{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZYM5K6ISHMUQNOI3MTUEEG5E37","short_pith_number":"pith:ZYM5K6IS","schema_version":"1.0","canonical_sha256":"ce19d579123b2906b91b64e8421ba4dfd4762ee5ad5180c0978c98f678ae93c2","source":{"kind":"arxiv","id":"1708.01307","version":1},"attestation_state":"computed","paper":{"title":"Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Bove, Gregorio Chinni","submitted_at":"2017-08-03T20:57:05Z","abstract_excerpt":"We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\\\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of squares with analytic coefficients is perturbed with a pseudodifferential operator of order strictly less than its subelliptic index it still has the Gevrey minimal regularity. We also prove a statement concerning real analytic hypoellipticity for the same type of pseudodifferential perturbations, provided the operator satisfies to some extra conditions (see Th"},"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":"1708.01307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-03T20:57:05Z","cross_cats_sorted":[],"title_canon_sha256":"ccfae0ced8025679bb9a0e05c8670329b00babe09005395584bd86d477785943","abstract_canon_sha256":"f4671d960ddb6960273d651b6a3399811dc3b562cebd85ba53ab2ef337d6092f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:37.724058Z","signature_b64":"hMEB0NaP4POtoU+y7YqW6/DYm+XCrbiFSJpwTQobVWAcGsQ+rJz5aYFRyAp4wqkKaiWZOwgNtBbEIfITzlQ9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce19d579123b2906b91b64e8421ba4dfd4762ee5ad5180c0978c98f678ae93c2","last_reissued_at":"2026-05-18T00:38:37.723379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:37.723379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Bove, Gregorio Chinni","submitted_at":"2017-08-03T20:57:05Z","abstract_excerpt":"We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\\\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of squares with analytic coefficients is perturbed with a pseudodifferential operator of order strictly less than its subelliptic index it still has the Gevrey minimal regularity. We also prove a statement concerning real analytic hypoellipticity for the same type of pseudodifferential perturbations, provided the operator satisfies to some extra conditions (see Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01307","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":"1708.01307","created_at":"2026-05-18T00:38:37.723486+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.01307v1","created_at":"2026-05-18T00:38:37.723486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01307","created_at":"2026-05-18T00:38:37.723486+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZYM5K6ISHMUQ","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZYM5K6ISHMUQNOI3","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZYM5K6IS","created_at":"2026-05-18T12:31:59.375834+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/ZYM5K6ISHMUQNOI3MTUEEG5E37","json":"https://pith.science/pith/ZYM5K6ISHMUQNOI3MTUEEG5E37.json","graph_json":"https://pith.science/api/pith-number/ZYM5K6ISHMUQNOI3MTUEEG5E37/graph.json","events_json":"https://pith.science/api/pith-number/ZYM5K6ISHMUQNOI3MTUEEG5E37/events.json","paper":"https://pith.science/paper/ZYM5K6IS"},"agent_actions":{"view_html":"https://pith.science/pith/ZYM5K6ISHMUQNOI3MTUEEG5E37","download_json":"https://pith.science/pith/ZYM5K6ISHMUQNOI3MTUEEG5E37.json","view_paper":"https://pith.science/paper/ZYM5K6IS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.01307&json=true","fetch_graph":"https://pith.science/api/pith-number/ZYM5K6ISHMUQNOI3MTUEEG5E37/graph.json","fetch_events":"https://pith.science/api/pith-number/ZYM5K6ISHMUQNOI3MTUEEG5E37/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZYM5K6ISHMUQNOI3MTUEEG5E37/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZYM5K6ISHMUQNOI3MTUEEG5E37/action/storage_attestation","attest_author":"https://pith.science/pith/ZYM5K6ISHMUQNOI3MTUEEG5E37/action/author_attestation","sign_citation":"https://pith.science/pith/ZYM5K6ISHMUQNOI3MTUEEG5E37/action/citation_signature","submit_replication":"https://pith.science/pith/ZYM5K6ISHMUQNOI3MTUEEG5E37/action/replication_record"}},"created_at":"2026-05-18T00:38:37.723486+00:00","updated_at":"2026-05-18T00:38:37.723486+00:00"}