Formal Verification of Whittaker-Type Zero-Invariant Fields and Receiver Symmetry Breaking in Lean 4 and SystemVerilog

Modern classical electrodynamics predominantly relies on transverse vector representations, routinely sidelining the classical scalar potential formulations introduced by Sir Edmund Taylor Whittaker in 1904. Critics have historically dismissed these potentials as non-physical mathematical artifacts due to the apparent absence of observable transverse radiation in pure scalar configurations. This paper presents a machine-checked formal verification in Lean 4, establishing two central results: (1) The mathematical existence of a non-trivial, zero-invariant state where transverse field components vanish identically while maintaining a non-zero longitudinal tension field; and (2) a rigorous proof that introducing a spatial inhomogeneity at a boundary explicitly breaks this zero invariant, forcing the hidden longitudinal tension to convert into an observable transverse signal: $$dx \neq 0$$ Finally, these theoretical guarantees are translated into synthesizable register-transfer logic and validated via automated SystemVerilog testbench simulation.