Maximum utility value returned by Athena

Read the equation

Substituting the maximizing location y=x into U gives x². This is the optimal objective value, not the value of the optimizing argument. The code returns this nonnegative scalar directly.

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

	return sum
}

// FAthena: F_Athena(x) = argmax_y U(x,y) (Strategy - utility maximization)
func FAthena(x float64) float64 {
	// Simplified: find max of utility function U(x,y) = -y² + 2xy
	// argmax_y: dU/dy = -2y + 2x = 0 => y* = x
	// U(x, x) = -x² + 2x² = x²
	return x * x
}

// FApollo: F_Apollo(x) = φ^x + φ^{-x} (Mathematics - golden ratio)
func FApollo(x float64) float64 {
	return math.Pow(PHI, x) + math.Pow(PHI, -x)
}

// FHermes: F_Hermes(x) = dx/dt approximation (Communication - rate of change)
func FHermes(x float64) float64 {

U(x, x) = -x² + 2x² = x²

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