Beyond LLMs, Sparse Distributed Memory, and Neuromorphics <A Hyper-Dimensional SRAM-CAM "VaCoAl" for Ultra-High Speed, Ultra-Low Power, and Low Cost>

This paper reports an unexpected finding: in a deterministic hyperdimensional computing (HDC) architecture **that inverts the conventional role of Galois-field algebra -- employing it not for error correction toward a unique answer but as an engine for relative similarity and path-quality ranking -- **a path-dependent semantic selection mechanism emerges, equivalent to spike-timing-dependent plasticity (STDP), with magnitude predictable a priori from a closed-form expression matching measured values. Addressing catastrophic forgetting, learning stagnation, and the Binding Problem at an algebraic level, we propose VaCoAl (Vague Coincident Algorithm) and its Python implementation PyVaCoAl on ultra-high-dimensional SRAM/DRAM-CAM. Rooted in Sparse Distributed Memory, it resolves orthogonalisation and retrieval in high-dimensional binary spaces via Galois-field diffusion, enabling low-load deployment. Crucially, VaCoAl embeds a cognitive bound -- the Frontier Size -- into its architecture, ranking candidates by path-integral confidence (CR2) to achieve compositional generalisation; this bounded-rationality design produces STDP-like selection that error-correction paradigms structurally cannot attain. We evaluated multi-hop reasoning on about 470k mentor-student relations from Wikidata, tracing up to 57 generations (over 25.5M paths). HDC bundling and unbinding with CR-based denoising quantify concept propagation over DAGs. Results show a reinterpretation of the Newton-Leibniz dispute and a phase transition from sparse convergence to a post-Leibniz "superhighway", with structural indicators supporting a Kuhnian paradigm shift. VaCoAl thus defines a third paradigm, HDC-AI, complementing LLMs with reversible, auditable multi-hop reasoning.