| # V5 — Hard Controlled Dynamics | |
| V4 showed that selective spectral regulation repaired the failure of global contraction, but the no-spectral-transition control remained highly competitive. V5 therefore changes the **benchmark difficulty rather than the stability mechanism**. | |
| The new benchmark preserves the same image/text/action API while adding inertial velocity, action-conditioned acceleration, wall bounces, a moving distractor, a central occluder, stochastic target occlusion, and longer training sequences. This is designed to make simple latent persistence insufficient. | |
| ## Primary experiment | |
| `PYTHONPATH=. python scripts/run_v5_benchmark.py --seeds 0 1 2 3 4 --horizons 5 10 20 30 50 100 --device cuda` | |
| Primary output: `results/v5_hard_dynamics/metrics_summary.csv`. | |
| Interpret the benchmark as an attribution experiment. Compare `swm_selective` with `swm`, `no_spectral_transition`, `koopman`, and `neural_operator`. Report image MSE, recurrent text accuracy, latent cosine separately; the joint score is diagnostic only. | |