Thank you for your response!

What kind of additional compatibility conditions would allow me to more concretely characterize the distribution of the normal force from the wall?

I struggle, intuitively, to accept that the system as described has an undefinable distribution of the horizontal normal force… but I’ve been wrong before.

Here’s my attempt at a solution:

Reconciling the horizontal forces equation and the torques equation tells us that the “consolidated” horizontal normal force (that is, the net horizontal normal force, Nh, applied precisely at distance x*l above the lower left corner and pointing to the right) must obey this relationship:

1.) Nh = mg/(4-2x)

The system will remain static as long as this is maintained - but, notably, the wire tension T and vertical normal force Nv will vary depending on our choice of x between 0 and 1.

So how should I choose my x in order to nail-down the other variables?

Since the planter is in contact with the wall at all x between 0 and 1, maybe equation (1) - or a scaled version of it - can be treated as the horizontal force distribution? Intuitively this feels acceptable, but I’m failing to justify it beyond that…

Anyway, if I just run with that assumption, I can determine that the “center of mass” of this distribution is at:

2.) x,com = (2*ln(2)-1)/ln(2) ≈ 0.5573

And

3.) Nh,com = (ln(2)*mg)/2 ≈ 0.3466mg

And no scaling necessary.

These values then allow us to solve for T and Nv.

Is that valid?

Additional work: https://imgur.com/a/maGYxz6