A Combinatorial Twin-Prime Hierarchy Associated with the Fine-Structure Constant

This study investigates a combinatorial mathematical hierarchy associated with the inverse fine-structure constant (α⁻¹ ≈ 137.035999177), a dimensionless parameter fundamental to quantum electromagnetic theory. Rather than seeking a physical derivation of α, the analysis examines whether structured partitions of twin prime numbers generate a deterministic combinatorial hierarchy associated with the observed value of α⁻¹. Using the twin primes {137,139}, n-dimensional families of prime-valued combinations are constructed whose sums equal the fixed targets 137 and 139. A hybrid coupling of these {139/137} structures yields a model value of α⁻¹ ≈ 137.036, corresponding to a fractional coupling parameter α′ = 0.036. Applying the same procedure to successive twin-prime pairs generates a hierarchy of coupled combinatorial field envelopes characterized by systematically varying fractional coupling parameters. The resulting hierarchy is investigated as an abstract representation of possible underlying field structure, not as a replacement for the physical spacetime framework in which quantum phenomena occur. The work is presented as a mathematical proof of concept, exploring whether a classical combinatorial construction can provide a conceptual framework for structural features associated with quantum physics and cosmology.