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RIGOUR

Definition:

[noun] the quality of being logically valid
Synonyms: cogency, validity, rigor
[noun] something hard to endure; "the asperity of northern winters"
Synonyms: asperity, grimness, hardship, rigor, severity, rigorousness
[noun] excessive sternness; "severity of character"; "the harshness of his punishment was inhuman"; "the rigors of boot camp"
Synonyms: severity, harshness, rigor, inclemency, hardness, stiffness