Read the equation
The next state depends on both the current state and the previous state, together with external inputs. This notation summarizes the family update, blending, gating, and normalization steps; F is a composite function rather than an additional closed-form equation. Reproducing a trajectory requires both starting states and the complete input sequence.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| Ψ | State vector, with sixteen family components and the documented normalization component |
| F | Composite transition function |
| inputs | External update inputs |
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Original context
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## 4.1 Single-Stack Master Equation
```
Ψ(t+1) = F(Ψ(t), Ψ(t-1), inputs)
```
**Where**:
- `Ψ(t)` = 17-dimensional meta-state vector (16 families + normalizer)
- `inputs` = {dx_norm, ed_error, utility, stability}
**Explanation**: This is the central equation governing all cognitive dynamics. The system maintains only two states (current and previous) for computational efficiency while enabling inertial effects.
## 4.2 Family Application with Weights
```
Ψ'_i(t+1) = w_i · f_i(Ψ_i(t), inputs)
```
**Where**:
- `w_i` = weight for family i (tunable parameter)
- `f_i` = family function i
**Explanation**: Each family's contribution is scaled by its weight, allowing the system to emphasize different cognitive modes.
Exact original notation
Ψ(t+1) = F(Ψ(t), Ψ(t-1), inputs)