VII. GOLDEN BASIS FUNCTIONS · Basis function: ψ_k(x)

Read the equation

This relation defines Basis function: ψ_k(x) in the source section “VII. GOLDEN BASIS FUNCTIONS · Basis function: ψ_k(x)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. 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 Basis function: ψ_k(x) as the quantity being defined or updated by this relation.

2. Evaluates oscillatory sine or cosine terms using the stated phase or frequency.

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

// ============================================================================
// VII. GOLDEN BASIS FUNCTIONS
// ============================================================================

class GoldenBasis {
public:
    // Basis function: ψ_k(x) = sin(2πφ^k · x) + cos(2πφ^k · x)
    static double psi(int k, double x) {
        double arg = 2.0 * M_PI * std::pow(PHI, k) * x;
        return std::sin(arg) + std::cos(arg);
    }

    // Generate basis vector for N terms
    static std::vector<double> basis_vector(double x, int N) {
        std::vector<double> result(N);
        for (int k = 0; k < N; ++k) {
            result[k] = psi(k, x);

Basis function: ψ_k(x) = sin(2πφ^k · x) + cos(2πφ^k · x)

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