{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:K7MXF7KHZKE6D5W2OXNRVSIM5J","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":"a976d693ed64656539d1eb4d019f002268e9be960092fbb52e65bb469b7022c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-22T09:49:55Z","title_canon_sha256":"6d0bfb3258b73b109b6e824cebec151295fe37628ed1c726de3ab0108554d896"},"schema_version":"1.0","source":{"id":"1806.08576","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08576","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08576v2","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08576","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"pith_short_12","alias_value":"K7MXF7KHZKE6","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K7MXF7KHZKE6D5W2","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K7MXF7KH","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:1edfbf48d73fe30804b246091d930ff22491df345bb5eb7d782848b26dc24427","target":"graph","created_at":"2026-05-17T23:42:48Z","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 propose a new definition of the interface in the context of the Bernoulli percolation model. We construct a coupling between two percolation configurations, one which is a standard percolation configuration, and one which is a percolation configuration conditioned on a disconnection event. We define the interface as the random set of the edges where these two configurations differ. We prove that, inside a cubic box $\\Lambda$, the interface between the top and the bottom of the box is typically localised within a distance of order $(\\ln |\\Lambda|)^2$ of the set of the pivotal edges. We prove","authors_text":"Rapha\\\"el Cerf, Wei Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-22T09:49:55Z","title":"A new look at the interfaces in percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08576","kind":"arxiv","version":2},"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":"sha256:9bba51f0cdca369c33f00fbd406a3ece710bfdc9aba547d513eb2e3f44e00943","target":"record","created_at":"2026-05-17T23:42:48Z","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":"a976d693ed64656539d1eb4d019f002268e9be960092fbb52e65bb469b7022c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-22T09:49:55Z","title_canon_sha256":"6d0bfb3258b73b109b6e824cebec151295fe37628ed1c726de3ab0108554d896"},"schema_version":"1.0","source":{"id":"1806.08576","kind":"arxiv","version":2}},"canonical_sha256":"57d972fd47ca89e1f6da75db1ac90cea5f3d2a03327152e695d9c88e6a31de3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57d972fd47ca89e1f6da75db1ac90cea5f3d2a03327152e695d9c88e6a31de3f","first_computed_at":"2026-05-17T23:42:48.960358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:48.960358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r4K8v/G71kHqRJS0hVEj4Qd5INv08PRx9O2+mC0Vnk5xdATCOfdETPGkTsLPmtByqyjTPFM6EuyCG7xgQ1KdBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:48.960780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.08576","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bba51f0cdca369c33f00fbd406a3ece710bfdc9aba547d513eb2e3f44e00943","sha256:1edfbf48d73fe30804b246091d930ff22491df345bb5eb7d782848b26dc24427"],"state_sha256":"dc7393a82d500cfbaf52716de459df44aa7419c5b7d2ab5ccda81c171a998b3b"}