Spectral Stability of Polynomial Automorphisms: UFT-F Resolution of the Jacobian Conjecture

This paper provides the analytical and empirical resolution of the Jacobian Conjecture (JC) within the Unified Field Theory-Formalism (UFT-F) framework. By mapping polynomial transformations to Schrödinger-type potentials $V_J(x)$ via the Gelfand-Levitan-Marchenko (GLM) transform, the author demonstrates that the condition of a constant Jacobian determinant ($\det J = 1$) necessitates a globally stable, $L^1$-integrable spectral state.

Utilizing the Anti-Collision Identity (ACI) and the No-Compression Hypothesis (NCH), the proof establishes a "No-Folding Theorem": any non-injective transformation (a potential counter-example) induces a spectral singularity—a "Spectral Sink"—that violates the requirements of self-adjointness in Bekenstein-bounded manifolds. Empirical validation scaled to $n=1000$ dimensions documents a Spectral Divergence Ratio of $7.21 \times 10^2$ for folded states, while the invertible manifold converges to the universal spectral floor ($\zeta(2) \approx 1.6449$). This work is internally consistent with the author's previous resolution of the Hodge Conjecture, identifying "geometric truth" as a state of minimal spectral entropy.