= Induced regularity template lemma
For fixed forbidden induced patterns, a regularity and Ramsey refinement uses internal <clique>/independent types and sparse, almost-complete, or intermediate cross pairs. A <clique> of intermediate pairs realizes every bounded induced pattern consistent with those internal types, using both <edge> and nonedge regularity. This is the induced embedding consequence used in <hereditary graph enumeration theorem>; the exceptional-pair budget can be arbitrarily small.
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