Hopf-Cole transformation maps Burgers to heat equation:
u = -2v * d(ln ψ)/dx
dψ/dt = v * d²ψ/dx² (exact via FFT)
Benchmark results:
N=512, v=0.01: 1.45x speedup
N=1024, v=0.01: 83.4x speedup
N=2048, v=0.01: 151.3x speedup
Key insight from adversarial review:
- RG assumption (nonlinear term vanishes) is FALSE
- But 1D Burgers IS integrable via Hopf-Cole
- Exact solution in O(N log N), no time stepping
- The 'insultingly easy' regime exists — just not via RG
This is the exact solution the agents found when they
broke the RG fixed point assumption.
