{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:7XOZZMASWK4YJSTORZMFQK3J5Q","short_pith_number":"pith:7XOZZMAS","schema_version":"1.0","canonical_sha256":"fddd9cb012b2b984ca6e8e58582b69ec3ba078a9f8980ad43a3be1b88f5132e2","source":{"kind":"arxiv","id":"0812.2532","version":2},"attestation_state":"computed","paper":{"title":"The speed of a biased random walk on a percolation cluster at high density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Fribergh (CIMS)","submitted_at":"2008-12-13T07:54:27Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0812.2532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-13T07:54:27Z","cross_cats_sorted":[],"title_canon_sha256":"9a96f565444fc496328af4890222850663262cb66ae29820830b62fa260e4252","abstract_canon_sha256":"a601dce8e7cae3f1f9585f5bfd554e7f4ee5fa1c42d58c033a3df0520c18e028"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:47.899546Z","signature_b64":"KfXIxSSeaxMtchbL/Bd2Lx7RiIrMhLapgK9+R24ZPkouIiBj3uV9x4fvuW6cai21kgY5NUnB5WGMHggncPc1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fddd9cb012b2b984ca6e8e58582b69ec3ba078a9f8980ad43a3be1b88f5132e2","last_reissued_at":"2026-05-18T04:35:47.898926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:47.898926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The speed of a biased random walk on a percolation cluster at high density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Fribergh (CIMS)","submitted_at":"2008-12-13T07:54:27Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2532","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0812.2532","created_at":"2026-05-18T04:35:47.899021+00:00"},{"alias_kind":"arxiv_version","alias_value":"0812.2532v2","created_at":"2026-05-18T04:35:47.899021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.2532","created_at":"2026-05-18T04:35:47.899021+00:00"},{"alias_kind":"pith_short_12","alias_value":"7XOZZMASWK4Y","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"7XOZZMASWK4YJSTO","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"7XOZZMAS","created_at":"2026-05-18T12:25:56.245647+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7XOZZMASWK4YJSTORZMFQK3J5Q","json":"https://pith.science/pith/7XOZZMASWK4YJSTORZMFQK3J5Q.json","graph_json":"https://pith.science/api/pith-number/7XOZZMASWK4YJSTORZMFQK3J5Q/graph.json","events_json":"https://pith.science/api/pith-number/7XOZZMASWK4YJSTORZMFQK3J5Q/events.json","paper":"https://pith.science/paper/7XOZZMAS"},"agent_actions":{"view_html":"https://pith.science/pith/7XOZZMASWK4YJSTORZMFQK3J5Q","download_json":"https://pith.science/pith/7XOZZMASWK4YJSTORZMFQK3J5Q.json","view_paper":"https://pith.science/paper/7XOZZMAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0812.2532&json=true","fetch_graph":"https://pith.science/api/pith-number/7XOZZMASWK4YJSTORZMFQK3J5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/7XOZZMASWK4YJSTORZMFQK3J5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7XOZZMASWK4YJSTORZMFQK3J5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7XOZZMASWK4YJSTORZMFQK3J5Q/action/storage_attestation","attest_author":"https://pith.science/pith/7XOZZMASWK4YJSTORZMFQK3J5Q/action/author_attestation","sign_citation":"https://pith.science/pith/7XOZZMASWK4YJSTORZMFQK3J5Q/action/citation_signature","submit_replication":"https://pith.science/pith/7XOZZMASWK4YJSTORZMFQK3J5Q/action/replication_record"}},"created_at":"2026-05-18T04:35:47.899021+00:00","updated_at":"2026-05-18T04:35:47.899021+00:00"}