{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:TLDLS2I3LGHBGFJJXDGRIGFGCZ","short_pith_number":"pith:TLDLS2I3","schema_version":"1.0","canonical_sha256":"9ac6b9691b598e131529b8cd1418a6165341ac6394983b2097a80309a8a30280","source":{"kind":"arxiv","id":"1203.1389","version":3},"attestation_state":"computed","paper":{"title":"A Monotonicity Result for the Range of a Perturbed Random Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lung-Chi Chen, Rongfeng Sun","submitted_at":"2012-03-07T06:43:33Z","abstract_excerpt":"We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of sites visited by the perturbed random walk up to time n is always larger than or equal to that for the unperturbed walk. This intriguing problem arises from the study of a particle among a Poisson system of moving traps with sub-diffusive trap motion. In particular, our result implies a variant of the Pascal principle, which asserts that among all determinis"},"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":"1203.1389","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-07T06:43:33Z","cross_cats_sorted":[],"title_canon_sha256":"88f186cc4171e2b0e860fad009cf86099f2c29611e40036e33c8176b2a82ea2f","abstract_canon_sha256":"f0d7f948781d98b16e0f9e25449fed70f2ec988900af677258f418b74c9bc3e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:46.240517Z","signature_b64":"f+N2qW7sRXETrQMJZI4lpCj56lFHEGwsP0nUMsqAcN0wml73kMOaV1/vW3KMacGAY5xJWjTalGypr7BAh/m+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ac6b9691b598e131529b8cd1418a6165341ac6394983b2097a80309a8a30280","last_reissued_at":"2026-05-18T03:38:46.239780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:46.239780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Monotonicity Result for the Range of a Perturbed Random Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lung-Chi Chen, Rongfeng Sun","submitted_at":"2012-03-07T06:43:33Z","abstract_excerpt":"We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of sites visited by the perturbed random walk up to time n is always larger than or equal to that for the unperturbed walk. This intriguing problem arises from the study of a particle among a Poisson system of moving traps with sub-diffusive trap motion. In particular, our result implies a variant of the Pascal principle, which asserts that among all determinis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1389","kind":"arxiv","version":3},"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":"1203.1389","created_at":"2026-05-18T03:38:46.239895+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.1389v3","created_at":"2026-05-18T03:38:46.239895+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1389","created_at":"2026-05-18T03:38:46.239895+00:00"},{"alias_kind":"pith_short_12","alias_value":"TLDLS2I3LGHB","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"TLDLS2I3LGHBGFJJ","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"TLDLS2I3","created_at":"2026-05-18T12:27:23.164592+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/TLDLS2I3LGHBGFJJXDGRIGFGCZ","json":"https://pith.science/pith/TLDLS2I3LGHBGFJJXDGRIGFGCZ.json","graph_json":"https://pith.science/api/pith-number/TLDLS2I3LGHBGFJJXDGRIGFGCZ/graph.json","events_json":"https://pith.science/api/pith-number/TLDLS2I3LGHBGFJJXDGRIGFGCZ/events.json","paper":"https://pith.science/paper/TLDLS2I3"},"agent_actions":{"view_html":"https://pith.science/pith/TLDLS2I3LGHBGFJJXDGRIGFGCZ","download_json":"https://pith.science/pith/TLDLS2I3LGHBGFJJXDGRIGFGCZ.json","view_paper":"https://pith.science/paper/TLDLS2I3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.1389&json=true","fetch_graph":"https://pith.science/api/pith-number/TLDLS2I3LGHBGFJJXDGRIGFGCZ/graph.json","fetch_events":"https://pith.science/api/pith-number/TLDLS2I3LGHBGFJJXDGRIGFGCZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TLDLS2I3LGHBGFJJXDGRIGFGCZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TLDLS2I3LGHBGFJJXDGRIGFGCZ/action/storage_attestation","attest_author":"https://pith.science/pith/TLDLS2I3LGHBGFJJXDGRIGFGCZ/action/author_attestation","sign_citation":"https://pith.science/pith/TLDLS2I3LGHBGFJJXDGRIGFGCZ/action/citation_signature","submit_replication":"https://pith.science/pith/TLDLS2I3LGHBGFJJXDGRIGFGCZ/action/replication_record"}},"created_at":"2026-05-18T03:38:46.239895+00:00","updated_at":"2026-05-18T03:38:46.239895+00:00"}