Discrete Pascal-Pyramid Topologies for Autonomous Reasoning Architectures

Current Large Language Models (LLMs) rely on computationally expensive transformer architectures that process reasoning linearly via unconstrained volumetric diffusion. This paper proposes a novel, geometrically grounded alternative: a hierarchical Square-Based Pascal’s Pyramid neural network. By utilizing the combinatorial weight structure of Pascal’s Pyramid alongside dynamic 90-degree base rotations, this framework enables highly efficient, non-linear routing of information. We demonstrate that perfect integer positioning optimizes memory access, while variable path lengths introduce a Ponderance mechanism, variable signal delays that mimic biological pauses for thought. Building upon the Central Dendritic Rush and Law of Geometric Friction established in V2, Version 3 introduces Neural Selection via Shadowbloom Resonance. We mathematically decouple generative synthesis from active computation by mapping the global latent parameter space to a Continuous Unit Polytope. Utilizing infinite-precision spatial hashing and the First-Jump Decomposition (FJD) operator, the architecture dynamically retrieves and instantiates only the exact phylogenetic neural clusters required for a specific thought. This dramatically reduces the active VRAM footprint and establishes a viable, hardware-stratified baseline for Autonomous Reasoning Architectures.