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What these certificates do
Many states issue a document — called a certificate of relief, certificate of rehabilitation, certificate of good conduct, or certificate of employability depending on the state — that removes automatic legal bars triggered by a conviction and creates a formal presumption of rehabilitation.
It does not hide or erase the conviction. What it does is give a licensing board, employer, or landlord an official finding to rely on, and in some states it limits their liability for hiring you.
No single authoritative source covers this nationally, so there is nothing to cite here. Treat it as orientation and confirm the detail where you live.