U(1)-Driven Local Holographic Horizons: Holographic Bit–Mode Balance and the α-Fixpoint

We present a local, experimentally testable mechanism in which the mode demand of an electromagnetic U(1) field is balanced against a locally defined, quantized holographic upper bound on classical bit capacity. We call this principle Holographic Bit–Mode Balance (HBMB). The HBMB does not operate at a preselected length scale; instead, it identifies a stable fixed point: a local, quantized horizon of radius R∗ where the number of horizon-allowed bits equals the number of redundancy-free U(1) modes realizable under given local boundary data. The fine-structure constant α is not an input parameter in this framework. It appears only after R∗ stabilizes, as the value of natural dimensionless electromagnetic ratios evaluated at the fixed point, such as the impedance–quantum-resistance ratio α = Z0/(2RK ). This provides a microscopic explanation for the observed spatiotemporal stability of α, and offers a minimal mathematical bridge between local holographic horizons and an α-fixpoint emerging from U(1) boundary physics and area-law information bounds.