{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HLYMHYJ6HOZZS25JTQ2DLMUDW2","short_pith_number":"pith:HLYMHYJ6","schema_version":"1.0","canonical_sha256":"3af0c3e13e3bb3996ba99c3435b283b6a0b09c7344024099b93d413fc2cc319d","source":{"kind":"arxiv","id":"1804.09787","version":1},"attestation_state":"computed","paper":{"title":"Interleaved group products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","math.GR"],"primary_cat":"math.CO","authors_text":"Emanuele Viola, W. T. Gowers","submitted_at":"2018-04-25T20:18:58Z","abstract_excerpt":"Let $G$ be the special linear group $\\mathrm{SL}(2,q)$. We show that if $(a_1,\\ldots,a_t)$ and $(b_1,\\ldots,b_t)$ are sampled uniformly from large subsets $A$ and $B$ of $G^t$ then their interleaved product $a_1 b_1 a_2 b_2 \\cdots a_t b_t$ is nearly uniform over $G$. This extends a result of the first author, which corresponds to the independent case where $A$ and $B$ are product sets. We obtain a number of other results. For example, we show that if $X$ is a probability distribution on $G^m$ such that any two coordinates are uniform in $G^2$, then a pointwise product of $s$ independent copies"},"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":"1804.09787","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-04-25T20:18:58Z","cross_cats_sorted":["cs.CC","math.GR"],"title_canon_sha256":"241a0206bde8da6deb36ee39280def11f7cb312137401d467bca1c7e3339239d","abstract_canon_sha256":"a4bd32ee3b4066e315f4948a27b90ac92d634c47d8c96b4ff9075243e1e94940"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:27.917891Z","signature_b64":"4sKxLulyYlomxnyTtogjS1x4UzfAOClYZhUyPSn2o4bgAWgrYF6N1MqcqS6sBSvmrku93c9C+iW4WdslPAvWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3af0c3e13e3bb3996ba99c3435b283b6a0b09c7344024099b93d413fc2cc319d","last_reissued_at":"2026-05-18T00:17:27.917399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:27.917399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interleaved group products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","math.GR"],"primary_cat":"math.CO","authors_text":"Emanuele Viola, W. T. Gowers","submitted_at":"2018-04-25T20:18:58Z","abstract_excerpt":"Let $G$ be the special linear group $\\mathrm{SL}(2,q)$. We show that if $(a_1,\\ldots,a_t)$ and $(b_1,\\ldots,b_t)$ are sampled uniformly from large subsets $A$ and $B$ of $G^t$ then their interleaved product $a_1 b_1 a_2 b_2 \\cdots a_t b_t$ is nearly uniform over $G$. This extends a result of the first author, which corresponds to the independent case where $A$ and $B$ are product sets. We obtain a number of other results. For example, we show that if $X$ is a probability distribution on $G^m$ such that any two coordinates are uniform in $G^2$, then a pointwise product of $s$ independent copies"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09787","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":"1804.09787","created_at":"2026-05-18T00:17:27.917481+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.09787v1","created_at":"2026-05-18T00:17:27.917481+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09787","created_at":"2026-05-18T00:17:27.917481+00:00"},{"alias_kind":"pith_short_12","alias_value":"HLYMHYJ6HOZZ","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HLYMHYJ6HOZZS25J","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HLYMHYJ6","created_at":"2026-05-18T12:32:28.185984+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/HLYMHYJ6HOZZS25JTQ2DLMUDW2","json":"https://pith.science/pith/HLYMHYJ6HOZZS25JTQ2DLMUDW2.json","graph_json":"https://pith.science/api/pith-number/HLYMHYJ6HOZZS25JTQ2DLMUDW2/graph.json","events_json":"https://pith.science/api/pith-number/HLYMHYJ6HOZZS25JTQ2DLMUDW2/events.json","paper":"https://pith.science/paper/HLYMHYJ6"},"agent_actions":{"view_html":"https://pith.science/pith/HLYMHYJ6HOZZS25JTQ2DLMUDW2","download_json":"https://pith.science/pith/HLYMHYJ6HOZZS25JTQ2DLMUDW2.json","view_paper":"https://pith.science/paper/HLYMHYJ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.09787&json=true","fetch_graph":"https://pith.science/api/pith-number/HLYMHYJ6HOZZS25JTQ2DLMUDW2/graph.json","fetch_events":"https://pith.science/api/pith-number/HLYMHYJ6HOZZS25JTQ2DLMUDW2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HLYMHYJ6HOZZS25JTQ2DLMUDW2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HLYMHYJ6HOZZS25JTQ2DLMUDW2/action/storage_attestation","attest_author":"https://pith.science/pith/HLYMHYJ6HOZZS25JTQ2DLMUDW2/action/author_attestation","sign_citation":"https://pith.science/pith/HLYMHYJ6HOZZS25JTQ2DLMUDW2/action/citation_signature","submit_replication":"https://pith.science/pith/HLYMHYJ6HOZZS25JTQ2DLMUDW2/action/replication_record"}},"created_at":"2026-05-18T00:17:27.917481+00:00","updated_at":"2026-05-18T00:17:27.917481+00:00"}