Unity-centered scalar score Φ(x)

Read the equation

The score is largest at x=1 and decreases symmetrically as x moves away from 1. It is continuous, positive for finite real x, and at most 1, with a sharp derivative change at x=1. This project uses it to weight importance and to label some model outputs; it is a scalar proximity score and is different from integrated-information quantities also denoted Φ.

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 function is not differentiable at x=1.

Original context

## 6.4 Consciousness Weighting Function

```
Φ(x) = 1 / (1 + |x - 1|)
```

**Explanation**: Items with importance near 1.0 get maximum weight (Φ = 1). Items with very low or very high importance get reduced weight. This creates a sweet spot around "normal" importance.

## 6.5 Coherence Between Two Agents

```
C_ij = (θ_i · θ_j) / (||θ_i|| · ||θ_j||)
```

**Explanation**: Cosine similarity between two agents' knowledge vectors. Value of 1 means identical knowledge; 0 means orthogonal; -1 means opposite.

---

# 7. Gate5000 Binary Substrate

## 7.1 DNA Phase Update

```
phase_DNA(t+1) = (phase_DNA(t) + δ) mod 1

Φ(x) = 1 / (1 + |x - 1|)

Related builds