{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CSZ527C63DADGA2LXCLX63VEWZ","short_pith_number":"pith:CSZ527C6","schema_version":"1.0","canonical_sha256":"14b3dd7c5ed8c033034bb8977f6ea4b654e60070f1aad657859dfbd2c039cd67","source":{"kind":"arxiv","id":"1304.4408","version":2},"attestation_state":"computed","paper":{"title":"Annealed estimates on the Green function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Marahrens, Felix Otto","submitted_at":"2013-04-16T11:59:25Z","abstract_excerpt":"We consider a random, uniformly elliptic coefficient field $a(x)$ on the $d$-dimensional integer lattice $\\mathbb{Z}^d$. We are interested in the spatial decay of the quenched elliptic Green function $G(a;x,y)$. Next to stationarity, we assume that the spatial correlation of the coefficient field decays sufficiently fast to the effect that a logarithmic Sobolev inequality holds for the ensemble $\\langle\\cdot\\rangle$. We prove that all stochastic moments of the first and second mixed derivatives of the Green function, that is, $\\langle|\\nabla_x G(x,y)|^p\\rangle$ and $\\langle|\\nabla_x\\nabla_y G("},"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":"1304.4408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T11:59:25Z","cross_cats_sorted":[],"title_canon_sha256":"4e434f2c432d2a55cf23982d521a4a899f3fd03685cd3b67fdf2ff6d1ac7f56d","abstract_canon_sha256":"c602f3107e500536b734124d9e4e53aa58e2c3b36a257d73a7ff05d2ed4ecdf9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:35.023433Z","signature_b64":"LWmD7mjI3VyejQn77Bu7k7T9TSLZRL5NXA7ScIFSkizZ1y31avPQ6EM4ZjryLsnnaQlT6sJDr+FMgqP4pOiTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14b3dd7c5ed8c033034bb8977f6ea4b654e60070f1aad657859dfbd2c039cd67","last_reissued_at":"2026-05-18T03:02:35.022721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:35.022721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Annealed estimates on the Green function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Marahrens, Felix Otto","submitted_at":"2013-04-16T11:59:25Z","abstract_excerpt":"We consider a random, uniformly elliptic coefficient field $a(x)$ on the $d$-dimensional integer lattice $\\mathbb{Z}^d$. We are interested in the spatial decay of the quenched elliptic Green function $G(a;x,y)$. Next to stationarity, we assume that the spatial correlation of the coefficient field decays sufficiently fast to the effect that a logarithmic Sobolev inequality holds for the ensemble $\\langle\\cdot\\rangle$. We prove that all stochastic moments of the first and second mixed derivatives of the Green function, that is, $\\langle|\\nabla_x G(x,y)|^p\\rangle$ and $\\langle|\\nabla_x\\nabla_y G("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4408","kind":"arxiv","version":2},"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":"1304.4408","created_at":"2026-05-18T03:02:35.022853+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.4408v2","created_at":"2026-05-18T03:02:35.022853+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4408","created_at":"2026-05-18T03:02:35.022853+00:00"},{"alias_kind":"pith_short_12","alias_value":"CSZ527C63DAD","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CSZ527C63DADGA2L","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CSZ527C6","created_at":"2026-05-18T12:27:40.988391+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/CSZ527C63DADGA2LXCLX63VEWZ","json":"https://pith.science/pith/CSZ527C63DADGA2LXCLX63VEWZ.json","graph_json":"https://pith.science/api/pith-number/CSZ527C63DADGA2LXCLX63VEWZ/graph.json","events_json":"https://pith.science/api/pith-number/CSZ527C63DADGA2LXCLX63VEWZ/events.json","paper":"https://pith.science/paper/CSZ527C6"},"agent_actions":{"view_html":"https://pith.science/pith/CSZ527C63DADGA2LXCLX63VEWZ","download_json":"https://pith.science/pith/CSZ527C63DADGA2LXCLX63VEWZ.json","view_paper":"https://pith.science/paper/CSZ527C6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.4408&json=true","fetch_graph":"https://pith.science/api/pith-number/CSZ527C63DADGA2LXCLX63VEWZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CSZ527C63DADGA2LXCLX63VEWZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CSZ527C63DADGA2LXCLX63VEWZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CSZ527C63DADGA2LXCLX63VEWZ/action/storage_attestation","attest_author":"https://pith.science/pith/CSZ527C63DADGA2LXCLX63VEWZ/action/author_attestation","sign_citation":"https://pith.science/pith/CSZ527C63DADGA2LXCLX63VEWZ/action/citation_signature","submit_replication":"https://pith.science/pith/CSZ527C63DADGA2LXCLX63VEWZ/action/replication_record"}},"created_at":"2026-05-18T03:02:35.022853+00:00","updated_at":"2026-05-18T03:02:35.022853+00:00"}