What defines a person's conviction under the Texas Private Security Act?

The correct choice highlights that a person's conviction under the Texas Private Security Act is specifically defined as a court judgment for an offense. This means that a conviction is a formal legal finding by a court that an individual has been found guilty of a crime, resulting in a legal record that reflects the individual’s culpability. Such convictions are critical for regulatory purposes, particularly in the security industry, where background checks and criminal histories are essential to assess an individual's suitability for employment in positions of responsibility.

In the context of the Texas Private Security Bureau, having an official court judgment is important because it establishes a clear and documented basis for determining an individual's qualifications and potential disqualifications for a license in the private security field. This legal definition ensures that only offenses that have gone through the judicial process, which validates the charges and concludes with a legally binding judgment, are considered when evaluating a person’s history.

The other options involve different aspects of legal proceedings or informal acknowledgments that do not meet the statutory criteria for a conviction under the act. An arrest without a court judgment does not equate to a conviction, as it does not reflect a determination of guilt. A verbal acknowledgment of an offense may indicate the person's admission but lacks the formal validation that comes with a court judgment.