As part of the preparations for their classic 1959-1960s series of Earthbound gravity-shift experiments, the Harvard group (Pound/Snider/Rebka) had to first build and test a precisely matched “recoil-less” emitter and absorber with a very narrow acceptance band, using the Mossbauer effect.
When they did this, they accidentally discovered a previously-unsuggested and unpredicted thermal redshift effect in the Mossbauer hardware, which they named the “SOD” effect (for “second order Doppler”) and which they had to overcome before proceeding with the main experiment.
The effect was not expected or predicted because special relativity's Doppler effects cancel exactly over a round trip, and because “extended SR” also arguably proves the absence of any additional acceleration effects, if "core SR" is correct.
There is certainly a predicted thermal redshift effect with the older Newtonian Doppler equations, but under SR the effect is not supposed to exist, and one could, in fact, use the existence or absence of thermal redshifts in recoilless materials as a fundamental test of special relativity.
SO -- did Pound and Snider accidentally provide an experimental disproof of SR?