{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:KJYT3PUQL2J3BJKKRZRRYJ4Y4Z","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":"b7df0b633f4f80e600f9cb9a055359694896247ef54d9d5ab13a06101bbfc239","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"1994-11-30T22:27:24Z","title_canon_sha256":"6c9b7c65303add02ea5e1927ce733929fc07ff351ac66236d6b8a8e27d8acc22"},"schema_version":"1.0","source":{"id":"math/9411202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9411202","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9411202v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9411202","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"KJYT3PUQL2J3","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"KJYT3PUQL2J3BJKK","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"KJYT3PUQ","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:43668f33dc65f8017b58a6e91ccb187ef83bf0da337088978496937af67267ed","target":"graph","created_at":"2026-05-18T01:05:50Z","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"},"paper":{"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","authors_text":"David S. Tartakoff","cross_cats":[],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"1994-11-30T22:27:24Z","title":"Global (and Local) Analyticity for Second Order Operators Constructed from Rigid Vector Fields on Products of Tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9411202","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":"sha256:3c799556348542c97d1fa83e6d652c8701251a879e37b27341f5a016a8137c62","target":"record","created_at":"2026-05-18T01:05:50Z","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":"b7df0b633f4f80e600f9cb9a055359694896247ef54d9d5ab13a06101bbfc239","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"1994-11-30T22:27:24Z","title_canon_sha256":"6c9b7c65303add02ea5e1927ce733929fc07ff351ac66236d6b8a8e27d8acc22"},"schema_version":"1.0","source":{"id":"math/9411202","kind":"arxiv","version":1}},"canonical_sha256":"52713dbe905e93b0a54a8e631c2798e670d6aaae5935f551b82b7f08f6fedc30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52713dbe905e93b0a54a8e631c2798e670d6aaae5935f551b82b7f08f6fedc30","first_computed_at":"2026-05-18T01:05:50.918234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:50.918234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xlVcS6NFoJIg38EL2nOlAsgphaZhbzogiweXfA2YbF0uVWRQyAzWi7DwKp1yMa9ku28d5PDBhOlmUztTMyykCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:50.918815Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9411202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c799556348542c97d1fa83e6d652c8701251a879e37b27341f5a016a8137c62","sha256:43668f33dc65f8017b58a6e91ccb187ef83bf0da337088978496937af67267ed"],"state_sha256":"bf8ca1d06bc0ea1208d03ca720c4226b89fabf27d89c343a88806872f54a88e7"}