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.