{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BCM6QJTVEBWK2JSJYD5SQVSXLU","short_pith_number":"pith:BCM6QJTV","schema_version":"1.0","canonical_sha256":"0899e82675206cad2649c0fb2856575d2388613d6122579aeb13bf8d06244009","source":{"kind":"arxiv","id":"1210.4745","version":1},"attestation_state":"computed","paper":{"title":"Diffusivity of a random walk on random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Boissard, James Norris, Serge Cohen, Thibault Espinasse","submitted_at":"2012-10-17T14:19:47Z","abstract_excerpt":"We consider a random walk $(Z^{(1)}_n, ..., Z^{(K+1)}_n) \\in \\mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor $\\sigma_K^2 = \\frac{2}{K+2}$ with respect to the case of the classical simple random walk without constraint."},"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":"1210.4745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-17T14:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"5ce6d93050328905f63f9c98d1b8ba2324f540a40b8160bedb9316177a107b63","abstract_canon_sha256":"466ab54092325a3d1ac6da080e67c699927d1a15dd764eeb6e3de76e2096e8e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:56.291368Z","signature_b64":"EBXc+Vcm2NMreV3ku+pT/F6Wi1iIrGHLLnNZWkYYpPfk1j3OPyX2QB6LerL/yRtxAEgWRNdQXjVGn0d72P3RBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0899e82675206cad2649c0fb2856575d2388613d6122579aeb13bf8d06244009","last_reissued_at":"2026-05-18T03:42:56.290743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:56.290743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diffusivity of a random walk on random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Boissard, James Norris, Serge Cohen, Thibault Espinasse","submitted_at":"2012-10-17T14:19:47Z","abstract_excerpt":"We consider a random walk $(Z^{(1)}_n, ..., Z^{(K+1)}_n) \\in \\mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor $\\sigma_K^2 = \\frac{2}{K+2}$ with respect to the case of the classical simple random walk without constraint."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4745","kind":"arxiv","version":1},"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":"1210.4745","created_at":"2026-05-18T03:42:56.290854+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4745v1","created_at":"2026-05-18T03:42:56.290854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4745","created_at":"2026-05-18T03:42:56.290854+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCM6QJTVEBWK","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCM6QJTVEBWK2JSJ","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCM6QJTV","created_at":"2026-05-18T12:26:58.693483+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/BCM6QJTVEBWK2JSJYD5SQVSXLU","json":"https://pith.science/pith/BCM6QJTVEBWK2JSJYD5SQVSXLU.json","graph_json":"https://pith.science/api/pith-number/BCM6QJTVEBWK2JSJYD5SQVSXLU/graph.json","events_json":"https://pith.science/api/pith-number/BCM6QJTVEBWK2JSJYD5SQVSXLU/events.json","paper":"https://pith.science/paper/BCM6QJTV"},"agent_actions":{"view_html":"https://pith.science/pith/BCM6QJTVEBWK2JSJYD5SQVSXLU","download_json":"https://pith.science/pith/BCM6QJTVEBWK2JSJYD5SQVSXLU.json","view_paper":"https://pith.science/paper/BCM6QJTV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4745&json=true","fetch_graph":"https://pith.science/api/pith-number/BCM6QJTVEBWK2JSJYD5SQVSXLU/graph.json","fetch_events":"https://pith.science/api/pith-number/BCM6QJTVEBWK2JSJYD5SQVSXLU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCM6QJTVEBWK2JSJYD5SQVSXLU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCM6QJTVEBWK2JSJYD5SQVSXLU/action/storage_attestation","attest_author":"https://pith.science/pith/BCM6QJTVEBWK2JSJYD5SQVSXLU/action/author_attestation","sign_citation":"https://pith.science/pith/BCM6QJTVEBWK2JSJYD5SQVSXLU/action/citation_signature","submit_replication":"https://pith.science/pith/BCM6QJTVEBWK2JSJYD5SQVSXLU/action/replication_record"}},"created_at":"2026-05-18T03:42:56.290854+00:00","updated_at":"2026-05-18T03:42:56.290854+00:00"}