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The distance d=|x′−x_c| enters both a unity score Φ(d) and a Gaussian centered at d=0. The Gaussian favors exact agreement, but Φ(d) favors distance one; at exact agreement Φ(0)=0.5. Their product is therefore not simply two identical measures of closeness and requires its own interpretation.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| C | Returned layer score |
| x_prime | Current state |
| x_c | Reference state |
| sigma | Gaussian scale |
| Phi | Unity score applied to distance |
How it works
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Assumptions & limits
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Original context
Read the surrounding source passage
double delta = std::abs(x_prime - x);
if (delta > 0.2) {
x_prime = x + 0.2 * (x_prime > x ? 1.0 : -1.0);
}
return math::clamp(x_prime);
}
// T₂₃: C = Φ(||X' - X_c||)·exp(-||X' - X_c||²/2σ²)
inline double L2_to_L3(double x_prime, double x_c, double sigma = 0.5) {
double diff = std::abs(x_prime - x_c);
double phi_term = math::phi_constraint(diff);
double gauss_term = math::gaussian_kernel(x_prime, x_c, sigma);
return phi_term * gauss_term;
}
// T₃₄: S = tanh(αC)·exp(iωt)
inline std::complex<double> L3_to_L4(double coherence, double time,
double alpha = 2.0, double omega = 0.01) {Exact original notation
T₂₃: C = Φ(||X' - X_c||)·exp(-||X' - X_c||²/2σ²)