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 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 coupling 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 mathematical framework whose internal organization exhibits structural analogs of selected features of quantum electromagnetic interactions, the Standard Model of Particle Physics, and cosmology. The work is presented as a mathematical proof of concept rather than a physical derivation, with a broader objective of exploring whether a classical mathematical construction can provide a conceptual description of quantum field theory.