{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:O567CNGZPUKEIGTDAYHZV67IFH","short_pith_number":"pith:O567CNGZ","schema_version":"1.0","canonical_sha256":"777df134d97d14441a63060f9afbe829c5caed3338e84a3793a54194456e8942","source":{"kind":"arxiv","id":"1604.06000","version":3},"attestation_state":"computed","paper":{"title":"Quantitative uniqueness for zero-order perturbations of generalized Baouendi-Grushin operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, Nicola Garofalo","submitted_at":"2016-04-20T15:20:50Z","abstract_excerpt":"Based on a variant of the frequency function approach of Almgren, we establish an optimal bound on the vanishing order of solutions to stationary Schr\\\"odinger equations associated to a class of subelliptic equations with variable coefficients whose model is the so-called Baouendi-Grushin operator. Such bound provides a quantitative form of strong unique continuation that can be thought of as an analogue of the recent results of Bakri and Zhu for the standard Laplacian."},"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":"1604.06000","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-20T15:20:50Z","cross_cats_sorted":[],"title_canon_sha256":"b33302b4a713e1c61b8f5d4e6f5b186e87acf88088c80d50d32300ccefae63e6","abstract_canon_sha256":"1436196c263ce8324df17ee7d12af473b950f7176932c5256e7ab3f48dd1c9dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:50.352842Z","signature_b64":"IGIz0902sZESvULlui5PLe64UK7m5MCwF1AB626eklbjX7M744JKK4ZbEaMXF5Xq5QkWyy8kyJwBRV943sTDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"777df134d97d14441a63060f9afbe829c5caed3338e84a3793a54194456e8942","last_reissued_at":"2026-05-18T00:52:50.352178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:50.352178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative uniqueness for zero-order perturbations of generalized Baouendi-Grushin operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, Nicola Garofalo","submitted_at":"2016-04-20T15:20:50Z","abstract_excerpt":"Based on a variant of the frequency function approach of Almgren, we establish an optimal bound on the vanishing order of solutions to stationary Schr\\\"odinger equations associated to a class of subelliptic equations with variable coefficients whose model is the so-called Baouendi-Grushin operator. Such bound provides a quantitative form of strong unique continuation that can be thought of as an analogue of the recent results of Bakri and Zhu for the standard Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06000","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":"1604.06000","created_at":"2026-05-18T00:52:50.352270+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.06000v3","created_at":"2026-05-18T00:52:50.352270+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06000","created_at":"2026-05-18T00:52:50.352270+00:00"},{"alias_kind":"pith_short_12","alias_value":"O567CNGZPUKE","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"O567CNGZPUKEIGTD","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"O567CNGZ","created_at":"2026-05-18T12:30:36.002864+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/O567CNGZPUKEIGTDAYHZV67IFH","json":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH.json","graph_json":"https://pith.science/api/pith-number/O567CNGZPUKEIGTDAYHZV67IFH/graph.json","events_json":"https://pith.science/api/pith-number/O567CNGZPUKEIGTDAYHZV67IFH/events.json","paper":"https://pith.science/paper/O567CNGZ"},"agent_actions":{"view_html":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH","download_json":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH.json","view_paper":"https://pith.science/paper/O567CNGZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.06000&json=true","fetch_graph":"https://pith.science/api/pith-number/O567CNGZPUKEIGTDAYHZV67IFH/graph.json","fetch_events":"https://pith.science/api/pith-number/O567CNGZPUKEIGTDAYHZV67IFH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH/action/storage_attestation","attest_author":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH/action/author_attestation","sign_citation":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH/action/citation_signature","submit_replication":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH/action/replication_record"}},"created_at":"2026-05-18T00:52:50.352270+00:00","updated_at":"2026-05-18T00:52:50.352270+00:00"}