{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:U2NY3ER34S5FICJ3AMUU22ZOEW","short_pith_number":"pith:U2NY3ER3","canonical_record":{"source":{"id":"1204.3239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-04-15T06:21:46Z","cross_cats_sorted":[],"title_canon_sha256":"a1053504ada0d550958394682103ad119741080451a0b564242753b08858e3c8","abstract_canon_sha256":"4e0f2ff682d08e607cce4e5d6d4fc07e9a15f25a4ad706d05921e83a516da60c"},"schema_version":"1.0"},"canonical_sha256":"a69b8d923be4ba54093b03294d6b2e25b18ca012cbba475b26747d9e09fd7073","source":{"kind":"arxiv","id":"1204.3239","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3239","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3239v1","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3239","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"U2NY3ER34S5F","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U2NY3ER34S5FICJ3","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U2NY3ER3","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:U2NY3ER34S5FICJ3AMUU22ZOEW","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-04-15T06:21:46Z","cross_cats_sorted":[],"title_canon_sha256":"a1053504ada0d550958394682103ad119741080451a0b564242753b08858e3c8","abstract_canon_sha256":"4e0f2ff682d08e607cce4e5d6d4fc07e9a15f25a4ad706d05921e83a516da60c"},"schema_version":"1.0"},"canonical_sha256":"a69b8d923be4ba54093b03294d6b2e25b18ca012cbba475b26747d9e09fd7073","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:52.146655Z","signature_b64":"VmK1wD9a0T6BjumZjMEWOghKm53wW5ukl7hT78cYliknQG8941sZKLwbxtnJKfPkGlryHbYONn8j8S8/gNo1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a69b8d923be4ba54093b03294d6b2e25b18ca012cbba475b26747d9e09fd7073","last_reissued_at":"2026-05-18T03:57:52.146122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:52.146122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3239","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PMEDcD23Okf77Th+FRWBBAoVVTMNIPTy7Ku/19Pa6jJWxZtub23XI+gNPElBnK5vuqCQCre4sAEvup+puBdqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:55:29.064442Z"},"content_sha256":"045ca69c34783d27f9cc2d3f4b1cf16e84103f465fb63fb32f246664ceb752ef","schema_version":"1.0","event_id":"sha256:045ca69c34783d27f9cc2d3f4b1cf16e84103f465fb63fb32f246664ceb752ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:U2NY3ER34S5FICJ3AMUU22ZOEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing Times of Self-Organizing Lists and Biased Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Amanda Pascoe Streib, Dana Randall, Prateek Bhakta, Sarah Miracle","submitted_at":"2012-04-15T06:21:46Z","abstract_excerpt":"Sampling permutations from S_n is a fundamental problem from probability theory. The nearest neighbor transposition chain \\cal{M}}_{nn} is known to converge in time \\Theta(n^3 \\log n) in the uniform case and time \\Theta(n^2) in the constant bias case, in which we put adjacent elements in order with probability p \\neq 1/2 and out of order with probability 1-p. Here we consider the variable bias case where we put adjacent elements x<y in order with probability p{x,y} and out of order with probability 1-p_{x,y}. The problem of bounding the mixing rate of M_{nn} was posed by Fill and was motivated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3239","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wIC3BI8SrZVIyeV+TRiPFgRLWtMUmlHm2MV4hy0CS+fXX7vmv5NrBJIJ87BL6gCbmmNM4YM9hVD6g1g63ycWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:55:29.064809Z"},"content_sha256":"61252f230c0b387d40ee89be2a77b33c6a2bbd6ae15aa2fb24b1718ee1ec37cc","schema_version":"1.0","event_id":"sha256:61252f230c0b387d40ee89be2a77b33c6a2bbd6ae15aa2fb24b1718ee1ec37cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2NY3ER34S5FICJ3AMUU22ZOEW/bundle.json","state_url":"https://pith.science/pith/U2NY3ER34S5FICJ3AMUU22ZOEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2NY3ER34S5FICJ3AMUU22ZOEW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T19:55:29Z","links":{"resolver":"https://pith.science/pith/U2NY3ER34S5FICJ3AMUU22ZOEW","bundle":"https://pith.science/pith/U2NY3ER34S5FICJ3AMUU22ZOEW/bundle.json","state":"https://pith.science/pith/U2NY3ER34S5FICJ3AMUU22ZOEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2NY3ER34S5FICJ3AMUU22ZOEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U2NY3ER34S5FICJ3AMUU22ZOEW","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":"4e0f2ff682d08e607cce4e5d6d4fc07e9a15f25a4ad706d05921e83a516da60c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-04-15T06:21:46Z","title_canon_sha256":"a1053504ada0d550958394682103ad119741080451a0b564242753b08858e3c8"},"schema_version":"1.0","source":{"id":"1204.3239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3239","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3239v1","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3239","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"U2NY3ER34S5F","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U2NY3ER34S5FICJ3","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U2NY3ER3","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:61252f230c0b387d40ee89be2a77b33c6a2bbd6ae15aa2fb24b1718ee1ec37cc","target":"graph","created_at":"2026-05-18T03:57:52Z","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":"Sampling permutations from S_n is a fundamental problem from probability theory. The nearest neighbor transposition chain \\cal{M}}_{nn} is known to converge in time \\Theta(n^3 \\log n) in the uniform case and time \\Theta(n^2) in the constant bias case, in which we put adjacent elements in order with probability p \\neq 1/2 and out of order with probability 1-p. Here we consider the variable bias case where we put adjacent elements x<y in order with probability p{x,y} and out of order with probability 1-p_{x,y}. The problem of bounding the mixing rate of M_{nn} was posed by Fill and was motivated","authors_text":"Amanda Pascoe Streib, Dana Randall, Prateek Bhakta, Sarah Miracle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-04-15T06:21:46Z","title":"Mixing Times of Self-Organizing Lists and Biased Permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3239","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":"sha256:045ca69c34783d27f9cc2d3f4b1cf16e84103f465fb63fb32f246664ceb752ef","target":"record","created_at":"2026-05-18T03:57:52Z","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":"4e0f2ff682d08e607cce4e5d6d4fc07e9a15f25a4ad706d05921e83a516da60c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-04-15T06:21:46Z","title_canon_sha256":"a1053504ada0d550958394682103ad119741080451a0b564242753b08858e3c8"},"schema_version":"1.0","source":{"id":"1204.3239","kind":"arxiv","version":1}},"canonical_sha256":"a69b8d923be4ba54093b03294d6b2e25b18ca012cbba475b26747d9e09fd7073","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a69b8d923be4ba54093b03294d6b2e25b18ca012cbba475b26747d9e09fd7073","first_computed_at":"2026-05-18T03:57:52.146122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:52.146122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VmK1wD9a0T6BjumZjMEWOghKm53wW5ukl7hT78cYliknQG8941sZKLwbxtnJKfPkGlryHbYONn8j8S8/gNo1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:52.146655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:045ca69c34783d27f9cc2d3f4b1cf16e84103f465fb63fb32f246664ceb752ef","sha256:61252f230c0b387d40ee89be2a77b33c6a2bbd6ae15aa2fb24b1718ee1ec37cc"],"state_sha256":"fecf73ee2211cf55a46fb27cf0866dbc2b84623c03d9fbedd8df48097eb6e6b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hErQbq80NpHKKJ/B8nTKRD5BVbqo4Bxw0KLXkXKUo0Na6T6YSORUlCMECN7eVaUdMieh+p0aSSRbJ5F2OiRTCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:55:29.066879Z","bundle_sha256":"e589fb73a6c283a7f58e61b1a2b35e11c2e15fa4b57f3d8c9cb61cb8e5777d94"}}