{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7XKNQCE5SEC263FNRGCTKUOAH3","short_pith_number":"pith:7XKNQCE5","schema_version":"1.0","canonical_sha256":"fdd4d8089d9105af6cad89853551c03efb73f8ff0e27db59e68e6b33b6f2e956","source":{"kind":"arxiv","id":"1305.0837","version":1},"attestation_state":"computed","paper":{"title":"Strong Convergence to the homogenized limit of parabolic equations with random coefficients II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arash Fahim, Joseph G. Conlon","submitted_at":"2013-05-03T20:22:43Z","abstract_excerpt":"This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation.\n  In [11] rate of convergence results in homogenization and estimates on the difference between the averaged Green's function and the homogenized Green's function for random environments which satisfy a Poincar\\'{e} inequality were obtained. Here these results are extended to certain environments in which correlations can have arbitrarily small power law decay. Similar results for discrete elliptic equatio"},"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":"1305.0837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-03T20:22:43Z","cross_cats_sorted":[],"title_canon_sha256":"3baff3b5d05cf1d7158329ed334c039b8c91722aea710aa68ae2186b9b115702","abstract_canon_sha256":"d8d077e60015ae80246b8c9cf8b3cd7fe7fe287068f0b99e63e51a00910ca17a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:31.592896Z","signature_b64":"6ndoJz7OruPj12Rmlo1jIvdU0sseIYDR+BKgXJP6DevMXlfX4olA26g+oedVKCow9mYGkCjVXh94uKxjjT0dAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdd4d8089d9105af6cad89853551c03efb73f8ff0e27db59e68e6b33b6f2e956","last_reissued_at":"2026-05-18T03:26:31.592242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:31.592242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong Convergence to the homogenized limit of parabolic equations with random coefficients II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arash Fahim, Joseph G. Conlon","submitted_at":"2013-05-03T20:22:43Z","abstract_excerpt":"This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation.\n  In [11] rate of convergence results in homogenization and estimates on the difference between the averaged Green's function and the homogenized Green's function for random environments which satisfy a Poincar\\'{e} inequality were obtained. Here these results are extended to certain environments in which correlations can have arbitrarily small power law decay. Similar results for discrete elliptic equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0837","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":"1305.0837","created_at":"2026-05-18T03:26:31.592346+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0837v1","created_at":"2026-05-18T03:26:31.592346+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0837","created_at":"2026-05-18T03:26:31.592346+00:00"},{"alias_kind":"pith_short_12","alias_value":"7XKNQCE5SEC2","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"7XKNQCE5SEC263FN","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"7XKNQCE5","created_at":"2026-05-18T12:27:38.830355+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/7XKNQCE5SEC263FNRGCTKUOAH3","json":"https://pith.science/pith/7XKNQCE5SEC263FNRGCTKUOAH3.json","graph_json":"https://pith.science/api/pith-number/7XKNQCE5SEC263FNRGCTKUOAH3/graph.json","events_json":"https://pith.science/api/pith-number/7XKNQCE5SEC263FNRGCTKUOAH3/events.json","paper":"https://pith.science/paper/7XKNQCE5"},"agent_actions":{"view_html":"https://pith.science/pith/7XKNQCE5SEC263FNRGCTKUOAH3","download_json":"https://pith.science/pith/7XKNQCE5SEC263FNRGCTKUOAH3.json","view_paper":"https://pith.science/paper/7XKNQCE5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0837&json=true","fetch_graph":"https://pith.science/api/pith-number/7XKNQCE5SEC263FNRGCTKUOAH3/graph.json","fetch_events":"https://pith.science/api/pith-number/7XKNQCE5SEC263FNRGCTKUOAH3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7XKNQCE5SEC263FNRGCTKUOAH3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7XKNQCE5SEC263FNRGCTKUOAH3/action/storage_attestation","attest_author":"https://pith.science/pith/7XKNQCE5SEC263FNRGCTKUOAH3/action/author_attestation","sign_citation":"https://pith.science/pith/7XKNQCE5SEC263FNRGCTKUOAH3/action/citation_signature","submit_replication":"https://pith.science/pith/7XKNQCE5SEC263FNRGCTKUOAH3/action/replication_record"}},"created_at":"2026-05-18T03:26:31.592346+00:00","updated_at":"2026-05-18T03:26:31.592346+00:00"}