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

We develop 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). HBMB does not operate at a preselected length scale; instead, it identifies a stable fixed point: a local holographic screen (horizon) of radius R* where the number of horizon-allowed bits equals the number of redundancy-free U(1) edge modes realizable under given local boundary data.On the QFT side we employ the entanglement first law together with the local modular Hamiltonian for a ball-shaped region to compute the leading response of the edge sector under homogeneous perturbations. On the geometric side we match the required area response using Raychaudhuri focusing in a controlled weak-focusing regime, explicitly stating the simplifying assumptions and limitations of the toy setup.The central result is an explicit evaluation of the U(1) accessibility fraction at the HBMB fixed point from a fluctuation-driven (current-source) impedance-divider model of screen dissipation, yielding: F_U(1)(R*) ≃ Z0 / (Z0 + 2 R_K) = α + O(α^2).The internal impedance scale is motivated from first principles of linear response (Kubo) and U(1) current conservation, which fix Z_int ~ R_K up to a dimensionless normalization factor (channel content and conventions).We further motivate the Compton-scale selection of R*, discuss UV-divergence cancellation in the ratio defining F_U(1), provide robustness checks against higher multipoles, and comment on the structural compatibility between logarithmic edge scaling and QED running.