{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:XMELRMG5UZ63LTBLAJEXU3KLIY","short_pith_number":"pith:XMELRMG5","schema_version":"1.0","canonical_sha256":"bb08b8b0dda67db5cc2b02497a6d4b461dd4316951f5d048826df424ee3a6331","source":{"kind":"arxiv","id":"1005.0927","version":4},"attestation_state":"computed","paper":{"title":"A monotonicity property for random walk in a partially random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mark Holmes, Rongfeng Sun","submitted_at":"2010-05-06T08:35:47Z","abstract_excerpt":"We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z^d that is an extension of a result of Bolthausen, Sznitman and Zeitouni (2003). We use this result, along with the lace expansion for self-interacting random walks, to prove a monotonicity result for the first coordinate of the speed of the random walk under some strong assumptions on the distribution of the environment."},"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":"1005.0927","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-06T08:35:47Z","cross_cats_sorted":[],"title_canon_sha256":"18cdc6e8eb8c64af5bf17fb21774ed2703116fc5c6256e85a4ebbddea7846926","abstract_canon_sha256":"806240493d06cc5613703469d411fc640f328b61b1977dcb666e3140c94bcd75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:58.452536Z","signature_b64":"XieiZmcH+2Tu6xt87MgVDUOe/RkqUTk6+MXfrlDTjnUI/iuZWT74SJlh6vO61FqP+gtBZSdTrRIuD8FhHBlgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb08b8b0dda67db5cc2b02497a6d4b461dd4316951f5d048826df424ee3a6331","last_reissued_at":"2026-05-18T00:56:58.452066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:58.452066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A monotonicity property for random walk in a partially random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mark Holmes, Rongfeng Sun","submitted_at":"2010-05-06T08:35:47Z","abstract_excerpt":"We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z^d that is an extension of a result of Bolthausen, Sznitman and Zeitouni (2003). We use this result, along with the lace expansion for self-interacting random walks, to prove a monotonicity result for the first coordinate of the speed of the random walk under some strong assumptions on the distribution of the environment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0927","kind":"arxiv","version":4},"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":"1005.0927","created_at":"2026-05-18T00:56:58.452142+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.0927v4","created_at":"2026-05-18T00:56:58.452142+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0927","created_at":"2026-05-18T00:56:58.452142+00:00"},{"alias_kind":"pith_short_12","alias_value":"XMELRMG5UZ63","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"XMELRMG5UZ63LTBL","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"XMELRMG5","created_at":"2026-05-18T12:26:17.028572+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/XMELRMG5UZ63LTBLAJEXU3KLIY","json":"https://pith.science/pith/XMELRMG5UZ63LTBLAJEXU3KLIY.json","graph_json":"https://pith.science/api/pith-number/XMELRMG5UZ63LTBLAJEXU3KLIY/graph.json","events_json":"https://pith.science/api/pith-number/XMELRMG5UZ63LTBLAJEXU3KLIY/events.json","paper":"https://pith.science/paper/XMELRMG5"},"agent_actions":{"view_html":"https://pith.science/pith/XMELRMG5UZ63LTBLAJEXU3KLIY","download_json":"https://pith.science/pith/XMELRMG5UZ63LTBLAJEXU3KLIY.json","view_paper":"https://pith.science/paper/XMELRMG5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.0927&json=true","fetch_graph":"https://pith.science/api/pith-number/XMELRMG5UZ63LTBLAJEXU3KLIY/graph.json","fetch_events":"https://pith.science/api/pith-number/XMELRMG5UZ63LTBLAJEXU3KLIY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XMELRMG5UZ63LTBLAJEXU3KLIY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XMELRMG5UZ63LTBLAJEXU3KLIY/action/storage_attestation","attest_author":"https://pith.science/pith/XMELRMG5UZ63LTBLAJEXU3KLIY/action/author_attestation","sign_citation":"https://pith.science/pith/XMELRMG5UZ63LTBLAJEXU3KLIY/action/citation_signature","submit_replication":"https://pith.science/pith/XMELRMG5UZ63LTBLAJEXU3KLIY/action/replication_record"}},"created_at":"2026-05-18T00:56:58.452142+00:00","updated_at":"2026-05-18T00:56:58.452142+00:00"}