Collins
World English Dictionary
rigour or (US) rigor (ˈrɪɡə)
 
n
1.  harsh but just treatment or action
2.  a severe or cruel circumstance; hardship: the rigours of famine
3.  strictness, harshness, or severity of character
4.  strictness in judgment or conduct; rigorism
5.  maths, logic logical validity or accuracy
6.  obsolete rigidity
 
[C14: from Latin rigor]
 
rigor or (US) rigor
 
n
 
[C14: from Latin rigor]

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
For a party that has trouble reconciling extravagant promises with financial
  rigour, this is no small step.
Questions will also be asked about the academic rigour of such programmes.
The policies include the successful pursuit of price stability, fiscal rigour,
  foreign investment and open trade.
Society needs highly trained critical thinkers to tackle complex problems with
  rigour and research skills.
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