Dionysus signature: absolute sine after removing complex phase

Read the equation

The intermediate value is exp(iωx)sin(x), and the function then takes its complex magnitude. Since the exponential has magnitude one, the returned result is exactly |sin(x)|. The phase factor is discarded, so this helper does not preserve the advertised complex oscillation in its output.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

// FPrometheus: F_Prometheus(x) = x·(1-x)·r (Innovation - logistic map)
func FPrometheus(x float64) float64 {
	r := 3.8 // Chaotic regime
	return r * x * (1.0 - x)
}

// FDionysus: F_Dionysus(x) = e^{iωt}·A(x) (Creativity - complex exponential)
func FDionysus(x float64) float64 {
	// Return magnitude of creative oscillation
	omega := 2.0 * math.Pi / BasePairsPerTurn
	c := cmplx.Exp(complex(0, omega*x)) * complex(math.Sin(x), 0)
	return cmplx.Abs(c)
}

// FArtemis: F_Artemis(x) = ∇·(D∇x) (Perception - diffusion operator)
func FArtemis(x float64) float64 {
	// Simplified: D·d²x/dx² ≈ D·(-x) for harmonic

FDionysus: F_Dionysus(x) = e^{iωt}·A(x) (Creativity - complex exponential)

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