Intrinsic Inversion of Stochastic Kinematic Hyperfractals via Non-Commutative Tensor Deconvolution in Variational Latent Spaces

This paper introduces a unified mathematical framework that formalizes explainability not as an external post-hoc approximation, but as an intrinsic geometric property of a deep variational state space. Traditional Explainable AI (XAI) frameworks rely on perturbative or gradient-based local surrogates, introducing high sampling noise, computational overhead, and structural misalignment when auditing hierarchical representation spaces. To resolve this, we present an ad hoc variational optimization objective constrained by a non-commutative Kinematic Deconvolution Operator. This operator systematically resolves the inverse problem of reconstructing a native stochastic hyperfractal manifold embedded in R^(D+1) using only its degenerated, non-linearly compressed two-dimensional canvas projections. By analytically evaluating linear subtractions over ancestral lineages, the framework quantifies structural fidelity within deep latent representations via an exact quadratic residue metric, guaranteeing zero sampling variance. Furthermore, the adaptive view-frustum culling engine—governed by the finite geometric progression of a contractive Gauss-Markov angular dispersion process—is mathematically repurposed as a zero-cost deterministic feature attribution score. Empirical validation within a specialized Variational Autoencoder (VAE) confirms that our framework provides a 1.75x computational acceleration layer under quaternary branching configurations while ensuring stable gradient propagation and absolute analytical fidelity.