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Combinatorics 11: R79).\n  A brace is minimal if deleting any edge results in a graph that is not a brace. From McCuaig's brace generation theorem, we derive our main theorem that may be viewed as an induction tool for minimal braces. As an application, we prove that a minimal brace of order $2n$ has size at most $5n-10$, when $n \\geq 6$, and"},"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":"1903.11170","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-26T21:55:59Z","cross_cats_sorted":[],"title_canon_sha256":"506178cdbecbd56ebbf2c07694e3efbd432f91f2b6904b4585548fe00dc3ab24","abstract_canon_sha256":"68844925a3d4b79d75cec9acfe7dbb1f50046b655ae2a3bda5dbdabae6ac604d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:03:13.181358Z","signature_b64":"7bRWRSyMbOaZEYA5W47blEc5cJahAUO8rjn7I64vxkrNtFAsYSS1ljeRe/6EN36M1tHpyNdKgKmcjRCxL7yCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fc55f106b448d8161c02a6af72201cfc7d5f6a658d75cc30e56fef3c8d09b9a","last_reissued_at":"2026-05-22T01:03:13.180541Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:03:13.180541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal Braces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcelo H. de Carvalho, Nishad Kothari, Phelipe A. 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