{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FEL6SY37CMUJETTNBYOHPEON6G","short_pith_number":"pith:FEL6SY37","schema_version":"1.0","canonical_sha256":"2917e9637f1328924e6d0e1c7791cdf193aa7e3e983b644633c7c7963d75f5a6","source":{"kind":"arxiv","id":"1307.5332","version":1},"attestation_state":"computed","paper":{"title":"Random walks on free solvable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laurent Saloff-Coste, Tianyi Zheng","submitted_at":"2013-07-19T20:21:41Z","abstract_excerpt":"For any finitely generated group G, let n ---> \\Phi_G(n) be the function that describes the rough asymptotic behavior of the probability of return to the identity element at time 2n of a symmetric simple random walk on G (this is an invariant of quasi-isometry). We determine this function when G is the free solvable group S_{d,r} of derived length d on r generators and some other related groups."},"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":"1307.5332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-19T20:21:41Z","cross_cats_sorted":[],"title_canon_sha256":"9ded9b88fad1c02e41cd67d17de119a97faf28998d475061836a786109e77ec3","abstract_canon_sha256":"07678ea20d6525bf951e1c2c90f25afbec9b957fc0998ea897feafb0930e726c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:56.083225Z","signature_b64":"PKiaS9r3XxovA/RPcgY40yV8SxkO/ztGXlXnmN3mFETfB3MswNfTQbxmuaQe4ssFPaaSIC0QAzsBGtFWOYAtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2917e9637f1328924e6d0e1c7791cdf193aa7e3e983b644633c7c7963d75f5a6","last_reissued_at":"2026-05-18T03:17:56.080911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:56.080911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random walks on free solvable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laurent Saloff-Coste, Tianyi Zheng","submitted_at":"2013-07-19T20:21:41Z","abstract_excerpt":"For any finitely generated group G, let n ---> \\Phi_G(n) be the function that describes the rough asymptotic behavior of the probability of return to the identity element at time 2n of a symmetric simple random walk on G (this is an invariant of quasi-isometry). We determine this function when G is the free solvable group S_{d,r} of derived length d on r generators and some other related groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5332","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":"1307.5332","created_at":"2026-05-18T03:17:56.082522+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.5332v1","created_at":"2026-05-18T03:17:56.082522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5332","created_at":"2026-05-18T03:17:56.082522+00:00"},{"alias_kind":"pith_short_12","alias_value":"FEL6SY37CMUJ","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FEL6SY37CMUJETTN","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FEL6SY37","created_at":"2026-05-18T12:27:45.050594+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/FEL6SY37CMUJETTNBYOHPEON6G","json":"https://pith.science/pith/FEL6SY37CMUJETTNBYOHPEON6G.json","graph_json":"https://pith.science/api/pith-number/FEL6SY37CMUJETTNBYOHPEON6G/graph.json","events_json":"https://pith.science/api/pith-number/FEL6SY37CMUJETTNBYOHPEON6G/events.json","paper":"https://pith.science/paper/FEL6SY37"},"agent_actions":{"view_html":"https://pith.science/pith/FEL6SY37CMUJETTNBYOHPEON6G","download_json":"https://pith.science/pith/FEL6SY37CMUJETTNBYOHPEON6G.json","view_paper":"https://pith.science/paper/FEL6SY37","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.5332&json=true","fetch_graph":"https://pith.science/api/pith-number/FEL6SY37CMUJETTNBYOHPEON6G/graph.json","fetch_events":"https://pith.science/api/pith-number/FEL6SY37CMUJETTNBYOHPEON6G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FEL6SY37CMUJETTNBYOHPEON6G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FEL6SY37CMUJETTNBYOHPEON6G/action/storage_attestation","attest_author":"https://pith.science/pith/FEL6SY37CMUJETTNBYOHPEON6G/action/author_attestation","sign_citation":"https://pith.science/pith/FEL6SY37CMUJETTNBYOHPEON6G/action/citation_signature","submit_replication":"https://pith.science/pith/FEL6SY37CMUJETTNBYOHPEON6G/action/replication_record"}},"created_at":"2026-05-18T03:17:56.082522+00:00","updated_at":"2026-05-18T03:17:56.082522+00:00"}