{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:G7VDLM3D6BBXXOMAIPUSPFZCFM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"674ab3ec934100aed04afd8a5ddc51656ba9cc1fecdbdfca4de0b088e3401759","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-09-14T17:39:50Z","title_canon_sha256":"f14addc1c1960d89a6716c15bf647e6b0c8e063ac3827f0df0f1be1f5652c9f4"},"schema_version":"1.0","source":{"id":"0909.2606","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2606","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2606v3","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2606","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"G7VDLM3D6BBX","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G7VDLM3D6BBXXOMA","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G7VDLM3D","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:e75fe854d1935acde6a0c22db806cd9ab041dc818adabfac8d26e24659673894","target":"graph","created_at":"2026-05-18T04:24:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider a diffusion process with coefficients that are periodic outside of an \"interface region\" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under diffusive rescaling. It is clear that outside of the interface, the limiting process must behave like Brownian motion, with diffusion matrices given by the standard theory of homogenization. The interesting behavior therefore occurs on the interface. Our main result is that the limiting process is a semimartingale whose bounded variation part is proportional to t","authors_text":"Charles Manson, Martin Hairer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-09-14T17:39:50Z","title":"Periodic homogenization with an interface: The multi-dimensional case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2606","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:88d1983105cf13ca0337b3c2aa852439c7fc4a9e17880530e26c5f221494c0d4","target":"record","created_at":"2026-05-18T04:24:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"674ab3ec934100aed04afd8a5ddc51656ba9cc1fecdbdfca4de0b088e3401759","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-09-14T17:39:50Z","title_canon_sha256":"f14addc1c1960d89a6716c15bf647e6b0c8e063ac3827f0df0f1be1f5652c9f4"},"schema_version":"1.0","source":{"id":"0909.2606","kind":"arxiv","version":3}},"canonical_sha256":"37ea35b363f0437bb98043e92797222b27db5f3625a8080bf5efe2f86fff8727","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37ea35b363f0437bb98043e92797222b27db5f3625a8080bf5efe2f86fff8727","first_computed_at":"2026-05-18T04:24:04.159950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:04.159950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iO82/NxGnt+BoL+uiZbBLD2uc0DTfxEb1fI3orwdp/q7MQBliL5WGbhtm8dAr5aePQ4lP/MR10tAgTbuOcmiAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:04.160575Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.2606","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88d1983105cf13ca0337b3c2aa852439c7fc4a9e17880530e26c5f221494c0d4","sha256:e75fe854d1935acde6a0c22db806cd9ab041dc818adabfac8d26e24659673894"],"state_sha256":"2f308eebab2dfefad667bb897eb851233ef4c9c11a3b3d70c6549c66930444f5"}