{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:R7AYJXEUMHMIXK2OOWIFKMFE7P","short_pith_number":"pith:R7AYJXEU","schema_version":"1.0","canonical_sha256":"8fc184dc9461d88bab4e75905530a4fbd1fa56a9dbacb851542739c36002cb59","source":{"kind":"arxiv","id":"1809.03546","version":1},"attestation_state":"computed","paper":{"title":"A log-Sobolev inequality for the multislice, with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.PR","authors_text":"Ryan O'Donnell, Xinyu Wu, Yuval Filmus","submitted_at":"2018-09-10T18:46:07Z","abstract_excerpt":"Let $\\kappa \\in \\mathbb{N}_+^\\ell$ satisfy $\\kappa_1 + \\dots + \\kappa_\\ell = n$ and let $\\mathcal{U}_\\kappa$ denote the \"multislice\" of all strings $u$ in $[\\ell]^n$ having exactly $\\kappa_i$ coordinates equal to $i$, for all $i \\in [\\ell]$. Consider the Markov chain on $\\mathcal{U}_\\kappa$, where a step is a random transposition of two coordinates of $u$. We show that the log-Sobolev constant $\\rho_\\kappa$ for the chain satisfies $$(\\rho_\\kappa)^{-1} \\leq n \\sum_{i=1}^{\\ell} \\tfrac{1}{2} \\log_2(4n/\\kappa_i),$$ which is sharp up to constants whenever $\\ell$ is constant. From this, we derive so"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.03546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-10T18:46:07Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"5f76a46d7b2f7848e613b2813f12d2edb2055b0dd9f4c43595f55f3623435edf","abstract_canon_sha256":"1418ad6549d3449a056d21e746c0fe622a6d66c3c3277b699a8d1fb05f24e92f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:00.516142Z","signature_b64":"d6anekdGpff1ry/EMZ9/EUg3Bbn8vNDEbnS9bkAl43lSu4Vtd5hHfUKykGUWpxDOc8hGctgwmF5T02VKppJUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fc184dc9461d88bab4e75905530a4fbd1fa56a9dbacb851542739c36002cb59","last_reissued_at":"2026-05-18T00:06:00.515501Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:00.515501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A log-Sobolev inequality for the multislice, with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.PR","authors_text":"Ryan O'Donnell, Xinyu Wu, Yuval Filmus","submitted_at":"2018-09-10T18:46:07Z","abstract_excerpt":"Let $\\kappa \\in \\mathbb{N}_+^\\ell$ satisfy $\\kappa_1 + \\dots + \\kappa_\\ell = n$ and let $\\mathcal{U}_\\kappa$ denote the \"multislice\" of all strings $u$ in $[\\ell]^n$ having exactly $\\kappa_i$ coordinates equal to $i$, for all $i \\in [\\ell]$. Consider the Markov chain on $\\mathcal{U}_\\kappa$, where a step is a random transposition of two coordinates of $u$. We show that the log-Sobolev constant $\\rho_\\kappa$ for the chain satisfies $$(\\rho_\\kappa)^{-1} \\leq n \\sum_{i=1}^{\\ell} \\tfrac{1}{2} \\log_2(4n/\\kappa_i),$$ which is sharp up to constants whenever $\\ell$ is constant. From this, we derive so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03546","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1809.03546","created_at":"2026-05-18T00:06:00.515591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.03546v1","created_at":"2026-05-18T00:06:00.515591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03546","created_at":"2026-05-18T00:06:00.515591+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7AYJXEUMHMI","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7AYJXEUMHMIXK2O","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7AYJXEU","created_at":"2026-05-18T12:32:50.500415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R7AYJXEUMHMIXK2OOWIFKMFE7P","json":"https://pith.science/pith/R7AYJXEUMHMIXK2OOWIFKMFE7P.json","graph_json":"https://pith.science/api/pith-number/R7AYJXEUMHMIXK2OOWIFKMFE7P/graph.json","events_json":"https://pith.science/api/pith-number/R7AYJXEUMHMIXK2OOWIFKMFE7P/events.json","paper":"https://pith.science/paper/R7AYJXEU"},"agent_actions":{"view_html":"https://pith.science/pith/R7AYJXEUMHMIXK2OOWIFKMFE7P","download_json":"https://pith.science/pith/R7AYJXEUMHMIXK2OOWIFKMFE7P.json","view_paper":"https://pith.science/paper/R7AYJXEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.03546&json=true","fetch_graph":"https://pith.science/api/pith-number/R7AYJXEUMHMIXK2OOWIFKMFE7P/graph.json","fetch_events":"https://pith.science/api/pith-number/R7AYJXEUMHMIXK2OOWIFKMFE7P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7AYJXEUMHMIXK2OOWIFKMFE7P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7AYJXEUMHMIXK2OOWIFKMFE7P/action/storage_attestation","attest_author":"https://pith.science/pith/R7AYJXEUMHMIXK2OOWIFKMFE7P/action/author_attestation","sign_citation":"https://pith.science/pith/R7AYJXEUMHMIXK2OOWIFKMFE7P/action/citation_signature","submit_replication":"https://pith.science/pith/R7AYJXEUMHMIXK2OOWIFKMFE7P/action/replication_record"}},"created_at":"2026-05-18T00:06:00.515591+00:00","updated_at":"2026-05-18T00:06:00.515591+00:00"}