Waveform Asymmetry from Multi-Field Dynamics in the Canvas Model: A Complete Derivation

The Canvas Model originally predicted a universal waveform asymmetry in bound states with T_{\text{rise}}/T_{\text{fall}} = \pi/2. This claim was falsified by the proof that the Unified Wave Equation (UWE) is exactly symmetric under \Phi \to -\Phi for a single field. However, the falsification only considered the global symmetry transformation \Phi \to -\Phi for all fields simultaneously. It did not consider individual sign flips, where each field flips independently of the others. This paper shows that while the UWE is symmetric under global sign flips, individual sign flips are allowed because each primitive has its own UWE with its own c_i and d_i weights. The symmetry of the multi-field system is broken when one field flips and the others do not. In the Canvas Model, spacetime itself emerges from the product of four fields: three space waves and one time wave. Each field has its own UWE with its own c and d weights, derived from the geometry of the internal space. The space waves have structural weight c_S = 1, while the time wave has c_T = \pi/2 from the Angle primitive (P7). Because different fields have different c values, they evolve at different rates. The rise of the product is limited by the slowest field (the time wave). The fall of the product is limited by the fastest field (the space waves). The absolute timescale factor cancels exactly in the ratio, giving: \frac{T_{\text{rise}}(P)}{T_{\text{fall}}(P)} = \sqrt{\frac{\pi}{2}} \approx 1.253 The asymmetry parameter is: \alpha_{\text{waveform}} = \frac{\sqrt{\pi} - \sqrt{2}}{\sqrt{\pi} + \sqrt{2}} \approx 0.1124 Why this matters: The waveform asymmetry is the geometric engine of CP violation, the arrow of time, and the matter-antimatter asymmetry in the Canvas Model. This paper provides a complete, rigorous derivation of the asymmetry from the primitives, resolving a long-standing problem in the framework. The derivation requires no fitted parameters and follows entirely from the primitives. The original claim T_{\text{rise}}/T_{\text{fall}} = \pi/2 was incorrect due to the single-field approximation, but the multi-field dynamics with individual sign flips produce a genuine asymmetry. Keywords: canvas model, waveform asymmetry, unified wave equation, CP violation, arrow of time, multi-field dynamics, primitives, phase space