{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:E6UZL27B2HGA5FRMWLBVUTD4FC","short_pith_number":"pith:E6UZL27B","schema_version":"1.0","canonical_sha256":"27a995ebe1d1cc0e962cb2c35a4c7c288b4945c5b2479c97a35c8b80723ce134","source":{"kind":"arxiv","id":"1407.3580","version":2},"attestation_state":"computed","paper":{"title":"Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod $n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael E. Bate, Stephen B. Connor","submitted_at":"2014-07-14T09:39:25Z","abstract_excerpt":"We analyse a random walk on the ring of integers mod $n$, which at each time point can make an additive `step' or a multiplicative `jump'. When the probability of making a jump tends to zero as an appropriate power of $n$ we prove the existence of a total variation pre-cutoff for this walk. In addition, we show that the process obtained by subsampling our walk at jump times exhibits a true cutoff, with mixing time dependent on whether the step distribution has zero mean."},"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":"1407.3580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-14T09:39:25Z","cross_cats_sorted":[],"title_canon_sha256":"3ac29e3674efe3d7729e54a0f2818466c81f69725fef5767a9ed8b6930af5c80","abstract_canon_sha256":"9ebc97c658ea3a7dd3795edc98e446137464e941da5542b64ca1e9d9c1dd74b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:02.009232Z","signature_b64":"0/UT0Dsmb8upenzAFF2azNPTPbyRz75RAGdayiyiLtGcEp+PnSPHu74jz5oIrrNwXVko1aUxWaZMp7lUAEPDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27a995ebe1d1cc0e962cb2c35a4c7c288b4945c5b2479c97a35c8b80723ce134","last_reissued_at":"2026-05-18T01:20:02.008479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:02.008479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod $n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael E. Bate, Stephen B. Connor","submitted_at":"2014-07-14T09:39:25Z","abstract_excerpt":"We analyse a random walk on the ring of integers mod $n$, which at each time point can make an additive `step' or a multiplicative `jump'. When the probability of making a jump tends to zero as an appropriate power of $n$ we prove the existence of a total variation pre-cutoff for this walk. In addition, we show that the process obtained by subsampling our walk at jump times exhibits a true cutoff, with mixing time dependent on whether the step distribution has zero mean."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3580","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":"1407.3580","created_at":"2026-05-18T01:20:02.008603+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.3580v2","created_at":"2026-05-18T01:20:02.008603+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3580","created_at":"2026-05-18T01:20:02.008603+00:00"},{"alias_kind":"pith_short_12","alias_value":"E6UZL27B2HGA","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"E6UZL27B2HGA5FRM","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"E6UZL27B","created_at":"2026-05-18T12:28:25.294606+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/E6UZL27B2HGA5FRMWLBVUTD4FC","json":"https://pith.science/pith/E6UZL27B2HGA5FRMWLBVUTD4FC.json","graph_json":"https://pith.science/api/pith-number/E6UZL27B2HGA5FRMWLBVUTD4FC/graph.json","events_json":"https://pith.science/api/pith-number/E6UZL27B2HGA5FRMWLBVUTD4FC/events.json","paper":"https://pith.science/paper/E6UZL27B"},"agent_actions":{"view_html":"https://pith.science/pith/E6UZL27B2HGA5FRMWLBVUTD4FC","download_json":"https://pith.science/pith/E6UZL27B2HGA5FRMWLBVUTD4FC.json","view_paper":"https://pith.science/paper/E6UZL27B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.3580&json=true","fetch_graph":"https://pith.science/api/pith-number/E6UZL27B2HGA5FRMWLBVUTD4FC/graph.json","fetch_events":"https://pith.science/api/pith-number/E6UZL27B2HGA5FRMWLBVUTD4FC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E6UZL27B2HGA5FRMWLBVUTD4FC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E6UZL27B2HGA5FRMWLBVUTD4FC/action/storage_attestation","attest_author":"https://pith.science/pith/E6UZL27B2HGA5FRMWLBVUTD4FC/action/author_attestation","sign_citation":"https://pith.science/pith/E6UZL27B2HGA5FRMWLBVUTD4FC/action/citation_signature","submit_replication":"https://pith.science/pith/E6UZL27B2HGA5FRMWLBVUTD4FC/action/replication_record"}},"created_at":"2026-05-18T01:20:02.008603+00:00","updated_at":"2026-05-18T01:20:02.008603+00:00"}