Theory, Framework and Architecture: Hamilton V4

This whitepaper outlines the mathematical foundation and architectural evolution of the Hamilton V4 framework, contrasting its capabilities directly against the limitations of legacy V1 and V2 iterations. The paper details how the system scales to a 100-million parameter engine designed to ingest 12-dimensional spatiotemporal telemetry streams and map them directly onto a stable, 3D prescriptive coordinate manifold. Crucially, the text defines a major paradigm shift away from traditional Large Language Models: instead of processing discrete "tokens" via static lookup tables, Hamilton V4 treats inputs as continuous phase-space states. By utilizing grouped attention sub-layers, the framework acts as a continuous-time manifold smoothing mechanism that normalizes gradient variances and eliminates drift prevelant in legacy versions.