{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KZCXFZPTRRR6QOQBCEBYL7NBWA","short_pith_number":"pith:KZCXFZPT","schema_version":"1.0","canonical_sha256":"564572e5f38c63e83a01110385fda1b0396da7177cbda93b0b3c1e9d098cc6c4","source":{"kind":"arxiv","id":"1908.08483","version":3},"attestation_state":"computed","paper":{"title":"Improved bounds for the sunflower lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.CO","authors_text":"Jiapeng Zhang, Kewen Wu, Ryan Alweiss, Shachar Lovett","submitted_at":"2019-08-22T16:33:22Z","abstract_excerpt":"A sunflower with $r$ petals is a collection of $r$ sets so that the intersection of each pair is equal to the intersection of all of them. Erd\\H{o}s and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must contain a sunflower with $r$ petals. The famous sunflower conjecture states that the bound on the number of sets can be improved to $c^w$ for some constant $c$. In this paper, we improve the bound to about $(\\log w)^w$. In fact, we prove the result for a robust notion of sunflowers, for which the bound we obtain is sharp up "},"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":"1908.08483","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-22T16:33:22Z","cross_cats_sorted":["cs.CC","cs.DM"],"title_canon_sha256":"cd0d1d12b14283818a228fda257bfd3653d07d6808caac5a4256b22d9598a7d8","abstract_canon_sha256":"e26425993d01c77e355bc4f54c0917fb34dfdea50f0e3735c3c8e8226485a414"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:09:54.190636Z","signature_b64":"/nNS73s90KBfNvnFLmd+ihm1SagTEzY94ovjTWjwxD39Yp1kEDkDrgOeYm0ecnFfSov37vzo8u74rLowCCMMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"564572e5f38c63e83a01110385fda1b0396da7177cbda93b0b3c1e9d098cc6c4","last_reissued_at":"2026-07-05T03:09:54.190234Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:09:54.190234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved bounds for the sunflower lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.CO","authors_text":"Jiapeng Zhang, Kewen Wu, Ryan Alweiss, Shachar Lovett","submitted_at":"2019-08-22T16:33:22Z","abstract_excerpt":"A sunflower with $r$ petals is a collection of $r$ sets so that the intersection of each pair is equal to the intersection of all of them. Erd\\H{o}s and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must contain a sunflower with $r$ petals. The famous sunflower conjecture states that the bound on the number of sets can be improved to $c^w$ for some constant $c$. In this paper, we improve the bound to about $(\\log w)^w$. In fact, we prove the result for a robust notion of sunflowers, for which the bound we obtain is sharp up "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08483","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08483/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.08483","created_at":"2026-07-05T03:09:54.190288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.08483v3","created_at":"2026-07-05T03:09:54.190288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08483","created_at":"2026-07-05T03:09:54.190288+00:00"},{"alias_kind":"pith_short_12","alias_value":"KZCXFZPTRRR6","created_at":"2026-07-05T03:09:54.190288+00:00"},{"alias_kind":"pith_short_16","alias_value":"KZCXFZPTRRR6QOQB","created_at":"2026-07-05T03:09:54.190288+00:00"},{"alias_kind":"pith_short_8","alias_value":"KZCXFZPT","created_at":"2026-07-05T03:09:54.190288+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.20132","citing_title":"Delta-system method: a survey","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KZCXFZPTRRR6QOQBCEBYL7NBWA","json":"https://pith.science/pith/KZCXFZPTRRR6QOQBCEBYL7NBWA.json","graph_json":"https://pith.science/api/pith-number/KZCXFZPTRRR6QOQBCEBYL7NBWA/graph.json","events_json":"https://pith.science/api/pith-number/KZCXFZPTRRR6QOQBCEBYL7NBWA/events.json","paper":"https://pith.science/paper/KZCXFZPT"},"agent_actions":{"view_html":"https://pith.science/pith/KZCXFZPTRRR6QOQBCEBYL7NBWA","download_json":"https://pith.science/pith/KZCXFZPTRRR6QOQBCEBYL7NBWA.json","view_paper":"https://pith.science/paper/KZCXFZPT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.08483&json=true","fetch_graph":"https://pith.science/api/pith-number/KZCXFZPTRRR6QOQBCEBYL7NBWA/graph.json","fetch_events":"https://pith.science/api/pith-number/KZCXFZPTRRR6QOQBCEBYL7NBWA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KZCXFZPTRRR6QOQBCEBYL7NBWA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KZCXFZPTRRR6QOQBCEBYL7NBWA/action/storage_attestation","attest_author":"https://pith.science/pith/KZCXFZPTRRR6QOQBCEBYL7NBWA/action/author_attestation","sign_citation":"https://pith.science/pith/KZCXFZPTRRR6QOQBCEBYL7NBWA/action/citation_signature","submit_replication":"https://pith.science/pith/KZCXFZPTRRR6QOQBCEBYL7NBWA/action/replication_record"}},"created_at":"2026-07-05T03:09:54.190288+00:00","updated_at":"2026-07-05T03:09:54.190288+00:00"}