{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:4TSD7PTOSETABSWC6GLGP7LUWT","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":"3e29b822803df4196cc180a64b7905a4c86919294e7aa6c67f07ca9be1a7e887","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2001-10-19T14:49:47Z","title_canon_sha256":"e7c577a432e2e47eead946f07147f70366ff184f1e938d2868f5683f25dbd5c4"},"schema_version":"1.0","source":{"id":"math/0110215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110215","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110215v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110215","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"4TSD7PTOSETA","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"4TSD7PTOSETABSWC","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"4TSD7PTO","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:8b052801557e77487173704db2230bbf6b1409091cdea5d266a9ae5bcc3555e3","target":"graph","created_at":"2026-05-18T01:38:29Z","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":"Consider uniformly elliptic random walk on $\\bbZ^d$ with independent jump rates across nearest neighbour bonds of the lattice. We show that the infinite volume effective diffusion matrix can be almost surely recovered as the limit of finite volume periodized effective diffusion matrices.","authors_text":"Dima Ioffe, Pietro Caputo","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2001-10-19T14:49:47Z","title":"Finite volume approximation of the effective diffusion matrix: The case of independent bond disorder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110215","kind":"arxiv","version":1},"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":"sha256:8fff7e2d15c945970bc0eece4e4bf5281c7cbf295ae7fc3893adc3687f610559","target":"record","created_at":"2026-05-18T01:38:29Z","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":"3e29b822803df4196cc180a64b7905a4c86919294e7aa6c67f07ca9be1a7e887","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2001-10-19T14:49:47Z","title_canon_sha256":"e7c577a432e2e47eead946f07147f70366ff184f1e938d2868f5683f25dbd5c4"},"schema_version":"1.0","source":{"id":"math/0110215","kind":"arxiv","version":1}},"canonical_sha256":"e4e43fbe6e912600cac2f19667fd74b4d257d2c68fde89d036af527bad2d506b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4e43fbe6e912600cac2f19667fd74b4d257d2c68fde89d036af527bad2d506b","first_computed_at":"2026-05-18T01:38:29.798349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.798349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7uOVeFcwm7MWG8SBDGMss3tf/38XRSXmpW5zum0r8XmX/TndmUdtpnd3YwFvfXjkAFty0Gfg52EUWV16065CAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.798794Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0110215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fff7e2d15c945970bc0eece4e4bf5281c7cbf295ae7fc3893adc3687f610559","sha256:8b052801557e77487173704db2230bbf6b1409091cdea5d266a9ae5bcc3555e3"],"state_sha256":"f79e3346585bb1f2499c5c3253cbe8b8d13cf9ae6dfa301cb83169bf2af29141"}