Pedigree
A registered record of an animal's ancestors — a family tree issued by a registry, not a guarantee of health or quality.
A pedigree certificate states who the parents and grandparents were and that a registry recorded them. That is genuinely useful: it is what makes a coefficient of inbreeding calculable and what lets a breeder trace an inherited problem back through a line.
What it does not do is certify anything about the animal in front of you. Health testing is separate, temperament is separate, and how the puppies were raised is separate again. A breeder who leads with papers and cannot produce health-test results for both parents has answered the easier question.