Collapse-Induced Unification of Physical Constants: The Structure Constants Manifold

We present a unit-free, collapse-driven framework for reconstructing fundamental physical constants using spectral resonance structures. Building on the Unified Resonant Structure Formula (URSF), we discover a collapse-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. This unification arises from a closed structural system defined by modal amplitude (φe), entropy compression(φ˜), and structural propagation factor (φc). We introduce the structure field equation F(x) = α(x) − φG(x) as a unification tensor, and demonstrate its vanishing in a resonance band centered around π −1 . The result is a complete, dimensionless constants manifold derived from internal structural dynamics, offering a new foundation for physical unification.