NON-LINEAR TOPOLOGICAL EMERGENCE: Evidence of Hadronic Transmutation and Fractal Octet Resonance (N=1136) in TIGM Solitons

This experimental report details the computational results of dynamic stress tests ("The Gauntlet Simulations") applied to the TIGM Electron Model (a 5D Klein Bottle topological soliton with a fundamental winding number of \alpha^{-1} \approx 137). The study aimed to verify the structural stability of the soliton under conditions of extreme entropy, simulating high-energy particle collisions. Utilizing a Phase Invariance Analysis via the Hilbert Transform, we observed a critical emergent phenomenon: under noise levels exceeding 1.5\sigma, the topological charge of the system did not dissipate. Instead, it underwent a spontaneous fractal multiplication, converging on a new stable Winding Number of N' = 1136. We interpret this "1136 Anomaly" as a geometric phase transition corresponding to an Octet Resonance (1136 \approx 8 \times 137). This finding suggests a purely topological mechanism for Hadronic Transmutation, proposing that heavy composite particles are not fundamental entities, but rather highly excited fractal states of the fundamental leptonic geometry.