SPECTRAL GAP COLLAPSE AND INFORMATION-THEORETIC OBSTRUCTIONS IN LWE-DERIVED HAMILTONIANS

The description on Zenodo serves as the primary metadata for search engines. It is best to use a structured abstract that highlights both the empirical breakthrough and the structural proof. Recommended Description Content: Title: Spectral Gap Collapse and Information-Theoretic Obstructions in LWE-Derived Hamiltonians Abstract: This research provides a formal functional-analytic investigation into the spectral robustness of Learning With Errors (LWE) manifolds, with a focus on the ML-KEM-512 standard. We introduce a contrastive toy model utilizing the Surya Sekhar Roy constant ($S_{sr} = 127.32$) to demonstrate artificial localization in $O(n^3)$ time, achieving an empirical resonance density of 99.9877%. However, we rigorously prove the Spectral Gap Collapse Theorem, demonstrating that for Hamiltonians honestly derived from public LWE data, the energy gap $\Delta_n$ vanishes exponentially. This result proves that ground-state isolation is physically obstructed by eigenstate crowding in the low-energy shell, confirming the spectral security of the ML-KEM standard. Key Results: Definition of the Surya Sekhar Roy constant ($S_{sr}$) for 512-dimensional manifolds. Proof of the exponential collapse of the spectral gap in LWE-based systems. Empirical evidence of singularity stabilization in discrete Hilbert spaces.