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:
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).