Aphrodite signature: golden-frequency cosine

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The cosine takes φx as its radian argument and returns a value between −1 and one. Its scalar-input period is 2π/φ, and it is even in x. The family’s harmony label does not alter this trigonometric feature.

Terms & definitions

How it works

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Original context

func FAres(x float64) float64 {
	m := 1.0 // Mass
	// F = ma, assume simple harmonic: a = -ω²x
	omega := AngularFrequency
	return m * (-omega * omega * x)
}

// FAphrodite: F_Aphrodite(x) = cos(φ·x) (Harmony - golden cosine)
func FAphrodite(x float64) float64 {
	return math.Cos(PHI * x)
}

// FHestia: F_Hestia(x) = ∫_{-∞}^{t} x(τ)·e^{-(t-τ)/τ_m} dτ (Memory - exponential decay)
func FHestia(x float64) float64 {
	// Simplified memory function: exponential weighted past
	tau_m := 10.0 // Memory time constant
	// For single value, approximate as x * tau_m
	return x * (1.0 - math.Exp(-1.0/tau_m))

FAphrodite: F_Aphrodite(x) = cos(φ·x) (Harmony - golden cosine)

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