noun
a lack of trust or belief in someone or something, especially when this is caused by a difference between what is said and what is done
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The politician's credibility gap widened as more inconsistencies in his statements were uncovered.
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I can't trust what he says anymore, there's a huge credibility gap.
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That guy's credibility gap is off the charts, I wouldn't believe a word he says.
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The company's credibility gap with consumers is like a deep chasm that will be hard to bridge.