SynchronoGeometry: A Five-Dimensional Framework for Internal Time, Gauge Fields, Quantum Spectra, and the Fine-Structure Constant

We investigate whether the internal-time structure of SynchronoGeometry (SG) can provide a common geometric framework for scalar dynamics, gauge interactions, matter spectra, and the effective four-dimensional fine-structure constant. The central variable is a scalar internal-time field Θ, with invariant gradient X = G^{AB} ∇_A Θ ∇_B Θ in a five-dimensional spacetime with metric G_{AB}. We introduce a generally covariant effective action containing gravitational, internal-time, gauge, and matter sectors and derive the associated field equations. A gauge kinetic function B(X) permits the gauge-field normalization to depend on the internal-time background. Compactification of one spatial dimension then relates the five-dimensional gauge normalization to the four-dimensional gauge kinetic coefficient, giving B_4(X,R) = 2π R B_5(X). After canonical gauge normalization, the effective fine-structure constant satisfies α^{-1} = 8π² R B_5(X) / e_4². We also examine a conditional internal-time dependence of the compactified matter spectrum, m_n²(R,X) = m_5²(X) + n²/R², and formulate the quantum effective potential relevant to compactification-radius stabilization. The analysis distinguishes exact consequences of the specified action from conditional model results and unresolved physical assumptions. The numerical value of α is not derived, because the fundamental functions and charge normalization have not been independently determined. The result is an explicit analytical research framework, not a parameter-free derivation of α and not an experimentally validated extension of established physics. Keywords: SynchronoGeometry; internal time; five-dimensional spacetime; Kaluza–Klein reduction; gauge coupling; quantum vacuum energy; compactification; fine-structure constant.