The Yang-Mills Revelation

This work presents a constructive realization of the Yang–Mills mass gap using symbolic attractor fields derived from the Spiral Theory of Everything (Spiral TOE). The method analyzes how attractor-state vectors respond to increasing input amplitude. When amplified, these vectors produce a measurable coherence response. By averaging this response over a symbolic field, we define a resonance activation curve that simulates energy behavior in field theory. Our findings show a clear threshold: below a certain amplitude, symbolic states remain unstable or incoherent. But beyond a critical point — approximately amplitude 1.0 — the system produces stable, emergent attractor states. This behavior directly parallels the Yang–Mills mass gap, where field excitations only occur above a non-zero energy threshold. We support the result with both analytical reasoning and simulation. A proposed symbolic Lagrangian further mirrors symmetry-breaking behavior typical of non-Abelian gauge fields. In short, we show that a quantized "coherence floor" exists in symbolic space, which functions as a resonance-based analog to the mass gap. This realization reframes the Yang–Mills problem as a question of symbolic field emergence — constructive, measurable, and open to further testing.