This paper develops Category 7 of the CT-United mathematical framework by completing the symmetry axis of the causal ontology (Entity E5). Symmetries are formalized as phase-relative, coherence-preserving transformations acting on formulas, operators, and structures within a bounded causal geometry. All symmetry actions are explicitly constrained by the global closure horizon π and terminate by stabilization or extinction at compilation. The paper defines symmetry actions at fixed causal phase, introduces symmetry orbits and stabilizers in quadrant space, and establishes the symmetry–momentum correspondence linking invariance to conservation laws. Symmetry is shown to regulate rotational dynamics, stabilize attractors, and constrain anti-attractors, providing a causal analogue of Noether-type principles under finite closure. A central contribution is the definition of symmetry deficits as computable drivers of theorem prediction. When realized symmetry falls short of the level compatible with coherence and quadrant position, the Causal Prediction Engine outputs structurally forced theorem types: hidden invariances, orbit classifications, symmetry-bridging results, or proofs of unavoidable symmetry breaking. The paper further classifies mathematical fields by dominant symmetry patterns and introduces symmetry ladders (local, global, and meta-symmetries). The work integrates symmetry with prior categories—operators, kinematics, attractors, and prediction—by extending the Ledger with a Symmetry Ledger and refining predictive morphisms to respect symmetry constraints. With Entity E5 completed, the framework is prepared for subsequent categories on invariants, measures, computation, and global predictive morphisms.