Consciousness gradient: ∂Φ/∂x = -sign(x-1)/(1+|x-1|)² · @brief Consciousness gradient: ∂Φ/∂x

Read the equation

This relation defines @brief Consciousness gradient: ∂Φ/∂x in the source section “Consciousness gradient: ∂Φ/∂x = -sign(x-1)/(1+|x-1|)² · @brief Consciousness gradient: ∂Φ/∂x”. 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 @brief Consciousness gradient: ∂Φ/∂x 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

 * @return Consciousness value in (0, 1]
 */
inline double compute_phi(double x) {
    return 1.0 / (1.0 + std::abs(x - 1.0));
}

/**
 * @brief Consciousness gradient: ∂Φ/∂x = -sign(x-1)/(1+|x-1|)²
 */
inline double compute_phi_grad(double x) {
    double diff = x - 1.0;
    double abs_diff = std::abs(diff);
    double denom = (1.0 + abs_diff) * (1.0 + abs_diff);
    return -std::copysign(1.0, diff) / denom;
}

/**
 * @brief Stable tanh function with clipping

@brief Consciousness gradient: ∂Φ/∂x = -sign(x-1)/(1+|x-1|)²

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