There have been some attempts at formally verifying lack of timing attacks (to the extent allowed by hardware). This is the one I know the most about: https://dl.acm.org/doi/pdf/10.1145/3314221.3314605 but there are likely others
E. Prouff and M. Rivain, Masking against Side-Channel Attacks: A Formal Security Proof, EUROCRYPT 2013, LNCS 7881
S. Dziembowski and K. Pietrzak, "Leakage-Resilient Cryptography, 10.1109/FOCS.2008.56.
Time complexity > Constant time: https://en.wikipedia.org/wiki/Time_complexity#Constant_time
"Masking against side-channel attacks: A formal security proof" (2013) https://link.springer.com/chapter/10.1007/978-3-642-38348-9_... https://scholar.google.com/scholar?cites=1479355492097437276...
"Leakage-Resilient Cryptography" (2008) https://ieeexplore.ieee.org/abstract/document/4690963 https://scholar.google.com/scholar?cites=5581902451405085906...