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

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

ical constants using spectral resonance structures. Building on the Unified Resonant Struc-

ture 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). This unification arises from a closed structural system defined......