{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2CO6KEJQS2FNZLOPT425BZOX5K","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":"8aa7e517269e73ad6a0cde3fd58cd7bbd287d83d609029a04cff407d2b01fc0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-10T08:52:22Z","title_canon_sha256":"eb863950f5a15849b1b1d1c2890e7027564ba07cb9a24b0a87b6816882a6958d"},"schema_version":"1.0","source":{"id":"1807.03531","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03531","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03531v1","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03531","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"2CO6KEJQS2FN","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2CO6KEJQS2FNZLOP","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2CO6KEJQ","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:aa9726ca0097603aaa33affb8c7c3a20c5c0c462f02051f6fef1dec67b76080a","target":"graph","created_at":"2026-05-18T00:11:10Z","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 prove a Harnack inequality for the solutions of a difference equation with non-elliptic balanced i.i.d. coefficients. Along the way we prove a (weak) quantitative homogenisation result, which we believe is of some interest too.","authors_text":"Jean-Dominique Deuschel, Moran Cohen, Noam Berger, Xiaoqin Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-10T08:52:22Z","title":"An elliptic Harnack inequality for random walk in balanced environments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03531","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":"sha256:752d1b1c96a566ebe0dab1a92952e6307e3b8d384b7ee6391f7305d49a1e9a96","target":"record","created_at":"2026-05-18T00:11:10Z","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":"8aa7e517269e73ad6a0cde3fd58cd7bbd287d83d609029a04cff407d2b01fc0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-10T08:52:22Z","title_canon_sha256":"eb863950f5a15849b1b1d1c2890e7027564ba07cb9a24b0a87b6816882a6958d"},"schema_version":"1.0","source":{"id":"1807.03531","kind":"arxiv","version":1}},"canonical_sha256":"d09de51130968adcadcf9f35d0e5d7ea96c6d01b1310d6ba44b506fb70bd68ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d09de51130968adcadcf9f35d0e5d7ea96c6d01b1310d6ba44b506fb70bd68ee","first_computed_at":"2026-05-18T00:11:10.149763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:10.149763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UuN7FUx063ZBT+SjYQTzxnGd1QXeAVeKCiRo2tdqvBszxZDXfr4oJCSV+YBPYWp1B5T00JLowEuD96tQ/kgYAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:10.150517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03531","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:752d1b1c96a566ebe0dab1a92952e6307e3b8d384b7ee6391f7305d49a1e9a96","sha256:aa9726ca0097603aaa33affb8c7c3a20c5c0c462f02051f6fef1dec67b76080a"],"state_sha256":"b9fcd18b64fa956a94000323828a2f643ead071e1870760a66210565a723f3c0"}