{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JDVCF6AJ37LXH2TUJ5F7WJEACY","short_pith_number":"pith:JDVCF6AJ","canonical_record":{"source":{"id":"1105.4402","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-23T04:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"b2088a306e1934974aebcfc34075ab7bab1ec1a9991f218d22b39664aa812136","abstract_canon_sha256":"14409e5aed7f2c59ef2cd433cf08f27b61b3ceed0c3fdd8a66ab218870802af9"},"schema_version":"1.0"},"canonical_sha256":"48ea22f809dfd773ea744f4bfb2480160f48aaa563a9576a44d571a6c1f1ecaf","source":{"kind":"arxiv","id":"1105.4402","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4402","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4402v2","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4402","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"JDVCF6AJ37LX","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JDVCF6AJ37LXH2TU","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JDVCF6AJ","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JDVCF6AJ37LXH2TUJ5F7WJEACY","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4402","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-23T04:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"b2088a306e1934974aebcfc34075ab7bab1ec1a9991f218d22b39664aa812136","abstract_canon_sha256":"14409e5aed7f2c59ef2cd433cf08f27b61b3ceed0c3fdd8a66ab218870802af9"},"schema_version":"1.0"},"canonical_sha256":"48ea22f809dfd773ea744f4bfb2480160f48aaa563a9576a44d571a6c1f1ecaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:10.348577Z","signature_b64":"iTvetjqq1w6/OzRox30iMWnFcscckWdMnKLpBmpOt+0vbxhx+Qk+Ml3O5T3E5o/qcxueyXQ+1oI0viGqEksEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48ea22f809dfd773ea744f4bfb2480160f48aaa563a9576a44d571a6c1f1ecaf","last_reissued_at":"2026-05-18T04:21:10.348076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:10.348076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4402","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iWFZUZw3GRMYl8H3uSVHRGiAKcT16HH+yahDAbTxCK1U7d2KZooQ4hOiaBH3hh/TcJfoR7GmZEsar03Gg4hXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:24:28.328567Z"},"content_sha256":"50be91e4e08d284ada2e24a9ba6a89bae0a8b8a394e47a1febee36967f3add2d","schema_version":"1.0","event_id":"sha256:50be91e4e08d284ada2e24a9ba6a89bae0a8b8a394e47a1febee36967f3add2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JDVCF6AJ37LXH2TUJ5F7WJEACY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing of the upper triangular matrix walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Allan Sly, Yuval Peres","submitted_at":"2011-05-23T04:59:09Z","abstract_excerpt":"We study a natural random walk over the upper triangular matrices, with entries in the field $\\Z_2$, generated by steps which add row $i+1$ to row $i$. We show that the mixing time of the lazy random walk is $O(n^2)$ which is optimal up to constants. Our proof makes key use of the linear structure of the group and extends to walks on the upper triangular matrices over the fields $\\Z_q$ for $q$ prime."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4402","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J/b0nURGxlCGHAgVbmGdUry58NMGQD7b0iucisr9P3zQvWtUguseWrppG8rxul+OPWYnHxYJWNRIEaXTqslQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:24:28.328931Z"},"content_sha256":"c961fca2d3acc619c75c297abccae55fc2a4141d2959a4bec269ed642ca473f4","schema_version":"1.0","event_id":"sha256:c961fca2d3acc619c75c297abccae55fc2a4141d2959a4bec269ed642ca473f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDVCF6AJ37LXH2TUJ5F7WJEACY/bundle.json","state_url":"https://pith.science/pith/JDVCF6AJ37LXH2TUJ5F7WJEACY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDVCF6AJ37LXH2TUJ5F7WJEACY/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":"2026-06-28T10:24:28Z","links":{"resolver":"https://pith.science/pith/JDVCF6AJ37LXH2TUJ5F7WJEACY","bundle":"https://pith.science/pith/JDVCF6AJ37LXH2TUJ5F7WJEACY/bundle.json","state":"https://pith.science/pith/JDVCF6AJ37LXH2TUJ5F7WJEACY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDVCF6AJ37LXH2TUJ5F7WJEACY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JDVCF6AJ37LXH2TUJ5F7WJEACY","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":"14409e5aed7f2c59ef2cd433cf08f27b61b3ceed0c3fdd8a66ab218870802af9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-23T04:59:09Z","title_canon_sha256":"b2088a306e1934974aebcfc34075ab7bab1ec1a9991f218d22b39664aa812136"},"schema_version":"1.0","source":{"id":"1105.4402","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4402","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4402v2","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4402","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"JDVCF6AJ37LX","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JDVCF6AJ37LXH2TU","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JDVCF6AJ","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:c961fca2d3acc619c75c297abccae55fc2a4141d2959a4bec269ed642ca473f4","target":"graph","created_at":"2026-05-18T04:21:10Z","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":"We study a natural random walk over the upper triangular matrices, with entries in the field $\\Z_2$, generated by steps which add row $i+1$ to row $i$. We show that the mixing time of the lazy random walk is $O(n^2)$ which is optimal up to constants. Our proof makes key use of the linear structure of the group and extends to walks on the upper triangular matrices over the fields $\\Z_q$ for $q$ prime.","authors_text":"Allan Sly, Yuval Peres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-23T04:59:09Z","title":"Mixing of the upper triangular matrix walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4402","kind":"arxiv","version":2},"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":"sha256:50be91e4e08d284ada2e24a9ba6a89bae0a8b8a394e47a1febee36967f3add2d","target":"record","created_at":"2026-05-18T04:21:10Z","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":"14409e5aed7f2c59ef2cd433cf08f27b61b3ceed0c3fdd8a66ab218870802af9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-23T04:59:09Z","title_canon_sha256":"b2088a306e1934974aebcfc34075ab7bab1ec1a9991f218d22b39664aa812136"},"schema_version":"1.0","source":{"id":"1105.4402","kind":"arxiv","version":2}},"canonical_sha256":"48ea22f809dfd773ea744f4bfb2480160f48aaa563a9576a44d571a6c1f1ecaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48ea22f809dfd773ea744f4bfb2480160f48aaa563a9576a44d571a6c1f1ecaf","first_computed_at":"2026-05-18T04:21:10.348076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:10.348076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iTvetjqq1w6/OzRox30iMWnFcscckWdMnKLpBmpOt+0vbxhx+Qk+Ml3O5T3E5o/qcxueyXQ+1oI0viGqEksEBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:10.348577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4402","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50be91e4e08d284ada2e24a9ba6a89bae0a8b8a394e47a1febee36967f3add2d","sha256:c961fca2d3acc619c75c297abccae55fc2a4141d2959a4bec269ed642ca473f4"],"state_sha256":"0e57e2eb6148164408fc42a9a2f20c5c6b0d7fd5baa6c204f1d93dee3e12600d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gB/SVQ7qsyip9uKUtjv3Q8u7OgwUhZv/KV4i8V6OBUh7Gelj2V3UTkEGFyMxOHYd8on2n8QHqixz7Fy0lQPICQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T10:24:28.330812Z","bundle_sha256":"7ed723229bfe8528a9599e8fb9ba0e8ea78071b1a0167a96a344ec698bb5a5ff"}}