Hera signature: sixteen weighted harmonics

Read the equation

The body computes Σₖ₌₁¹⁶sin(kx)/k. Its indexed terms are harmonics derived from the same scalar x, not readings of sixteen independently stored family activations. It is a finite periodic feature sum that can have positive or negative values.

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

// FArtemis: F_Artemis(x) = ∇·(D∇x) (Perception - diffusion operator)
func FArtemis(x float64) float64 {
	// Simplified: D·d²x/dx² ≈ D·(-x) for harmonic
	D := 0.1 // Diffusion coefficient
	return -D * x
}

// FHera: F_Hera(x) = Σ_k w_k·x_k (Integration - weighted sum)
func FHera(x float64) float64 {
	// Integrate contributions from all families
	sum := 0.0
	for k := 1; k <= NumStrands; k++ {
		wk := 1.0 / float64(k) // Weight decreases with distance
		xk := math.Sin(float64(k) * x)
		sum += wk * xk
	}
	return sum
}

FHera: F_Hera(x) = Σ_k w_k·x_k (Integration - weighted sum)

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