I learned recently an interesting halachic idea that you can discern an unclear case from how future unfolds. That is, if a korban intention was not stated clearly, you might be able to ascertain it from the actions that followed. This is applicable to unverifiable giur – if you see some years later that the ger is behaving appropriately (at a minimal level – keeping kosher, lighting shabbos candles), then the giyur can be confirmed retroactively. Consult your local beis din, don’t try it at home.
