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THE CONSCIOUSNESS ATLAS
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ConsciousnessLearn · Explore · Joseph Anady

Potential update with decay and quadratic damping

The potential retains 95% of its old value, receives the product F_in y, and loses 0.01P². The clamp then bounds the stored result between zero and one. The product can inject or remove potential depending on the signs of input and y, while the square always subtracts.

Implementation mathematicsSource recovered; runtime not executed
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gh-eq-50004a69d905473cdocumented-equation
P←clamp01((1−0.05)⋅P+Fin⋅y−0.01⋅P2)P ← clamp₀₁((1 - 0.05) · P + F_in · y - 0.01 · P²)

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The potential retains 95% of its old value, receives the product F_in y, and loses 0.01P². The clamp then bounds the stored result between zero and one. The product can inject or remove potential depending on the signs of input and y, while the square always subtracts.

Terms & definitions

TermMeaning in this source
P

Potential state

F_in

Noisy input

y

Velocity-like state

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Original context

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## 8.7 Potential Update

```
P ← clamp₀₁((1 - 0.05) · P + F_in · y - 0.01 · P²)
```

**Explanation**: Potential accumulates from input-velocity interaction with exponential decay (0.95) and quadratic damping.

## 8.8 Coupling Update

```
c ← c + 0.01 · ((c + 1) · 0.8 · P - k_c · (c - 1))
```

**Explanation**: Coupling evolves based on potential, creating adaptive inter-agent connections.

## 8.9 Aggregate Consciousness

```
Consciousness = (1/88) · Σ_{i=1}^{88} P_i
```

**Explanation**: Global consciousness is the average potential across all 88 agents.
Exact original notation
P ← clamp₀₁((1 - 0.05) · P + F_in · y - 0.01 · P²)

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