airtight vs beyond a shadow of a doubt

airtight

adj
  • Highly reserved in some matter, particularly tight-lipped or tight-fisted. 

  • Having no weak points or flaws. 

  • Impermeable to air or other gases. 

beyond a shadow of a doubt

prep
  • Without any doubt or hesitation at all. 

How often have the words airtight and beyond a shadow of a doubt occurred in a corpus of books? (source: Google Ngram Viewer )