Scalable Harmonic Vector Equilibrium (S-HVE): Neuromorphic Routing and 2D-to-3D Isotropic Projections via Discrete Attractor Gradients

A scalable integer-based framework is disclosed for neuromorphic routing, spatial encoding, and 2D-to-3D sensory projection, operating without floating-point arithmetic (IEEE 754). The system scales the Harmonic Vector Equilibrium (HVE) integer metric via the Least Common Multiple (LCM) sequence OEIS A003418, achieving zero-phase-drift across 16-bit, 32-bit, and 64-bit hardware tiers. Memory constraints are explicitly managed: full LUT (Look-Up Table) storage for L12 and L22, and phase-accumulator-only DDS (Direct Digital Synthesis) for L42. A native 2D-to-3D projection maps hexagonal sensor arrays directly onto a cuboctahedral 12-vector processing matrix, bypassing trigonometric transforms. A discrete attractor gradient routes phase quanta in constant time (O(1) per hop) with deterministic 150-nanosecond latency on 240 MHz RISC-V/ESP32. This disclosure serves as defensive prior art against overly broad patents on integer-only spatial computing, zero-drift phase control, and neuromorphic Spiking Neural Network (SNN) routing, with explicit extended applications in autonomous swarm robotics, programmable metamaterials, volumetric memory, and topological quantum computing.