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The body returns x(1−e⁻⁰·¹), approximately 0.0951626x. It does not read prior inputs or a memory buffer, so it cannot evaluate the displayed exponentially weighted historical integral by itself. A stateful leaky recurrence could approximate such memory, but it would require storing the preceding accumulated value.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Current scalar input |
| tau_m | Declared time constant 10 |
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
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Original context
Read the surrounding source passage
}
// 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))
}
// FZeus: F_Zeus(x) = Π_k F_k(x_k) (Coordination - product of all)
// Zeus coordinates all family contributions without circular reference
func FZeus(x float64) float64 {Exact original notation
FHestia: F_Hestia(x) = ∫_{-∞}^{t} x(τ)·e^{-(t-τ)/τ_m} dτ (Memory - exponential decay)