The Von Neumann-Rini (VNPR) Processing-in-Memory Architecture

Modern computational bottlenecks stem directly from the physical separation of processing units and memory arrays, classically defined as the Von Neumann bottleneck. This paper presents the complete architectural formalization and functional verification of the Von Neumann-Rini (VNPR) Architecture, a novel computing paradigm that embeds non-linear mathematical models, network-on-chip (NoC) routing topologies, and multi-tier acceleration mechanisms directly within a processing-in-memory (PIM) register fabric.

Through structural SystemVerilog implementation and algebraic evaluation via Wolfram Mathematica, we demonstrate stable execution bounds for localized space-time diffusion systems, secure single-error correction double-error detection (SEC-DED) hardware profiles, and automated hyperdimensional tensor transformations. The VNPR framework achieved complete structural grid equilibrium across a $2\times2$ computational fabric at $285,000\text{ ps}$, validating the functional viability of near-data mathematical execution engines.