Non-Commutative Geometric Foundations for the Emergence of Spatial Dimensions and Physical Structures from Complex-Time Spectral Triples

We develop an associative, non-commutative geometric formulation of the Single Monad Model (SMM) and the Duality of Time Theory (DTT), establishing a bridge between discrete inner-time cycles and continuous outer-time flow. Within a spectral triple construction, the three spatial dimensions emerge dynamically from hierarchical temporal compactification, while mass, energy, and gauge symmetries follow from spectral properties of temporal operators. The associativity of the operator algebra guarantees global coherence, while non-commutativity generates quantized spectra, together providing a stable foundation for emergent 3D geometry. This construction reconciles discreteness with continuity and demonstrates how physical constants and interactions may be derived from temporal spectra, offering new insights into quantum gravity, cosmology, and deep mathematical structures such as zeta functions.