{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B57C5GHSHOR62ZEONUEXMSTVCQ","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":"1b94b8b33a74ff56267e62945aec8d664960ed032ee152103f9e28a225f91039","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-15T22:20:16Z","title_canon_sha256":"ceab78de4fa4b8239dfe60e62c4f42bce68034f089b6a62d05c4ba6adfc13f90"},"schema_version":"1.0","source":{"id":"1407.4163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4163","created_at":"2026-05-18T02:47:30Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4163v1","created_at":"2026-05-18T02:47:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4163","created_at":"2026-05-18T02:47:30Z"},{"alias_kind":"pith_short_12","alias_value":"B57C5GHSHOR6","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B57C5GHSHOR62ZEO","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B57C5GHS","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:8f368a88f135bd729b6e3e775d40e1cabd3953fa5193e56d8037c3d391310f2b","target":"graph","created_at":"2026-05-18T02:47:30Z","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 consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-in-time constraint $\\|\\nabla u(\\cdot,t)\\|_p\\leq 1$ we show that any function can be mixed to scale $\\epsilon$ in time $O(|\\log\\epsilon|^{1+\\nu_p})$, with $\\nu_p=0$ for $p<\\tfrac{3+\\sqrt 5}2$ and $\\nu_p\\leq \\tfrac 13$ for $p\\geq \\tfrac{3+\\sqrt 5}2$. Known lower bounds show that this rate is optimal for $p\\in(1,\\tfrac{3+\\sqrt 5}2)$. We also show that any set which is mixed to scale $\\epsilon$ but not much more than that","authors_text":"Andrej Zlatos, Yao Yao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-15T22:20:16Z","title":"Mixing and Un-mixing by Incompressible Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4163","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":"sha256:883e455cbdd74464147b44996b372b3f96447ffb19ad054935d1c50ba947f20d","target":"record","created_at":"2026-05-18T02:47:30Z","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":"1b94b8b33a74ff56267e62945aec8d664960ed032ee152103f9e28a225f91039","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-15T22:20:16Z","title_canon_sha256":"ceab78de4fa4b8239dfe60e62c4f42bce68034f089b6a62d05c4ba6adfc13f90"},"schema_version":"1.0","source":{"id":"1407.4163","kind":"arxiv","version":1}},"canonical_sha256":"0f7e2e98f23ba3ed648e6d09764a75142621bc0e1ac4dd5e61b9b023458bc4f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f7e2e98f23ba3ed648e6d09764a75142621bc0e1ac4dd5e61b9b023458bc4f9","first_computed_at":"2026-05-18T02:47:30.967827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:30.967827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9DerpyE5blpElvUkt5Tj/nROMB634k17vCggc1Gsg9GX3X/UVR0uee1A431JrDVRAtGpnjsPOtjxa/5pOKR+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:30.968285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:883e455cbdd74464147b44996b372b3f96447ffb19ad054935d1c50ba947f20d","sha256:8f368a88f135bd729b6e3e775d40e1cabd3953fa5193e56d8037c3d391310f2b"],"state_sha256":"c5bef217d2d3e22b3de8661b555d3422a7210f511d634c19bc632e45e0e9bb25"}