Symmetry-Protected Phases in a 1D Active Solid with Mechanochemical Feedback.

We present a framework for mechanochemical self-organization in active solids where elasticity is reciprocally coupled to Hopf oscillators. Our model reveals a rich landscape of symmetry-protected phases identified through amplitude equations and group-theoretic analysis. We uncover a universal transition to compression-driven oscillation death, providing a physical basis for localized signaling dampening in biological tissues that resolves inconsistencies in previous models. Our work demonstrates that complex self-organization in active solids can be classified purely through symmetry arguments.