It's recommended, yet not required to have 2 weeks of consistent activity on the server you chose to apply on. Your application is decent as for your recent punishments - I highly doubt you have any due to your "activity" in the last 2 weeks on TTT. Improve your presence in the community by playing more, be polite and try your best to avoid any kind of action which could possibly lead to an inconvenience/rulebreak. Best of luck!
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