Intellectual Rigour

Exposition or consideration that is based on careful, thorough and reasoned logic, verifiable evidence, and valid scientific methodology and/or validated mathematical process.

Note that one should probably make a distinction between "internal rigor" and "external rigor". Internal rigor means a model or description is clear and internally consistent, that is does not contradict itself or "crash". "External rigor" is applying such model or description to the real world in terms of applicability or fit to the "real world". -t

(Is "rigour" the British spelling?)

Yes, it's the British spelling. A model or description that contains a contradiction may still be otherwise rigorous. Rigorous does not imply flawless.

I've never heard of this "internal rigour" or "external rigour". CitationNeeded.

I don't know if those are the "proper" names. I intend describe concepts, not definitions. If there are better ways to describe them, feel free to offer that to readers.