{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:IOGLVNRACBBWUY7KWPAXOF36MH","short_pith_number":"pith:IOGLVNRA","schema_version":"1.0","canonical_sha256":"438cbab62010436a63eab3c177177e61f684775fbcf8721000b5aca800019f8d","source":{"kind":"arxiv","id":"1203.5096","version":3},"attestation_state":"computed","paper":{"title":"On second order elliptic equations with a small parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Mark Freidlin, Wenqing Hu","submitted_at":"2012-03-22T19:54:03Z","abstract_excerpt":"The Neumann problem with a small parameter $$(\\dfrac{1}{\\epsilon}L_0+L_1)u^\\epsilon(x)=f(x) \\text{for} x\\in G, .\\dfrac{\\partial u^\\epsilon}{\\partial \\gamma^\\epsilon}(x)|_{\\partial G}=0$$ is considered in this paper. The operators $L_0$ and $L_1$ are self-adjoint second order operators. We assume that $L_0$ has a non-negative characteristic form and $L_1$ is strictly elliptic. The reflection is with respect to inward co-normal unit vector $\\gamma^\\epsilon(x)$. The behavior of $\\lim\\limits_{\\epsilon\\downarrow 0}u^\\epsilon(x)$ is effectively described via the solution of an ordinary differential "},"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":"1203.5096","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-22T19:54:03Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d38a8947c2b1c619f4eb82b72b863afbd146d3cb55d5c9a5615d9b7c7a10bbf0","abstract_canon_sha256":"8a2f9fc741feb333a4c0046845bdc868f089ac2a10d8cacd83195fcf6709bb29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:58.466630Z","signature_b64":"N40meal4NqPnuEOLDlhUgFVAXN0Nfe5qicAIjtRtRHa5z2AfhVLnWQW5wVs/Bs4lQcTGnpHXg9dkGu6EdPVzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"438cbab62010436a63eab3c177177e61f684775fbcf8721000b5aca800019f8d","last_reissued_at":"2026-05-18T03:13:58.466115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:58.466115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On second order elliptic equations with a small parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Mark Freidlin, Wenqing Hu","submitted_at":"2012-03-22T19:54:03Z","abstract_excerpt":"The Neumann problem with a small parameter $$(\\dfrac{1}{\\epsilon}L_0+L_1)u^\\epsilon(x)=f(x) \\text{for} x\\in G, .\\dfrac{\\partial u^\\epsilon}{\\partial \\gamma^\\epsilon}(x)|_{\\partial G}=0$$ is considered in this paper. The operators $L_0$ and $L_1$ are self-adjoint second order operators. We assume that $L_0$ has a non-negative characteristic form and $L_1$ is strictly elliptic. The reflection is with respect to inward co-normal unit vector $\\gamma^\\epsilon(x)$. The behavior of $\\lim\\limits_{\\epsilon\\downarrow 0}u^\\epsilon(x)$ is effectively described via the solution of an ordinary differential "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5096","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":""},"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":"1203.5096","created_at":"2026-05-18T03:13:58.466197+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.5096v3","created_at":"2026-05-18T03:13:58.466197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5096","created_at":"2026-05-18T03:13:58.466197+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOGLVNRACBBW","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOGLVNRACBBWUY7K","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOGLVNRA","created_at":"2026-05-18T12:27:09.501522+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/IOGLVNRACBBWUY7KWPAXOF36MH","json":"https://pith.science/pith/IOGLVNRACBBWUY7KWPAXOF36MH.json","graph_json":"https://pith.science/api/pith-number/IOGLVNRACBBWUY7KWPAXOF36MH/graph.json","events_json":"https://pith.science/api/pith-number/IOGLVNRACBBWUY7KWPAXOF36MH/events.json","paper":"https://pith.science/paper/IOGLVNRA"},"agent_actions":{"view_html":"https://pith.science/pith/IOGLVNRACBBWUY7KWPAXOF36MH","download_json":"https://pith.science/pith/IOGLVNRACBBWUY7KWPAXOF36MH.json","view_paper":"https://pith.science/paper/IOGLVNRA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.5096&json=true","fetch_graph":"https://pith.science/api/pith-number/IOGLVNRACBBWUY7KWPAXOF36MH/graph.json","fetch_events":"https://pith.science/api/pith-number/IOGLVNRACBBWUY7KWPAXOF36MH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOGLVNRACBBWUY7KWPAXOF36MH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOGLVNRACBBWUY7KWPAXOF36MH/action/storage_attestation","attest_author":"https://pith.science/pith/IOGLVNRACBBWUY7KWPAXOF36MH/action/author_attestation","sign_citation":"https://pith.science/pith/IOGLVNRACBBWUY7KWPAXOF36MH/action/citation_signature","submit_replication":"https://pith.science/pith/IOGLVNRACBBWUY7KWPAXOF36MH/action/replication_record"}},"created_at":"2026-05-18T03:13:58.466197+00:00","updated_at":"2026-05-18T03:13:58.466197+00:00"}