Is it permissible for a claimant to swear an oath before a judge concerning approximate dates or numbers based on memory due to the absence of precise documents, such as estimating overtime hours or the service start date, while knowing the possibility of inaccuracy in the estimation?

You are permitted to take an oath if you are certain that what you are swearing about is your right or less than your right. You are not permitted to take an oath if you are not certain, even if you strongly believe it is your right, because the default assumption is that the company's liability is cleared, and it is not removed except with certainty. Oaths in the context of claims must be definitive. If you are not certain of your right and you swear definitively, you would be a liar.