Legal Question in Construction Law in California

Before the contractor's work is complete, it may only send the owner a preliminary notice. When a preliminary notice has been sent, the contractor may record a mechanic's lien upon "completion" of the work, as defined in Civil Code section 8180, which can be actual completion, cessation of labor for 60 continuous days, or occupation or use by the owner coupled with cessation of labor.

You seem to have a bona fide dispute over liability. I would recommend using whatever dispute resolution methods are written into the contract, e.g., mediation, arbitration, etc. Contractors' ability to use the mechanic's lien gives them a powerful tool to enforce payment of the contract price by a suit to enforce the lien.

If your contract doesn't provide for a dispute resolution method, I'd suggest offering to submit the dispute to arbitration by a well-qualified third party, and/or that you retain an expert to inspect the crack and give you an opinion as to its cause. Note that there is some legal precedent for the notion that a contractor is not liable for damage that occurs when its work triggers a pre-existing condition and a job-site problem results.

The first thing you need to do is determine whether the crack is cosmetic or structural, i.e., does it actually meaningfully affect the integrity of the structure, and what the cost of repair would be if it is structural. Construction work is never perfect, and unless you can get a reputable expert to say the crack is a substantial defect, the contractor has a right to do a cosmetic patch and expect payment. If it is structural, your first step is to present that information to the contractor and demand they deal with it. If they refuse, you can refuse to pay them, and either sue them for the damage, or wait for them to record a lien and file an action to enforce it and then defend and cross-claim based on the damage.