Learning family: additive input accumulation

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Each application adds one tenth of dx_norm to the current scalar. With a fixed input d, the isolated recurrence has the exact solution xₙ=x₀+0.1nd. This can serve as an update increment, but it has no decay or saturation by itself and should only be described as weight learning when x is actually a trainable weight in the surrounding implementation.

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## 3.6 Family 5: Learning / Weight Update

```
f₅(x) = x + 0.1 · dx_norm
```

**Equation Type**: Delta rule: W_{t+1} = W_t + ΔW

**Explanation**: Accumulates change signals over time, implementing basic learning through weight adjustment. This family stores learned patterns.

## 3.7 Family 6: Mutual Information

```
f₆(x) = 0.5 · (x + σ(dx_norm))
```

**Equation Type**: Information measure: I(X;Y)

**Explanation**: Balances current state with sigmoid-transformed input. The averaging operation measures shared information between internal state and external input.

## 3.8 Family 7: Rate-Distortion

```
f₇(x) = x - 0.05 · ed_error + 0.05 · utility

f₅(x) = x + 0.1 · dx_norm

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