{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5IO53ARYKVPV4U42WCJBA5QGXR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"074795954bfcf2928a47cec3558e35739d0bbdc1991eab353612b240de16323c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-12T18:24:28Z","title_canon_sha256":"f6a9863350237ba2385905d200cf04b8af673e0b57ee98fc35252ebbaed78558"},"schema_version":"1.0","source":{"id":"1112.2650","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2650","created_at":"2026-05-18T04:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2650v1","created_at":"2026-05-18T04:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2650","created_at":"2026-05-18T04:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"5IO53ARYKVPV","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5IO53ARYKVPV4U42","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5IO53ARY","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:59fce66991709d3fece4f65c117ecde075f998860f7b131acccf699053150c23","target":"graph","created_at":"2026-05-18T04:06:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The well-known Gilbert-Shannon-Reeds model for riffle shuffles assumes that the cards are initially cut 'about in half' and then riffled together. We analyze a natural variant where the initial cut is biased. Extending results of Fulman (1998), we show a sharp cutoff in separation and L-infinity distances. This analysis is possible due to the close connection between shuffling and quasisymmetric functions along with some complex analysis of a generating function.","authors_text":"Kannan Soundararajan, Persi Diaconis, Sami Assaf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-12T18:24:28Z","title":"Riffle shuffles with biased cuts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2650","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:202ac917e916ad16fa480bd7a5d6c42b67acbb7f75a5011096fd349a292f6e1c","target":"record","created_at":"2026-05-18T04:06:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"074795954bfcf2928a47cec3558e35739d0bbdc1991eab353612b240de16323c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-12T18:24:28Z","title_canon_sha256":"f6a9863350237ba2385905d200cf04b8af673e0b57ee98fc35252ebbaed78558"},"schema_version":"1.0","source":{"id":"1112.2650","kind":"arxiv","version":1}},"canonical_sha256":"ea1ddd8238555f5e539ab092107606bc5ef52aaa6b93e5da230efc76de69fe64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea1ddd8238555f5e539ab092107606bc5ef52aaa6b93e5da230efc76de69fe64","first_computed_at":"2026-05-18T04:06:33.737741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:33.737741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sgggn8QwbWgsJMDK3syUOSrQS1hIj8r2f5q4KUxIjkZU8AFmtqRVj7WaJ3nmDAsR5j0hHZtzk6aSOtT63mMkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:33.738424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:202ac917e916ad16fa480bd7a5d6c42b67acbb7f75a5011096fd349a292f6e1c","sha256:59fce66991709d3fece4f65c117ecde075f998860f7b131acccf699053150c23"],"state_sha256":"f63eda2f3744bbd43d61851a5c23f8d85d9328ae766d5cf9cded6b22cf223def"}