Who holds the license, and since when
Ask for the license number before anything else, and look it up on the Contractors State License Board website. The record shows the licensee, the qualifying individual, the classifications, the bond and workers' compensation status, and the issue date. A second story needs the Class B General Building classification. If the company sells under one name and the record shows another, ask why, and ask which one signs your agreement. The record for CSLB #1113888 is one search away (opens in a new tab).
The issue date tells you how long the licensee has answered for its work in California. A brand with years in other states can have a California license that is months old. Neither fact is disqualifying on its own; both belong in the open before you sign.