Riemann curvature expression versus an index-only return value

Read the equation

The reference expression combines derivatives and products of connection coefficients to measure curvature. The body does not perform those operations: it returns φ⁻¹(l−i)(j−k)/n², which depends on dimension and index labels but not on the coordinate values. That surrogate does not establish the Riemann curvature tensor of the metric defined in this file.

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 gamma
}

// RiemannCurvature computes R^l_ijk curvature tensor component
func RiemannCurvature(x []float64, l, i, j, k int) float64 {
	// R^l_ijk = ∂_j Γ^l_ik - ∂_k Γ^l_ij + Γ^l_mj Γ^m_ik - Γ^l_mk Γ^m_ij
	// Simplified golden-scaled curvature
	n := float64(len(x))
	return PHI_INV * (float64(l-i) * float64(j-k)) / (n * n)
}

// RicciScalar computes the scalar curvature R = g^ij R_ij
func RicciScalar(x []float64) float64 {
	n := len(x)
	if n == 0 {
		return 0.0

R^l_ijk = ∂_j Γ^l_ik - ∂_k Γ^l_ij + Γ^l_mj Γ^m_ik - Γ^l_mk Γ^m_ij

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