{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:Q74HHS5DELWPGFLSGVSIXGA6P4","short_pith_number":"pith:Q74HHS5D","schema_version":"1.0","canonical_sha256":"87f873cba322ecf3157235648b981e7f2247c8e2595102c505b80accfe577614","source":{"kind":"arxiv","id":"1202.2139","version":1},"attestation_state":"computed","paper":{"title":"Partial Gaussian bounds for degenerate differential operators II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. F. M. ter Elst, E. M. Ouhabaz","submitted_at":"2012-02-09T21:58:22Z","abstract_excerpt":"Let $A = - \\sum \\partial_k \\, c_{kl} \\, \\partial_l$ be a degenerate sectorial differential operator with complex bounded mesaurable coefficients. Let $\\Omega \\subset \\mathds{R}^d$ be open and suppose that $A$ is strongly elliptic on $\\Omega$. Further, let $\\chi \\in C_{\\rm b}^\\infty(\\mathds{R}^d)$ be such that an $\\varepsilon$-neighbourhood of $\\supp \\chi$ is contained in $\\Omega$. Let $\\nu \\in (0,1]$ and suppose that the ${c_{kl}}_{|\\Omega} \\in C^{0,\\nu}(\\Omega)$. Then we prove (H\\\"older) Gaussian kernel bounds for the kernel of the operator $u \\mapsto \\chi \\, S_t (\\chi \\, u)$, where $S$ is 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":"1202.2139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-09T21:58:22Z","cross_cats_sorted":[],"title_canon_sha256":"8d70795bbb4fd2ad73ff338876549cde1c409ab3401e66b6185c8ac78b239f48","abstract_canon_sha256":"1dbbcd4c829dff61d675886b71d30c18766c117b5052b53948a0490f0ccdaf17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:38.049678Z","signature_b64":"54vB50d7Ub05SWYc/n77LQKzoHNpmuRxMkP1kQ4ovPldFDGacmBNmUbgGaCRWcgnabjnQA86saGaTdRRth1ZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87f873cba322ecf3157235648b981e7f2247c8e2595102c505b80accfe577614","last_reissued_at":"2026-05-18T04:02:38.048933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:38.048933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial Gaussian bounds for degenerate differential operators II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. F. M. ter Elst, E. M. Ouhabaz","submitted_at":"2012-02-09T21:58:22Z","abstract_excerpt":"Let $A = - \\sum \\partial_k \\, c_{kl} \\, \\partial_l$ be a degenerate sectorial differential operator with complex bounded mesaurable coefficients. Let $\\Omega \\subset \\mathds{R}^d$ be open and suppose that $A$ is strongly elliptic on $\\Omega$. Further, let $\\chi \\in C_{\\rm b}^\\infty(\\mathds{R}^d)$ be such that an $\\varepsilon$-neighbourhood of $\\supp \\chi$ is contained in $\\Omega$. Let $\\nu \\in (0,1]$ and suppose that the ${c_{kl}}_{|\\Omega} \\in C^{0,\\nu}(\\Omega)$. Then we prove (H\\\"older) Gaussian kernel bounds for the kernel of the operator $u \\mapsto \\chi \\, S_t (\\chi \\, u)$, where $S$ is th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2139","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":"1202.2139","created_at":"2026-05-18T04:02:38.049057+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.2139v1","created_at":"2026-05-18T04:02:38.049057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2139","created_at":"2026-05-18T04:02:38.049057+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q74HHS5DELWP","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q74HHS5DELWPGFLS","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q74HHS5D","created_at":"2026-05-18T12:27:18.751474+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/Q74HHS5DELWPGFLSGVSIXGA6P4","json":"https://pith.science/pith/Q74HHS5DELWPGFLSGVSIXGA6P4.json","graph_json":"https://pith.science/api/pith-number/Q74HHS5DELWPGFLSGVSIXGA6P4/graph.json","events_json":"https://pith.science/api/pith-number/Q74HHS5DELWPGFLSGVSIXGA6P4/events.json","paper":"https://pith.science/paper/Q74HHS5D"},"agent_actions":{"view_html":"https://pith.science/pith/Q74HHS5DELWPGFLSGVSIXGA6P4","download_json":"https://pith.science/pith/Q74HHS5DELWPGFLSGVSIXGA6P4.json","view_paper":"https://pith.science/paper/Q74HHS5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.2139&json=true","fetch_graph":"https://pith.science/api/pith-number/Q74HHS5DELWPGFLSGVSIXGA6P4/graph.json","fetch_events":"https://pith.science/api/pith-number/Q74HHS5DELWPGFLSGVSIXGA6P4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q74HHS5DELWPGFLSGVSIXGA6P4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q74HHS5DELWPGFLSGVSIXGA6P4/action/storage_attestation","attest_author":"https://pith.science/pith/Q74HHS5DELWPGFLSGVSIXGA6P4/action/author_attestation","sign_citation":"https://pith.science/pith/Q74HHS5DELWPGFLSGVSIXGA6P4/action/citation_signature","submit_replication":"https://pith.science/pith/Q74HHS5DELWPGFLSGVSIXGA6P4/action/replication_record"}},"created_at":"2026-05-18T04:02:38.049057+00:00","updated_at":"2026-05-18T04:02:38.049057+00:00"}