Discrete family: utility smoothing

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This family forms a weighted average of the current state and utility, with weights 0.9 and 0.1. A constant utility u is a stable fixed point, and deviations from it shrink by a factor 0.9 on each update. If both inputs lie in [0,1], the next state also lies in that interval.

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Original context

## 3.2 Family 1: Discrete Dynamics

```
f₁(x) = 0.9 · x + 0.1 · utility
```

**Equation Type**: Discrete state transition: x_{t+1} = F(x_t, u_t)

**Explanation**: Implements exponential smoothing between current state and utility signal. The 90/10 split creates memory of past states while responding to new inputs. Used for step-by-step reasoning.

## 3.3 Family 2: Reaction-Diffusion

```
f₂(x) = x + 0.05 · (softsign(dx_norm) - x)
```

**Equation Type**: Simplified reaction-diffusion: ∂x/∂t = D∇²x + f(x)

**Explanation**: Models pattern formation and spreading activation. The softsign function bounds the diffusion term, preventing runaway reactions. Used for spatial reasoning and pattern recognition.

## 3.4 Family 3: Optimization

```
f₃(x) = x + 0.2 · softsign(utility - x)

f₁(x) = 0.9 · x + 0.1 · utility

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