This paper introduces the RTA Framework for Mathematics, a dimensional projection model that proposes to redefine mathematics as the structured emergence of symbolic, geometric, and harmonic patterns constrained by information-theoretic principles. Rather than treating mathematics as a purely axiomatic or abstract system, RTA posits that all mathematical structures arise from projection constraints on higher-dimensional information spaces, governed by principles of entropy minimization, harmonic balance, and recursive self-similarity. This paper begins with the simplest symbolic expressions in one dimension, showing how numerical and algebraic structures emerge from fundamental constraints. These expressions are then projected into higher-dimensional geometric spaces—revealing the role of oscillations, harmonics, and resonance in shaping more complex mathematical behavior. From this foundation, I examine three historically significant problems—Riemann, Collatz, and Kayeka—and propose that each is a manifestation of a distinct dimensional geometry: harmonic resonance, entropic spiral collapse, and recursive symbolic structuring, respectively. Together, these results suggest that mathematics itself is not a human invention, but the natural consequence of a structured universe operating under a universal projection law. This framework reinterprets mathematical complexity as the layered expression of dimensional geometry, bounded by constraints imposed by entropy and symmetry. The RTA framework potentially offers not only solutions to long-standing mathematical puzzles but a new foundational theory for understanding what mathematics is, where it comes from, and how it governs all emergent structure across domains.