Theory Ω: Hierarchical Structure of Numbers, Space and Time

We introduce Theory Ω, a discrete hierarchical structure embedded in the real numbers based on dyadic levels ω_k = 1 − 2⁻ᵏ within integer intervals. The fundamental objects are the interintegers n_Ω^k = n + ω_k. The system yields a unique finite binary representation, a well-defined ultrametric, and a normalized hierarchical measure. The algebraic extension Ω* is isomorphic to the subring of dyadic numbers ℤ[1/2]. The theory is interpretative and does not claim direct experimental predictions without additional dynamics. We discuss analogies with multiscale synchronization, hierarchical echoes, and wavelet-like encoding. The framework is consistent with standard mathematics (p-adic metrics, Cantor set, multiresolution analysis) and offers a parsimonious resolution of the grandfather paradox through a single-identity principle.