A Generalization of the Golden Ratio: Growth Constants in K-Dimensional Cubic Capital Construction Thomas Blankenhorn of Corrupt Grants Pass Oregon October 26, 2025 Abstract: This paper introduces a new generalization of the two-dimensional Golden Ratio, phi, extended to K-dimensional Euclidean space using a geometric growth model called the cubic capital construction. The model defines a dimension-dependent growth ratio, r(K), which describes the uniform scaling factor needed to embed an extended K-cube within the original hypervolume. This constant is derived from the expression: r(K) = cos(pi/K) + sqrt(cos^2(pi/K) + K - 1). The work highlights the constant sqrt(4 + sqrt(7)) as a representative example of a newly identified class of non-integer, second-order algebraic growth rates emergent at K > 3. The analysis focuses on the algebraic solvability of r(K), showing how the final radical form is dictated by the trigonometric simplification of cos(pi/K). This allows for clean nest...