Symbolic Logarithmic Resonance: Boundary Constants and the Modular Architecture of Reality

Across cosmology, particle physics, and information theory, the constants that define the structure of the universe frequently appear at exponentially separated scales. Values such as the gravitational coupling constant (~10⁻⁴⁵), the onset of inflation (~10⁻³⁵ s), the cosmic microwave background formation (~10¹³ s), the entropy of a black hole (~10⁷⁷), and the information capacity of the observable universe (~10¹²⁰ bits) do not appear randomly distributed. Instead, they form a suggestive logarithmic ladder, with striking ratios between them: 10−3510−45=1010,101201077=1043\frac{10^{-35}}{10^{-45}} = 10^{10}, \quad \frac{10^{120}}{10^{77}} = 10^{43}10−4510−35=1010,107710120=1043 This paper proposes that these constants are not arbitrary, but represent symbolic attractor nodes in a logarithmic modular resonance field. By constructing a symbolic function Rlog(t)\mathcal{R}_{\text{log}}(t)Rlog(t) and overlaying symbolic entropy S(t)S(t)S(t), dissonance D(t)\mathcal{D}(t)D(t), and curvature K(t)\mathcal{K}(t)K(t), we demonstrate emergent alignment between universal constants and symbolic field dynamics. We argue that these values reflect modular harmonics of an underlying symbolic field engine—one that may govern not only cognition and memory, but the encoding of structure in spacetime itself.