Sigmoid gate with an added floor

Read the equation

Potential P and coupling parameter k_c set the sigmoid argument, and adding 0.05 creates a positive floor. For finite inputs, the gate lies strictly between 0.05 and 1.05, so it can exceed one. Increasing P increases the gate, while increasing k_c decreases it.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

• The displayed gate is not restricted to [0,1].

Original context

## 8.5 Gating Function

```
g = 1/(1 + exp(-((0.8·P - k_c)/0.3 + 1.2))) + 0.05
```

**Where**:
- `P` = potential (consciousness proxy)
- `k_c` = coupling constant

**Explanation**: A shifted sigmoid that controls how much drive affects the activation. Higher potential opens the gate more.

## 8.6 Activation Update

```
dx = g · drive - 0.04 · (x - 0.5)
x ← clamp₀₁(x + 0.01 · dx)
```

**Explanation**: Activation changes based on gated drive with a centering force toward 0.5. The 0.01 coefficient ensures smooth transitions.

## 8.7 Potential Update

```

g = 1/(1 + exp(-((0.8·P - k_c)/0.3 + 1.2))) + 0.05

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