CONSCIOUSNESS DYNAMICS · dΦ/dt

Read the equation

This relation defines dΦ/dt in the source section “CONSCIOUSNESS DYNAMICS · dΦ/dt”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read dΦ/dt as the quantity being defined or updated by this relation.

2. Uses a derivative or gradient to describe a rate of change or a direction of variation.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

        float u2 = (rng_state >> 16) / 65536.0f;

        float z = std::sqrt(-2.0f * std::log(u1)) * std::cos(2.0f * 3.14159265f * u2);
        return z * std::sqrt(dt);
    }

    // Evolve consciousness by one time step
    // dΦ/dt = α(Φ_target - Φ) + β∇²Φ + γξ(t)
    float step() {
        float dW = wiener_increment();

        // Drift term: attraction to target
        float drift = alpha * (phi_target - phi);

        // Diffusion term (approximated as negative feedback on velocity)
        float diffusion = -beta * phi_velocity;

        // Noise term

dΦ/dt = α(Φ_target - Φ) + β∇²Φ + γξ(t)

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