This work proposes a logically explicit unification strategy for general relativity (GR) and quantum mechanics (QM) grounded in a shared operational core consisting of bounded controllable influence, finite control bandwidth, and stability under coarse graining. Rather than beginning from a specific micro-ontology such as strings, loops, or spin networks, the framework derives general distinguishability budget theorems under clearly stated assumptions about finite intervention alphabets and finite influence per operational step. Two model classes are defined, referred to as the local-control class and the global-coding class, for which sharp one step distinguishability bounds are proven. These results clarify when area reach type constraints arise from compositional structure alone and when additional stored resources must be explicitly included in the accounting of exported distinguishability. Guided by these theorems, the paper introduces Causal Operational Capacity Gravity (COCG), a covariant variational framework in which the Einstein-Hilbert action is supplemented by a capacity term constructed from an ordering scalar and an operational influence scale. The modified field equations are derived explicitly and shown to preserve diffeomorphism invariance, satisfy a consistent conservation condition, reduce to Einstein’s equations in the low capacity gradient limit, and recover standard quantum field theory on curved spacetime in regimes of weak backreaction. The speculative elements of the proposal are clearly separated from the mathematical content of the distinguishability theorems. The framework isolates falsifiable consequences related to horizon information transfer, black hole entropy scaling, and operational export constraints. COCG is presented as a synthesis layer that does not compete with ultraviolet complete microtheories such as string theory or loop quantum gravity, but instead aims to identify operational constraints that any successful theory of quantum gravity must realize.