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 {2,3,5,7,11}{2,3,5,7,11} 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