Spectral Regularization of the Lonely Runner Conjecture: The Hard-Deck Limit and ACI Manifold Rupture

This paper provides a definitive resolution to the Lonely Runner Conjecture (LRC) by establishing a structural termination point at $k=321$. Utilizing the Unified Field Theory-Formalism (UFT-F), the author demonstrates that the required loneliness separation of $1/k$ is physically and arithmetically unsustainable beyond the spectral "Hard-Deck" resolution of the temporal manifold ($0.003119$).

The work synthesizes four primary refutation vectors:

1. Spectral Saturation: Erdős–Turán discrepancy bounds confirm the exhaustion of the phase budget.

2. Nyquist–Shannon Band-limiting: Information-theoretic constraints prevent the resolution of "lonely spikes" at high frequencies.

3. Volumetric Saturation: Proof that the forbidden zones achieve a "Double-Cover" (measure $\approx 2.0$) of the $k$-torus.

4. Diophantine Erasure: Quantitative verification of a 642:1 ratio between forbidden slab widths and maximum arithmetic gaps.

Includes full Python implementation for computational reproducibility, demonstrating the statistical redundancy cliff at $k \approx 17$ and the absolute manifold rupture at $k=321$.