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For a diagonal matrix function $A$, let $\\nabla A \\nabla_W = \\sum_{k=1}^d \\partial_{x_k}(a_k\\partial_{W_k})$ be a generalized second-order differential operator. We are interested in studying the homogenization of generalized second-order difference operators, that is, we are interested in the convergence of the solution of the equation $$\\lambda u_N - \\nabla^N A^N \\nabla_W^N u_N = f^N$$ to the solution of the equation $$\\la"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.03414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-14T03:56:46Z","cross_cats_sorted":[],"title_canon_sha256":"4cb3beda7efbd40093a9ca5e5d45354d8f62a5b9edc868868498949dc4c1c050","abstract_canon_sha256":"66a627f97d5f423dd2298723165492fa70f745ccfc545a7b632df0a256687d48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:52.535039Z","signature_b64":"zl+40aSaYK6C+zMITGVbIxwFSEV7NKiXVftCMfGpHqiON+tzFD40Y3FQ976H7/5nn8XPvbxWhRxbENvHJFdgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09b7551a0dbb18dafba07ee20badc816bba428567c473a79c7c4c64f2dc2e37f","last_reissued_at":"2026-05-18T01:18:52.534406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:52.534406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogenization of generalized second-order elliptic difference operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandre B. 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We are interested in studying the homogenization of generalized second-order difference operators, that is, we are interested in the convergence of the solution of the equation $$\\lambda u_N - \\nabla^N A^N \\nabla_W^N u_N = f^N$$ to the solution of the equation $$\\la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03414","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":"1508.03414","created_at":"2026-05-18T01:18:52.534512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.03414v2","created_at":"2026-05-18T01:18:52.534512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03414","created_at":"2026-05-18T01:18:52.534512+00:00"},{"alias_kind":"pith_short_12","alias_value":"BG3VKGQNXMMN","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BG3VKGQNXMMNV65A","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BG3VKGQN","created_at":"2026-05-18T12:29:14.074870+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/BG3VKGQNXMMNV65AP3RAXLOIC2","json":"https://pith.science/pith/BG3VKGQNXMMNV65AP3RAXLOIC2.json","graph_json":"https://pith.science/api/pith-number/BG3VKGQNXMMNV65AP3RAXLOIC2/graph.json","events_json":"https://pith.science/api/pith-number/BG3VKGQNXMMNV65AP3RAXLOIC2/events.json","paper":"https://pith.science/paper/BG3VKGQN"},"agent_actions":{"view_html":"https://pith.science/pith/BG3VKGQNXMMNV65AP3RAXLOIC2","download_json":"https://pith.science/pith/BG3VKGQNXMMNV65AP3RAXLOIC2.json","view_paper":"https://pith.science/paper/BG3VKGQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.03414&json=true","fetch_graph":"https://pith.science/api/pith-number/BG3VKGQNXMMNV65AP3RAXLOIC2/graph.json","fetch_events":"https://pith.science/api/pith-number/BG3VKGQNXMMNV65AP3RAXLOIC2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BG3VKGQNXMMNV65AP3RAXLOIC2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BG3VKGQNXMMNV65AP3RAXLOIC2/action/storage_attestation","attest_author":"https://pith.science/pith/BG3VKGQNXMMNV65AP3RAXLOIC2/action/author_attestation","sign_citation":"https://pith.science/pith/BG3VKGQNXMMNV65AP3RAXLOIC2/action/citation_signature","submit_replication":"https://pith.science/pith/BG3VKGQNXMMNV65AP3RAXLOIC2/action/replication_record"}},"created_at":"2026-05-18T01:18:52.534512+00:00","updated_at":"2026-05-18T01:18:52.534512+00:00"}