Inquiry about the p-value in results

[xueyagaga]

Dear author
When I am reading https://lingam.readthedocs.io/en/latest/tutorial/lingam.html, a question puzzles me.

As shown in the tutorial's results, there is a chain between x3 and x4. Such a structure denotes the dependence of x3 and x4.
However, the p-value between x3 and x4 is 0.681 (>0.05). In my understanding, this means the null hypothesis (errors e3 and e4 are independent) cannot be rejected.
Thus, the dependence of x3 and x4, the independence of e3 and e4, seems to create a conflict here.
So, How exactly should we understand the p-values in LINGAM results？And What is the distinction of independence between variables and independence between errors?
Best regards

[sshimizu2006]

If the null hypthesis, independence btw e3 and e4, were rejected, it here means that the corresponding variables x3 and x4 would have hidden common causes and suggests users to try to find such hidden common causes and add such variables in the analysis. It is not related to wheter there is a chain between the variables x3 and x4.