substantiate
To prove something is true by giving clear evidence.
To substantiate something means to provide evidence or proof that shows it's true. When you substantiate a claim, you back it up with facts, examples, or solid reasons instead of just asking people to trust you.
Imagine telling your parents you need new running shoes because your old ones have holes. If you substantiate your claim by showing them the actual holes, you've given them evidence they can see. A scientist substantiates her theory with careful experiments and data. A lawyer substantiates his case with documents, witnesses, and physical evidence.
Without substantiation, claims are just opinions or guesses. Anyone can say “I'm the fastest runner in school,” but you substantiate that claim by winning races. A news reporter substantiates a story by interviewing witnesses and checking facts. Teachers often ask students to substantiate their answers by showing their work or citing evidence from the text.
The opposite of substantiating is making unsubstantiated claims: stating things without proof. When someone makes serious accusations without substantiating them, people quickly doubt that person's credibility.