= Fano stability
{c}
For every $\rho>0$, some $\delta>0$ makes every sufficiently large Fano-free three-<uniform hypergraph> of density at least $3/4-\delta$ admit a partition with at most $\rho n^3$ internal triples. The argument compares four <hypergraph link graphs> around a tetrahedron. Forbidden rainbow perfect matchings in their edge-coloured union force an approximate pattern with multiplicity two within the parts and four between them. A positive internal triple density would produce a complete tripartite six-vertex template, and its pairs together with a link vertex would complete a Fano plane.
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