Realize the required axion alignment in heterotic compactification

Construct a specific heterotic compactification that realizes the alignment and multi-harmonic structure required for the effective $10^{-28}$ eV axion direction, thereby providing a microscopic test of the unified axion-cosmology scenario.

Background

The proposed resolution of the Hubble tension requires a light axion eigen-direction with an effective decay constant substantially larger than the microscopic heterotic axion decay constants. The same multi-axion system must also generate a multi-harmonic effective potential whose lower-order terms are sufficiently suppressed to produce rapid post-critical dilution.

The paper does not derive these alignment and harmonic relations from an explicit string construction. A concrete heterotic compactification realizing them would establish whether the required effective axion sector can arise from the underlying theory rather than being imposed phenomenologically.