Spectral Geroch conjecture and noncompact area enlargeable summands

What the math gives to ML

The paper defines a Schrödinger-type spectral constant as the bottom Rayleigh quotient of the operator -Δ_g+γ scal_g and uses positivity of this quantity as a global geometric obstruction. The transferable mechanism is a variational test for localized low-energy modes, which can detect instability missed by pointwise Jacobian penalties. A neural implementation can apply this to a learned embedding manifold by constructing a pullback metric, discretizing the Rayleigh quotient with localized basis functions, and penalizing a low generalized eigenvalue. The topology-specific obstruction does not transfer directly, so the proposed use is an empirical spectral regularizer rather than a theorem about neural representations.