Cosine similarity between coefficient vectors

Read the equation

The dot product divided by both vector lengths measures directional alignment, producing a value in [−1,1] for nonzero real vectors. A value of 1 means positive collinearity, including vectors with different magnitudes; zero means orthogonality. It compares the stored numerical representations and does not establish identical knowledge.

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 expression is undefined when either vector has zero norm.

Original context

## 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.

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# 7. Gate5000 Binary Substrate

## 7.1 DNA Phase Update

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

**Where**:
- `δ = 0.013618` (DNA delta constant)

**Explanation**: The DNA phase advances by a small golden-ratio-related increment each step, creating quasi-periodic patterns.

## 7.2 Fibonacci Phase Update

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

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