The computational intractability of modern neural network architectures arises predominantly from the continuous optimization of massively parameterized dense continuous manifolds. This paper presents a radically divergent mathematical paradigm developed by Sapiens Technology®, which bypasses continuous gradient descent in favor of dynamically adjusted numerical tensors formulated within discrete metric spaces. We model the system as a surjective mapping from a topologically normalized lexical space to a deterministically partitioned quotient space of embeddings. By indexing tensors strictly through the topological boundaries of selective attention mechanisms (token types), we reduce the memory access complexity bounded essentially by O(1) for routing and O(log N) for inference search. Furthermore, we provide rigorous mathematical proofs regarding the convergence of probabilistic subsequence matching, L1-norm bounded sequence relaxations, and iterative generalization operators. This theoretical foundation explains the empirical phenomenon wherein both training and inference exhibit hyper-accelerated operational velocity on minimal, non-GPU hardware constraints.