Residual-Driven Unification of Physical Constants: The Structure Constants Manifold

We present a unit-free, residual-driven framework for reconstructing fundamen-

tal physical constants using spectral resonance structures. Building on the Unified

Resonant Structure Formula (URSF), we discover a residual-induced unification

manifold in which the gravitational constant φG and the fine-structure constant α

naturally coincide at specific modal resonance points, governed by the condition

φc = 1, which emerges as a derived state from the residual field δ(x, t)...