The fermion doubling problem presents a longstanding topological barrier to defining chiral gauge theories on a discrete lattice. In his November 3, 2026 paper, A Note On Lattice Definition of Gauge Theories With Chiral Fermions, Edward Witten explores continuum interpolations of admissible lattice gauge fields to regularize chiral fermions, yet notes that such approaches yield a non-positive chiral fermion path integral, rendering Monte Carlo evaluations impractical. To resolve this lattice index trap, this derivation introduces an asymmetric gauge regularization construction that bypasses the classical constraints of a symmetric 4-torus. By introducing a continuous 4π global phase invariance coupled with an incommensurable radiometric thermodynamic variance (κ≈1.437824 GHz), the flat periodic boundary is subjected to a non-linear coordinate deformation.
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