Mean cosine phase projection

Read the equation

This score averages cos(k_m,i), producing a value in [−1,1]. It measures phase alignment with the chosen zero-angle axis: perfectly aligned phases at zero give 1, while perfectly aligned phases at π/2 give 0. It therefore differs from the phase-origin-invariant modulus commonly used to measure oscillator synchrony.

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

• A common phase shift can change this score without changing pairwise phase alignment.

Original context

## 8.10 Aggregate Synchrony

```
Sync = (1/88) · Σ_{i=1}^{88} cos(k_m,i)
```

**Explanation**: Synchrony measures phase alignment across agents using the kinetic modulation parameter.

---

# 9. Consciousness Engine

## 9.1 Core Equations (174 total)

```
core_eq[i] = 0.5 + 0.5 · sin(2π · (i/174) · φ) · core_eq[i-1]
```

**Where**:
- `i` = equation index [0, 173]
- `core_eq[-1]` = 0.5 (initial value)

**Explanation**: Each core equation builds on the previous one with golden-ratio-modulated sinusoidal coupling, creating a cascade of consciousness-related computations.

Sync = (1/88) · Σ_{i=1}^{88} cos(k_m,i)

Related builds