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Diaconis,Hit and run as a unifying device, Journal de la Soci´ et´ e Francaise Statistique, 148 (4) (2007), 5-28","work_id":"7ec6259e-ad53-4d5b-b4c0-74276cacc249","year":2007}],"snapshot_sha256":"503f39e449a200638216ca5fed8b267d237f5b09913832747f1d24a87814f575"},"source":{"id":"2605.16244","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T18:21:41.765804Z","id":"62c7cc60-158b-4cf2-ae59-8897b049b72e","model_set":{"reader":"grok-4.3"},"one_line_summary":"Burnside processes on parking functions and Dyck paths mix in O(n log n) time, yielding approximate uniform sampling algorithms for increasing parking functions, Dyck paths, and polygon triangulations.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The Burnside process on parking functions and labeled Dyck paths mixes in O(n log n) steps and yields uniform sampling algorithms.","strongest_claim":"Our main result shows that both processes are rapidly mixing, with mixing times upper bounded by O(n log n).","weakest_assumption":"The specific group actions (S_n permuting coordinates for parking functions and labels for Dyck paths) allow the general Burnside process to have uniform stationary distribution on orbits and to mix rapidly under the stated dynamics, as described in the abstract for the two special cases."}},"verdict_id":"62c7cc60-158b-4cf2-ae59-8897b049b72e"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5e96362eda81d4837f85c58496c4969ba71873f25a191a3da08e823d505c806b","target":"record","created_at":"2026-05-20T00:01:59Z","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":"3a68423b3039916e47f8706e197b01c0832daa73d4ee6a33fa3896b7e2b971e1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-15T17:49:11Z","title_canon_sha256":"8ab681cc07bd2a3c39798632792eb5beebf1ac2866b0f9a9cb4cb337d9da069a"},"schema_version":"1.0","source":{"id":"2605.16244","kind":"arxiv","version":1}},"canonical_sha256":"73ad8a2ecd69e6645c26f1028febfad105ef50663b2075330c186c8686f557b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73ad8a2ecd69e6645c26f1028febfad105ef50663b2075330c186c8686f557b6","first_computed_at":"2026-05-20T00:01:59.808464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:59.808464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TygiBPH+SQk3Swxi84RQL2cFaxJXVSAXegvSQGMR1a552qFgcbwGQBFg50Td59kjxQDb4PVEUAANSzV5Grt9Dg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:59.809325Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e96362eda81d4837f85c58496c4969ba71873f25a191a3da08e823d505c806b","sha256:e2258f9da00f686bf1c2330eca78cd7883e458ca9926be7617bf1be66cec77ed"],"state_sha256":"afcc621dff20fe44be506f9d29e241631187f6952b92a61675ec7b00860bd57d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szLOBMIdC90HGI6JaP80IPolGmHEAA8MhAlt6I/x6J/hyY0eu8sMXSO7UCAgWvs5z8QUJyYi4vjqyYJtgM7mDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:56:19.482110Z","bundle_sha256":"861f641798e70a67241936b3d0bdd517db5d82c0c38fd1d6c0b71616a5a28d79"}}