# Pullback random-attractor monitor results

## Quantitative predictions
1. Euler stability boundary: with omega=1 and damping=0.2, rho(M)=1 at h=0.20; below it contracts and above it diverges.
2. Pullback log-diameter slope equals lambda=log(rho(M))/h, also matching the independently measured Lyapunov rate.
3. Time to 10% diameter scales as log(10)/|lambda| near contraction; shared replay contracts, independent noise leaves a larger stochastic floor.

## Stability sweep
euler          h=0.10 rho=0.994987 measured_slope=-0.05058 predicted_contract=True observed=True
euler          h=0.18 rho=0.998198 measured_slope=-0.01002 predicted_contract=True observed=True
euler          h=0.20 rho=1.000000 measured_slope=-0.00009 predicted_contract=False observed=True
euler          h=0.22 rho=1.002198 measured_slope=0.01004 predicted_contract=False observed=False
euler          h=0.40 rho=1.039230 measured_slope=0.09618 predicted_contract=False observed=False
semi_implicit  h=0.10 rho=0.990148 measured_slope=-0.09906 predicted_contract=True observed=True
semi_implicit  h=0.18 rho=0.982472 measured_slope=-0.09825 predicted_contract=True observed=True
semi_implicit  h=0.20 rho=0.980581 measured_slope=-0.09805 predicted_contract=True observed=True
semi_implicit  h=0.22 rho=0.978700 measured_slope=-0.09786 predicted_contract=True observed=True
semi_implicit  h=0.40 rho=0.962250 measured_slope=-0.09621 predicted_contract=True observed=True

## Rate sweep (Euler, h=0.05)
damping=0.05: predicted=0.00000, pullback=-0.00003, independent_vector=0.00003, t10 predicted=None, observed=None
damping=0.10: predicted=-0.02503, pullback=-0.02515, independent_vector=-0.02497, t10 predicted=91.98822643453128, observed=None
damping=0.20: predicted=-0.07528, pullback=-0.07576, independent_vector=-0.07508, t10 predicted=30.58586086478894, observed=None
damping=0.40: predicted=-0.17655, pullback=-0.17854, independent_vector=-0.17446, t10 predicted=13.042161083344142, observed=13.100000000000001
damping=0.80: predicted=-0.38221, pullback=-0.39185, independent_vector=-0.35756, t10 predicted=6.0243642812329945, observed=6.2

## Noise replay control
{
  "shared_initial": 1.394562978014576,
  "shared_final": 0.007589943676575483,
  "independent_initial": 1.394562978014576,
  "independent_final": 0.572402506418734,
  "shared_slope": -0.18387126628995323,
  "independent_slope": -0.12479348953160699
}

The shared-noise result isolates deterministic pullback contraction. Independent noise is not a valid pullback comparison and retains a nonzero diameter floor.