{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:565H2TVVR7GVQLFC7SHK4OBQE6","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":"39d978e8d217ac96731be608d58067713125b6d42f0f95309d6a19aef9f9e304","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-09T13:59:36Z","title_canon_sha256":"439801480a74d730dd90d180db123a941faf2d91ecbf964d9b83f66f385f30fb"},"schema_version":"1.0","source":{"id":"1808.03171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03171","created_at":"2026-05-18T00:08:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03171v1","created_at":"2026-05-18T00:08:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03171","created_at":"2026-05-18T00:08:29Z"},{"alias_kind":"pith_short_12","alias_value":"565H2TVVR7GV","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"565H2TVVR7GVQLFC","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"565H2TVV","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:aab32c9617fb73fd3e4d06d1d86db00f1fddad0015486794faa1a2894f3fbd2b","target":"graph","created_at":"2026-05-18T00:08:29Z","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":"We consider biased random walks in a one-dimensional percolation model. This model goes back to Axelson-Fisk and H\\\"aggstr\\\"om and exhibits the same phase transition as biased random walk on the infinite cluster of supercritical Bernoulli bond percolation on $\\mathbb{Z}^d$, namely, for some critical value $\\lambda_{\\mathrm{c}} >0$ of the bias, it holds that the asymptotic linear speed $\\overline{\\mathrm{v}}$ of the walk is strictly positive if the bias $\\lambda$ is strictly smaller than $\\lambda_{\\mathrm{c}}$, whereas $\\overline{\\mathrm{v}}=0$ if $\\lambda \\geq \\lambda_{\\mathrm{c}}$.\n  We show ","authors_text":"Jan-Erik L\\\"ubbers, Matthias Meiners","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-09T13:59:36Z","title":"The speed of critically biased random walk in a one-dimensional percolation model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03171","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:b12490c53090e64787a0da87321f1d480bc89a47fea0735eff792b2f32c032ff","target":"record","created_at":"2026-05-18T00:08:29Z","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":"39d978e8d217ac96731be608d58067713125b6d42f0f95309d6a19aef9f9e304","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-09T13:59:36Z","title_canon_sha256":"439801480a74d730dd90d180db123a941faf2d91ecbf964d9b83f66f385f30fb"},"schema_version":"1.0","source":{"id":"1808.03171","kind":"arxiv","version":1}},"canonical_sha256":"efba7d4eb58fcd582ca2fc8eae3830278e02686e22c85624cb327dda1a36d310","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efba7d4eb58fcd582ca2fc8eae3830278e02686e22c85624cb327dda1a36d310","first_computed_at":"2026-05-18T00:08:29.982584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:29.982584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IGJ489L2GEbzFJ/pCbwHjSP7s/7HG7Uj6qzPdGSqyX0gy5GuhXr4pPllSpgkqz1QAEKrii0Wh/a14g0BKb/mBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:29.982978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b12490c53090e64787a0da87321f1d480bc89a47fea0735eff792b2f32c032ff","sha256:aab32c9617fb73fd3e4d06d1d86db00f1fddad0015486794faa1a2894f3fbd2b"],"state_sha256":"07b96f61abb4f637aebb7c02f9caacc902de36eeb2c2a44eeaf0d65d6e9e9131"}