Core-Decomposition Derivation of the Fine-Structure Constant and the Electron Charge

Based on the core-decomposition recurrence (ak−2) ak+1=k (ak−2) ak+1=k and its continuum limit, we define the core constant p=ln⁡43+125⋅7⋅11p=ln34+25⋅7⋅111. We then propose the conjectural closed-form expressions α=p/ (4π2) α=p/ (4π2) for the fine-structure constant and e=p/πε0ℏce=p/πε0ℏc for the electron charge. These expressions contain no free parameters and depend only on the first five primes 2, 3, 5, 7, 112, 3, 5, 7, 11 and the natural logarithm. Numerical evaluation gives 1/α≈137. 0361/α≈137. 036, close to the experimental value 137. 035999084137. 035999084. The derivation is heuristic; the results are presented as conjectures within the core-decomposition framework