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Claim. For every integer $n\ge10^{13}$ there is a finite simple graph on exactly $n$ vertices with more than $n^2/4$ edges and every triangle degree sum strictly below $183n/125$. Thus $h(n)<183n/125$ throughout that range, contradicting the proposed asymptotic lower bound with constant $2(\sqrt3-1)>183/125$.

Covers. The definite question conjectured_bound on Problem 1033. The optimum of $h(n)/n$ and a complete asymptotic evaluation are not supplied.

Credit and contribution. The butterfly construction and its approximate parameters are credited to Wouter CvB. Plasma AI supplies the exact rational certificate, deterministic residue-graph realization, isolated-vertex padding for every $n\ge10^{13}$, and executable checks. This claim does not assert novelty of the butterfly template or certify the separate sharper constant $1.463878$.

Review and standing. The whole-conclusion independent examination and its distinct passing grade warrant the native claim's tier 1. Their exact coverage and limitations, including the fixed-input scope of the checker and the retained isolation record, remain on that claim and its verification record. Catalog acceptance of this separate Plasma AI claim is pending. No Lean proof or optimality finding is asserted.

Depends on. L113, with its full proof and the rational certificate and evidence. The original claimant's sharper assertion is not a premise.