Read the equation
The reference contraction R=gⁱʲRᵢⱼ would require an inverse metric and a Ricci tensor. The implementation instead returns −φn(n−1)/(2n²) for nonempty input, a constant determined solely by dimension. It also differs by a factor 1/n² from its nearby simplified comment, so this returned score should not be presented as a computed curvature of the declared coordinate metric.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| R | Function return labelled Ricci scalar |
| n | Vector dimension |
| phi | Golden ratio |
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
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
}
// Simplified: R ≈ -n(n-1)φ/2 for golden manifold
return -float64(n*(n-1)) * PHI * 0.5 / float64(n*n)
}
Exact original notation
RicciScalar computes the scalar curvature R = g^ij R_ij