{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:7XOZZMASWK4YJSTORZMFQK3J5Q","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":"a601dce8e7cae3f1f9585f5bfd554e7f4ee5fa1c42d58c033a3df0520c18e028","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-13T07:54:27Z","title_canon_sha256":"9a96f565444fc496328af4890222850663262cb66ae29820830b62fa260e4252"},"schema_version":"1.0","source":{"id":"0812.2532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.2532","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"0812.2532v2","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.2532","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"7XOZZMASWK4Y","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7XOZZMASWK4YJSTO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7XOZZMAS","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:01ad25431069cd8b5b4921bf442719a9c5e035f8dca8b743cf68580a560e9119","target":"graph","created_at":"2026-05-18T04:35:47Z","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 study the speed of a biased random walk on a percolation cluster on $\\Z^d$ in function of the percolation parameter $p$. We obtain a first order expansion of the speed at $p=1$ which proves that percolating slows down the random walk at least in the case where the drift is along a component of the lattice.","authors_text":"Alexander Fribergh (CIMS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-13T07:54:27Z","title":"The speed of a biased random walk on a percolation cluster at high density"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2532","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":"sha256:54c2f04d45bfee2a09c2d020d70ee64c7c973600f59ee6a7f80c51746a1c9f45","target":"record","created_at":"2026-05-18T04:35:47Z","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":"a601dce8e7cae3f1f9585f5bfd554e7f4ee5fa1c42d58c033a3df0520c18e028","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-13T07:54:27Z","title_canon_sha256":"9a96f565444fc496328af4890222850663262cb66ae29820830b62fa260e4252"},"schema_version":"1.0","source":{"id":"0812.2532","kind":"arxiv","version":2}},"canonical_sha256":"fddd9cb012b2b984ca6e8e58582b69ec3ba078a9f8980ad43a3be1b88f5132e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fddd9cb012b2b984ca6e8e58582b69ec3ba078a9f8980ad43a3be1b88f5132e2","first_computed_at":"2026-05-18T04:35:47.898926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:47.898926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KfXIxSSeaxMtchbL/Bd2Lx7RiIrMhLapgK9+R24ZPkouIiBj3uV9x4fvuW6cai21kgY5NUnB5WGMHggncPc1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:47.899546Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.2532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54c2f04d45bfee2a09c2d020d70ee64c7c973600f59ee6a7f80c51746a1c9f45","sha256:01ad25431069cd8b5b4921bf442719a9c5e035f8dca8b743cf68580a560e9119"],"state_sha256":"92aba914c27230868fc17ba69ba1da640584861657ad4b203abbb12fe703c8c8"}