31 weeks and 3cm dilate and 76% effaced is labor close?

I hope not: Hopefully you are writing this from being on bedrest and in consultation with a high risk OB and your own ob. Many things can be done to slow down or stop preterm labor. Every day you can give your baby inside is a huge benefit on the outside and long term. Please avail yourself and your child the best treatments for stopping preterm labor, for maturing baby's lungs, etc, for best outcome.

PREMATURE LABOR: Yes especially accompanied by close interval of uterine contractions.

Depends: First pregnancy? Size of previous? Length of labor? What has been the progression? And accuracy of your dates. A number of important variables but effacing and dilating are always toward the end!