SESync results matrix sometimes flips

[Mnzs1701]

Thank you for your extraordinary work, I was attempting to use SESync for a realtime SLAM, however I am facing an issue, while running SESync periodically, the results.xhat matrix inverts values abruptly.
The SESync Result is as follows:

[ INFO] [1689674506.598137576]: SESync x: -0.709801 y: -0.002066
[ INFO] [1689674506.649726984]: SESync x: -0.709801 y: -0.002066
[ INFO] [1689674506.698200718]: SESync x: -0.734062 y: -0.000417
[ INFO] [1689674506.748467310]: SESync x: -0.734062 y: -0.000417
[ INFO] [1689674506.798415183]: SESync x: 0.001456 y: 0.759772
[ INFO] [1689674506.848358097]: SESync x: 0.001456 y: 0.759772
[ INFO] [1689674506.898409615]: SESync x: 0.001456 y: 0.759772
[ INFO] [1689674506.948645089]: SESync x: -0.783955 y: 0.002026
[ INFO] [1689674506.998515216]: SESync x: -0.783955 y: 0.002026
[ INFO] [1689674507.048347022]: SESync x: -0.783955 y: 0.002026

The x and y values get interchanged for a certain set of measurements and abruptly return to normal. The code I am using to access these values is

results = SESync::SESync(measurements, opts);  
int latest_result = results.xhat.cols()/3;      

double x ,y;
x = results.xhat.col(latest_result-1)[0];
y = results.xhat.col(latest_result-1)[1];

If one more value is added and SESync is rerun the output returns to normal. It appears to invert almost randomly. I have printed two consecutive result matrices into a google sheet here

Thanks in advance!

[Mnzs1701]

It looks like I can fix this by changing the reflector matrix here. Currently the code does reflection over the x axis using the following matrix

1  0 
0 -1

Intead we need to reflect over the y=x line

0  1
1  0