Can adding two random quantities create a second peak? For ordinary independence, symmetric distributions with one central peak have a well-known shape-preservation property. Free probability uses a different notion of independence, important in operator algebras and random-matrix limits. The question here is whether free addition also preserves symmetric unimodality. This unrefereed candidate gives an affirmative written proof. The main statement allows unbounded distributions and even an atom at the center. The proof represents each input as a mixture of centered uniform distributions. It then studies an inequality for their complex transforms. A moment argument reduces a possible failure to two radii, one at an endpoint. Careful treatment of a radius escaping to infinity closes that reduction. Established subordination theorems connect the transform inequality back to free addition. A separate corollary gives a continuous output density with a unique central maximum. It requires bounded input densities that satisfy the paper's local continuity assumption. It does not promise smoothness across finite support edges. The package contains the full analytic argument and nine exact symbolic checks of selected algebra. Those checks do not certify the whole theorem. Internal AI review is not independent mathematical validation, and historical priority has not been established. This is an Evidence Press unrefereed candidate release. The full paper and evidence are linked. The voice is AI-generated using an OpenAI synthetic voice. This briefing is a communication aid, not additional mathematical evidence.