We propose a unified field framework based on a quantum-fractal-logical structure that integrates prime number theory, quantum coherence, and logical inference into a single formalism. The model is built upon a fractal space equipped with Hausdorff measure, a self-regulating fractal operator acting on logical modes, and a quantum integral that selects coherent resonances. These resonant peaks are interpreted as emergent particles and fundamental interactions. Applying this structure, we reconstruct the prime counting function with ~99% accuracy up to x=106x = 10^6x=106, reformulate the 3-SAT problem as a coherence condition (avoiding brute-force search), and demonstrate an estimated 80% reduction in quantum decoherence. This approach opens a path toward unifying discrete and continuous mathematics, logic, and physics under a coherent, scalable, and computationally relevant geometry.