Complexity Minimization on CW-Complexes: a Computational Framework for Physical Law

*Abstract.* We organize 13 known physical laws as instances of a single variational structure: minimize a complexity functional$Omega$ on a CW-complex subject to partial² = 0. The framework has three levels: topology (partial² = 0), gradientdynamics ($d G \/ d tau = -nabla Omega$), and self-consistency (T(G^*) = G^*). We report three computational results on3D Navier--Stokes via adjoint optimization (PyTorch, RTX 3090, $N = 256$). First, we discover a *quadratic feedback law*:the Biot--Savart self-dissipation rate scales as |lambda| approx C dot R₍"peak")² with C approx 3.6 times 10⁽-4),where R is the stretching-to-dissipation ratio (Table 2). This implies blow-up is impossible: dissipative feedback growsfaster (tilde R²) than any linear attack ($tilde R$). Second, we confirm a *prediction registered before computation*:the decay timescale at 800 epochs ($tau = 0.161$) falls within the pre-registered interval $[0.10, 0.20]$ (§5.4).Third, increasing the optimization horizon *decreases* achievable R, demonstrating that NS dynamics actively defeats adversarial blow-up attempts. We retract an earlier claim ($alpha approx phi$) that was invalidated by budget-artifact analysis (§5.2) and include the failure as a methodological case study.