= Positive definite Tits form indecomposable classification
The <Ringel lemma on bricks> makes every indecomposable a <brick module>; positive definiteness and the <Ringel form> then force $q_Q=1$ and rigidity. Conversely, a maximal-orbit representation at a positive root cannot split: nonzero cross extensions increase orbit dimension, while vanishing cross extensions make the quadratic form of a split sum at least two. Open dense orbits give uniqueness. A compact bound on the integer roots gives finite representation type.
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