{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Y5XJT4E5TMJQW5FHMBINV74GAM","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":"a9ed65920d73e1163cf1d6627acb3ac9a53784f53aeb65647f76771f3610f0ff","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T11:00:52Z","title_canon_sha256":"46ed2005cdb1413e0b3bb9b1a8fed5baf496325e52b27bcae2454e3993840c64"},"schema_version":"1.0","source":{"id":"2606.02667","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02667","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02667v1","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02667","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"Y5XJT4E5TMJQ","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_16","alias_value":"Y5XJT4E5TMJQW5FH","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_8","alias_value":"Y5XJT4E5","created_at":"2026-06-03T00:05:05Z"}],"graph_snapshots":[{"event_id":"sha256:fae09ceb65d61dd55e8b6a3fdde771afe9fbc60572e73613131b5f3da2532168","target":"graph","created_at":"2026-06-03T00:05:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.02667/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f(k,s)$ denote the minimum integer $m$ such that any family $\\mathcal{F}$ consisting of $k$-sized sets of cardinality at least $m$ always contain a sunflower of size $s$. The Erd\\H{o}s-Rado Sunflower Conjecture states that for every $s >2$, there is an constant $C=C(s)$ such that $f(k,s) \\leq C^k$. In this paper, we prove the conjecture.","authors_text":"Tapas Kumar Mishra","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T11:00:52Z","title":"Erd\\H{o}s Rado Sunflower (Conjecture) Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02667","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":"sha256:6a052750e7a11b1e72e1d154cf675c3d810ef07be4642329b7fde0ba03dd6a70","target":"record","created_at":"2026-06-03T00:05:05Z","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":"a9ed65920d73e1163cf1d6627acb3ac9a53784f53aeb65647f76771f3610f0ff","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T11:00:52Z","title_canon_sha256":"46ed2005cdb1413e0b3bb9b1a8fed5baf496325e52b27bcae2454e3993840c64"},"schema_version":"1.0","source":{"id":"2606.02667","kind":"arxiv","version":1}},"canonical_sha256":"c76e99f09d9b130b74a76050daff860313afb247d343a168e16db546d8a1b137","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c76e99f09d9b130b74a76050daff860313afb247d343a168e16db546d8a1b137","first_computed_at":"2026-06-03T00:05:05.976981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T00:05:05.976981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k4KW19KLAIeuuYBIdnaMjoN9BZ3euQ+9o0KfCKAk1wLNMXGLHqzevvYHCK7otRI+X9s5aapNtVPaHfyW/eP6CQ==","signature_status":"signed_v1","signed_at":"2026-06-03T00:05:05.977356Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02667","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a052750e7a11b1e72e1d154cf675c3d810ef07be4642329b7fde0ba03dd6a70","sha256:fae09ceb65d61dd55e8b6a3fdde771afe9fbc60572e73613131b5f3da2532168"],"state_sha256":"5ef845c440333a62436572d35fed2c8aab13a0e13abd382f798fae734494dba4"}