# Stanchian

The *Stanchian* of a system is the condition by which all causal paths in the metric of the system tend to zero.

For a system *S* with metric , the condition of being Stanchian is:

as .

where k are the "heights" of the weighted path, according to its time-like affinity.

**Note that all heights in a Stanchian system tend to zero**. So, Stanchian systems are self-Stanchian when the paths are themselves the heights of the system.

The condition of being Stanchian is frame-independent. Thus, in all Stanchian systems,

where is the Jacobian of the transformations .

The Stanchian was first defined by Xela M. Alakas by considering tachyonic signals in F-theory, but was given the modern form in terms of differential geometry by Agellio Stanch (both Cretans).