Hello,
as already stated, there's that very long thread in the other (correct) category, where exactly such an effect is described.
The temperature sensing BE diode rectifies any AC disturbances and shifts the temperature stabilization point.
A few ppm as you observe, are typical.
Those disturbances can be mitigated by grounding the circuitry to the case, that is also the effect you see, as the capacitor obviously shorts RF signals.
Most probably your AC supply induces magnetic filed, and/or electrical fields into the LTZ circuitry.. The transformer might be too close.
Therefore, for testing remove transformer, rectifier and stabilizer from the case, connect the LTZ1000 via a long shielded cable and additionally filter the DC supply.
Make sure, that there is no switch mode PSU near your LTZ1000 circuitry, best would be nowhere in the room the circuit is situated, and not in the AC mains grid.
Those PSUs extremely disturb the LTZ.
Then, leave the capacitor away and test some grounding schemes.
With some testing, you will quickly learn, what is the source of noise, and which is the undisturbed output volatge of the LTZ circuit.
The original circuitry from the datasheet can be used very successful after noise optimization, but it stays sensitive.
Andreas, from the thread I've mentioned, added several caps to the temperature sensing part of the circuit, and the whole circuitry got much more stable.
Btw.: As you are one of the few users of the non-A version, (besides myself), at which temperature do you stabilize the LTZ?
It seems to be 65-70°C (13.5k over 1k), that's a pity, too hot.. 45°C (12k over 1k) is totally sufficient, and gives a much better 1 year stability
Frank