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The previous best known lower bound states that $I_2(n,4)=\\Omega(n^{4/3+o(1)})$. We improve this lower bound by showing that $I_2(n,4)= \\Omega(n^{3/2-o(1)})$ using techniques in additive number theory."},"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":"1908.03523","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T16:26:23Z","cross_cats_sorted":[],"title_canon_sha256":"3948b0b2e95fd50cff38ebf3728b32ed328e9c7239857d038c9cd456b04b0267","abstract_canon_sha256":"56f4e69e6f39a65be28287995cbb8d4eb4225a38b601823d39fcb6c4bc3bb5ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:58:23.973265Z","signature_b64":"AJchW9+h1xUDSAT/5Sfv4Ix5y4vCo3eql2J+WsPhTUo0kMVYZ7rMv/Xe/wuALVZrX8IVYjsBYM7xt5LL9agUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4860c16f3a2cbf00c4089f97ae677a3d5861efa9f7aab861ca8b1efa6723d978","last_reissued_at":"2026-07-05T00:58:23.972916Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:58:23.972916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $2$-parent-identifying set systems of block size $4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shohei Satake, Yujie Gu","submitted_at":"2019-08-09T16:26:23Z","abstract_excerpt":"Parent-identifying set system is a kind of combinatorial structures with applications to broadcast encryption. 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