The Reference Frame (TRF) presents a unified geometric algebra framework grounded in five ontological elements — Null, Zero, Epsilon, One, and Infinity — whose multiplicative interactions are governed by an axiomatic Cayley table encoding the boundary conditions of physical reality. From this discrete foundation, three metric signatures (i² = −1, d² = 0, j² = +1) emerge as the exhaustive classification of real 2-dimensional unital associative algebras, generating rotation, translation, and boost symmetries respectively. Together they compose the Motor operator M = (1 + (i+d+j) ε) ^∞, a single expression from which the Poincaré group ISO (1, 3), quantum orbital geometries, spinor decomposition, electromagnetic field structure, and cosmological expansion are derived as consequences. A radial interference equation parameterized by booster amplitude and harmonic frequency reproduces atomic orbital morphologies — s, p, d, dᵦ², f, and a novel golden-ratio configuration — at approximately 25 floating-point operations per vertex. The framework proposes that the exponential morphism (the Engine) is not merely a calculational tool but the structural carrier of time translation, encoding P₀ as a morphism rather than an independent spatial generator.
Andrew Hill (Tue,) studied this question.