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We prove the following stability result: the Schauder and Sobolev estimates associated with the corresponding parabolic Cauchy problem remain valid, with the same constant, for the parabolic Cauchy problem associated with a second order perturbation of L, namely for L + Tr(S(t)D 2) where S(t) is a non-negative N x N matrix depending continuously"},"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":"2107.06012","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-07-13T12:03:56Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9372f836953b13350aee748c12ffd15e0980ae480fc460470519bbbee84c0048","abstract_canon_sha256":"f2c5c318b148ebd0ab91ad626b38c2b1c08595cd7b570df8314414b93b5229c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:17:32.857875Z","signature_b64":"yUhX3HwPf9+qQoG2itStjgNwPZG+wC/WHZs4d375yKP+/1YOlljIhyIOh1Jt47Cyk+SwwWvwngdfdaK4bKhtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df2bee50731c9c4a397ad0ed57034da9eed34d84f46e19183ad5bd22ea246b9e","last_reissued_at":"2026-07-05T03:17:32.857507Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:17:32.857507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poisson process and sharp constants in Lp and Schauder estimates for a class of degenerate Kolmogorov operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"E. 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We prove the following stability result: the Schauder and Sobolev estimates associated with the corresponding parabolic Cauchy problem remain valid, with the same constant, for the parabolic Cauchy problem associated with a second order perturbation of L, namely for L + Tr(S(t)D 2) where S(t) is a non-negative N x N matrix depending continuously"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.06012","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.06012/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2107.06012","created_at":"2026-07-05T03:17:32.857568+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.06012v3","created_at":"2026-07-05T03:17:32.857568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.06012","created_at":"2026-07-05T03:17:32.857568+00:00"},{"alias_kind":"pith_short_12","alias_value":"34V64UDTDSOE","created_at":"2026-07-05T03:17:32.857568+00:00"},{"alias_kind":"pith_short_16","alias_value":"34V64UDTDSOEUOL2","created_at":"2026-07-05T03:17:32.857568+00:00"},{"alias_kind":"pith_short_8","alias_value":"34V64UDT","created_at":"2026-07-05T03:17:32.857568+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/34V64UDTDSOEUOL22DWVOA2NVH","json":"https://pith.science/pith/34V64UDTDSOEUOL22DWVOA2NVH.json","graph_json":"https://pith.science/api/pith-number/34V64UDTDSOEUOL22DWVOA2NVH/graph.json","events_json":"https://pith.science/api/pith-number/34V64UDTDSOEUOL22DWVOA2NVH/events.json","paper":"https://pith.science/paper/34V64UDT"},"agent_actions":{"view_html":"https://pith.science/pith/34V64UDTDSOEUOL22DWVOA2NVH","download_json":"https://pith.science/pith/34V64UDTDSOEUOL22DWVOA2NVH.json","view_paper":"https://pith.science/paper/34V64UDT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.06012&json=true","fetch_graph":"https://pith.science/api/pith-number/34V64UDTDSOEUOL22DWVOA2NVH/graph.json","fetch_events":"https://pith.science/api/pith-number/34V64UDTDSOEUOL22DWVOA2NVH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/34V64UDTDSOEUOL22DWVOA2NVH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/34V64UDTDSOEUOL22DWVOA2NVH/action/storage_attestation","attest_author":"https://pith.science/pith/34V64UDTDSOEUOL22DWVOA2NVH/action/author_attestation","sign_citation":"https://pith.science/pith/34V64UDTDSOEUOL22DWVOA2NVH/action/citation_signature","submit_replication":"https://pith.science/pith/34V64UDTDSOEUOL22DWVOA2NVH/action/replication_record"}},"created_at":"2026-07-05T03:17:32.857568+00:00","updated_at":"2026-07-05T03:17:32.857568+00:00"}