{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:KJYT3PUQL2J3BJKKRZRRYJ4Y4Z","short_pith_number":"pith:KJYT3PUQ","schema_version":"1.0","canonical_sha256":"52713dbe905e93b0a54a8e631c2798e670d6aaae5935f551b82b7f08f6fedc30","source":{"kind":"arxiv","id":"math/9411202","version":1},"attestation_state":"computed","paper":{"title":"Global (and Local) Analyticity for Second Order Operators Constructed from Rigid Vector Fields on Products of Tori","license":"","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David S. Tartakoff","submitted_at":"1994-11-30T22:27:24Z","abstract_excerpt":"We prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid (variable coefficient) quadratic polynomials in real vector fields satisfying the H\\\"ormander condition and where $P$ satisfies a `maximal' estimate. We also prove an analyticity result that is local in some variables and global in others for operators whose prototype is\n  $$ P= \\left({\\partial \\over {\\partial x_1}}\\right)^2 + \\left({\\partial \\over {\\partial x_2}}\\right)^2 + \\left(a(x_1,x_2){\\partial \\over {\\partial t}}\\right)^2.$$\n (with analytic $a(x), a(0)=0,$ natu"},"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":"math/9411202","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"1994-11-30T22:27:24Z","cross_cats_sorted":[],"title_canon_sha256":"6c9b7c65303add02ea5e1927ce733929fc07ff351ac66236d6b8a8e27d8acc22","abstract_canon_sha256":"b7df0b633f4f80e600f9cb9a055359694896247ef54d9d5ab13a06101bbfc239"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:50.918815Z","signature_b64":"xlVcS6NFoJIg38EL2nOlAsgphaZhbzogiweXfA2YbF0uVWRQyAzWi7DwKp1yMa9ku28d5PDBhOlmUztTMyykCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52713dbe905e93b0a54a8e631c2798e670d6aaae5935f551b82b7f08f6fedc30","last_reissued_at":"2026-05-18T01:05:50.918234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:50.918234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global (and Local) Analyticity for Second Order Operators Constructed from Rigid Vector Fields on Products of Tori","license":"","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David S. Tartakoff","submitted_at":"1994-11-30T22:27:24Z","abstract_excerpt":"We prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid (variable coefficient) quadratic polynomials in real vector fields satisfying the H\\\"ormander condition and where $P$ satisfies a `maximal' estimate. We also prove an analyticity result that is local in some variables and global in others for operators whose prototype is\n  $$ P= \\left({\\partial \\over {\\partial x_1}}\\right)^2 + \\left({\\partial \\over {\\partial x_2}}\\right)^2 + \\left(a(x_1,x_2){\\partial \\over {\\partial t}}\\right)^2.$$\n (with analytic $a(x), a(0)=0,$ natu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9411202","kind":"arxiv","version":1},"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":"math/9411202","created_at":"2026-05-18T01:05:50.918311+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9411202v1","created_at":"2026-05-18T01:05:50.918311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9411202","created_at":"2026-05-18T01:05:50.918311+00:00"},{"alias_kind":"pith_short_12","alias_value":"KJYT3PUQL2J3","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"KJYT3PUQL2J3BJKK","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"KJYT3PUQ","created_at":"2026-05-18T12:25:47.102015+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/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z","json":"https://pith.science/pith/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z.json","graph_json":"https://pith.science/api/pith-number/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z/graph.json","events_json":"https://pith.science/api/pith-number/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z/events.json","paper":"https://pith.science/paper/KJYT3PUQ"},"agent_actions":{"view_html":"https://pith.science/pith/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z","download_json":"https://pith.science/pith/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z.json","view_paper":"https://pith.science/paper/KJYT3PUQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9411202&json=true","fetch_graph":"https://pith.science/api/pith-number/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z/graph.json","fetch_events":"https://pith.science/api/pith-number/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z/action/storage_attestation","attest_author":"https://pith.science/pith/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z/action/author_attestation","sign_citation":"https://pith.science/pith/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z/action/citation_signature","submit_replication":"https://pith.science/pith/KJYT3PUQL2J3BJKKRZRRYJ4Y4Z/action/replication_record"}},"created_at":"2026-05-18T01:05:50.918311+00:00","updated_at":"2026-05-18T01:05:50.918311+00:00"}