{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:O567CNGZPUKEIGTDAYHZV67IFH","short_pith_number":"pith:O567CNGZ","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"},"canonical_sha256":"777df134d97d14441a63060f9afbe829c5caed3338e84a3793a54194456e8942","source":{"kind":"arxiv","id":"1604.06000","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06000","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06000v3","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06000","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"O567CNGZPUKE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O567CNGZPUKEIGTD","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O567CNGZ","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:O567CNGZPUKEIGTDAYHZV67IFH","target":"record","payload":{"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"},"canonical_sha256":"777df134d97d14441a63060f9afbe829c5caed3338e84a3793a54194456e8942","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"},"source_kind":"arxiv","source_id":"1604.06000","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+sv99NA1yGrZXrLwJ25P43i1nx+sZ04mUgB3+SmLJgZW0vsuXwD13ENV0M+PWWtcL8IgyRWCVb6msHp/AyW1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:35:19.436449Z"},"content_sha256":"e8a618cd7b62b746496db12267b42afb0c37964aa7152577db4974337fe201e5","schema_version":"1.0","event_id":"sha256:e8a618cd7b62b746496db12267b42afb0c37964aa7152577db4974337fe201e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:O567CNGZPUKEIGTDAYHZV67IFH","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xMswMQ/94GLe3ULTK90KZ06yVdkSyeRzRbHTxGqCTIBeYHYO8AwIozdhJ2+YiznH9s+HJU2uhNW5vSlZNWm+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:35:19.436797Z"},"content_sha256":"aa69160b60711179a33361ce228285ea47a85de28437c912b65aee63aea00d65","schema_version":"1.0","event_id":"sha256:aa69160b60711179a33361ce228285ea47a85de28437c912b65aee63aea00d65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH/bundle.json","state_url":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O567CNGZPUKEIGTDAYHZV67IFH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T12:35:19Z","links":{"resolver":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH","bundle":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH/bundle.json","state":"https://pith.science/pith/O567CNGZPUKEIGTDAYHZV67IFH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O567CNGZPUKEIGTDAYHZV67IFH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O567CNGZPUKEIGTDAYHZV67IFH","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":"1436196c263ce8324df17ee7d12af473b950f7176932c5256e7ab3f48dd1c9dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-20T15:20:50Z","title_canon_sha256":"b33302b4a713e1c61b8f5d4e6f5b186e87acf88088c80d50d32300ccefae63e6"},"schema_version":"1.0","source":{"id":"1604.06000","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06000","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06000v3","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06000","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"O567CNGZPUKE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O567CNGZPUKEIGTD","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O567CNGZ","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:aa69160b60711179a33361ce228285ea47a85de28437c912b65aee63aea00d65","target":"graph","created_at":"2026-05-18T00:52:50Z","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":"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.","authors_text":"Agnid Banerjee, Nicola Garofalo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-20T15:20:50Z","title":"Quantitative uniqueness for zero-order perturbations of generalized Baouendi-Grushin operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06000","kind":"arxiv","version":3},"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:e8a618cd7b62b746496db12267b42afb0c37964aa7152577db4974337fe201e5","target":"record","created_at":"2026-05-18T00:52:50Z","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":"1436196c263ce8324df17ee7d12af473b950f7176932c5256e7ab3f48dd1c9dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-20T15:20:50Z","title_canon_sha256":"b33302b4a713e1c61b8f5d4e6f5b186e87acf88088c80d50d32300ccefae63e6"},"schema_version":"1.0","source":{"id":"1604.06000","kind":"arxiv","version":3}},"canonical_sha256":"777df134d97d14441a63060f9afbe829c5caed3338e84a3793a54194456e8942","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"777df134d97d14441a63060f9afbe829c5caed3338e84a3793a54194456e8942","first_computed_at":"2026-05-18T00:52:50.352178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:50.352178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IGIz0902sZESvULlui5PLe64UK7m5MCwF1AB626eklbjX7M744JKK4ZbEaMXF5Xq5QkWyy8kyJwBRV943sTDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:50.352842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06000","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8a618cd7b62b746496db12267b42afb0c37964aa7152577db4974337fe201e5","sha256:aa69160b60711179a33361ce228285ea47a85de28437c912b65aee63aea00d65"],"state_sha256":"25c843d39c35957a7503a22db77783536f77084eceb9a6f7fb57237320e108d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpWH1CuvhQiwqgBkUi7XLFFmSCXsLnzX5SBFW0uCiZkC3wjNxrtSbsU/iddz6+NfJ/8UrZHh2eUl54f8gMD/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:35:19.438934Z","bundle_sha256":"fdb4e6155f5cce491d7b823eca96e6ab709a4c82aa6f6bdb43ddb7d9373fb0fc"}}