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 functionalOmega 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.