R³I³ Framework: 1 = (-i) × i — The Formula of the Matter Spectrum

The R³I³ Framework derives the complete spectrum of stable matter from a single geometric identity known since Descartes (1637): 1 = (-i) × i. Combined with Euler's formula e^(iΔθ) = cosΔθ + i sinΔθ (1748) and a time invariance axiom fixing the Planck time as the minimum indivisible unit of the temporal axis, the framework derives seventeen physical quantities without any free parameters. These include: the fine-structure constant α⁻¹ = 137.035999084 (exact match to CODATA 2018), the electron, proton, and neutron g-factors unified by g = 2(1 + tanΔθ) (errors 0.008%, 0.07%, and exact match respectively), the proton charge radius r_p = 0.835 fm derived from Descartes' cardioid r = a(1 − cosθ) through four geometric substitutions, the neutron negative mean-square charge radius ⟨r_n²⟩ = −0.109 fm² (negative sign from i² = −1 in the I³ → R³ projection), the CMB frequency ν_CMB = 161.28 GHz (COBE FIRAS: 160.23 GHz, error 0.67%), the speed of light c = 2.997924580 × 10⁸ m/s derived from the geometric count N = (4/3)π(ν_P / 1 Hz)³ = 2.67 × 10¹³⁰, the gravitational constant G = 6.72 × 10⁻¹¹ m³kg⁻¹s⁻² (CODATA: 6.67430 × 10⁻¹¹, error 0.7%), and the proton-to-electron mass ratio m_p/m_e = 1836 as the ratio of Compton frequencies of two phase states of the same geometric entity. The nine-state matter spectrum spans from the electron (Δθ = 0°) to the GPDC black hole (Δθ → 90°). All four fundamental forces are unified in a single Lagrangian with zero free parameters. The framework does not fit parameters. It identifies the mathematical symbols that have existed for centuries as physical ontology. R³ is the real part. I³ is the imaginary part. The complex plane is the geometry of physical space.