182cac027f6f6eef89191e23e","last_reissued_at":"2026-05-18T00:27:31.647141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:31.647141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a bilinear Strichartz estimate on irrational tori and some application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bobby Wilson, Chenjie Fan, Gigliola Staffilani, Hong Wang","submitted_at":"2016-12-26T23:40:32Z","abstract_excerpt":"We prove a bilinear Strichartz type estimate for irrational tori via a decoupling type argument, \\cite{bourgain2014proof}, recovering and generalizing the result of \\cite{de2006global}. As a corollary, we derive a global well-posedness result for the cubic defocusing NLS on two dimensional irrational tori with data of infinite energy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08460","kind":"arxiv","version":3},"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":"1612.08460","created_at":"2026-05-18T00:27:31.647265+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08460v3","created_at":"2026-05-18T00:27:31.647265+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08460","created_at":"2026-05-18T00:27:31.647265+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ZJ4Y67JLL7L","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ZJ4Y67JLL7LYDVM","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ZJ4Y67J","created_at":"2026-05-18T12:29:58.707656+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/4ZJ4Y67JLL7LYDVM74UG7N2HRX","json":"https://pith.science/pith/4ZJ4Y67JLL7LYDVM74UG7N2HRX.json","graph_json":"https://pith.science/api/pith-number/4ZJ4Y67JLL7LYDVM74UG7N2HRX/graph.json","events_json":"https://pith.science/api/pith-number/4ZJ4Y67JLL7LYDVM74UG7N2HRX/events.json","paper":"https://pith.science/paper/4ZJ4Y67J"},"agent_actions":{"view_html":"https://pith.science/pith/4ZJ4Y67JLL7LYDVM74UG7N2HRX","download_json":"https://pith.science/pith/4ZJ4Y67JLL7LYDVM74UG7N2HRX.json","view_paper":"https://pith.science/paper/4ZJ4Y67J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08460&json=true","fetch_graph":"https://pith.science/api/pith-number/4ZJ4Y67JLL7LYDVM74UG7N2HRX/graph.json","fetch_events":"https://pith.science/api/pith-number/4ZJ4Y67JLL7LYDVM74UG7N2HRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ZJ4Y67JLL7LYDVM74UG7N2HRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ZJ4Y67JLL7LYDVM74UG7N2HRX/action/storage_attestation","attest_author":"https://pith.science/pith/4ZJ4Y67JLL7LYDVM74UG7N2HRX/action/author_attestation","sign_citation":"https://pith.science/pith/4ZJ4Y67JLL7LYDVM74UG7N2HRX/action/citation_signature","submit_replication":"https://pith.science/pith/4ZJ4Y67JLL7LYDVM74UG7N2HRX/action/replication_record"}},"created_at":"2026-05-18T00:27:31.647265+00:00","updated_at":"2026-05-18T00:27:31.647265+00:00"}