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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. |
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| deepseek_review | ||
| lean_expert_agent | ||
| hash_benchmark.csv | ||
| hash_benchmark.json | ||
| hopf_cole_benchmark.json | ||
| qr_spatial_benchmark.json | ||