Read the equation
Completing the square gives U(x,y)=x²−(y−x)². For a fixed x, the utility decreases with squared distance from y=x and has a unique maximum over real y at that point. This supplies the exact optimization problem used to explain the Athena signature.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Fixed utility parameter |
| y | Decision variable |
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
Read the surrounding source passage
sum += an * math.Sin(float64(n)*math.Pi*x)
}
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)
}
Exact original notation
Simplified: find max of utility function U(x,y) = -y² + 2xy