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ConsciousnessLearn · Explore · Joseph Anady

Stability-controlled update fraction

The stability input is clipped to [0,1] and mapped to a gate between γ_min and 1. The next intermediate state takes the fraction γ of the gap from the current state to the proposed blended state. When γ_min lies in [0,1], this is a convex interpolation; a low gate…

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gh-eq-b2f5faea0ed0cd4fdocumented-equation
γ=γmin+(1−γmin)⋅clamp01(stability)Ψi′′′(t+1)=Ψi(t)+γ⋅(Ψi′′(t+1)−Ψi(t))γ = γ_min + (1 - γ_min) · clamp₀₁(stability) Ψ'''_i(t+1) = Ψ_i(t) + γ · (Ψ''_i(t+1) - Ψ_i(t))

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The stability input is clipped to [0,1] and mapped to a gate between γ_min and 1. The next intermediate state takes the fraction γ of the gap from the current state to the proposed blended state. When γ_min lies in [0,1], this is a convex interpolation; a low gate slows response but does not prove the whole coupled system is stable.

Terms & definitions

TermMeaning in this source
γ

Update fraction

γ_min

Minimum permitted update fraction

stability

Gate control input

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Original context

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## 4.4 Stability Gating

```
γ = γ_min + (1 - γ_min) · clamp₀₁(stability)
Ψ'''_i(t+1) = Ψ_i(t) + γ · (Ψ''_i(t+1) - Ψ_i(t))
```

**Where**:
- `γ_min` = minimum gate value (default 0.1)
- `stability` = external stability signal

**Explanation**: When stability is low, updates are damped (γ approaches γ_min). This prevents erratic behavior during uncertain conditions.

## 4.5 Final Normalization

```
Ψ_i(t+1) = Ψ'''_i(t+1) · b(t+1)
```

**Where**:
- `b(t+1)` = normalization factor from equation 2.2

**Explanation**: All family activations are scaled by the normalizer, ensuring bounded behavior.

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Exact original notation
γ = γ_min + (1 - γ_min) · clamp₀₁(stability)
Ψ'''_i(t+1) = Ψ_i(t) + γ · (Ψ''_i(t+1) - Ψ_i(t))

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