I have always understood a phrase consisting of two nouns, where the latter alone has ה"א הידיעה, to be in סמיכות. Consequently, דיין האמת ought to be pointed דַּיַּן הָאֱמֶת, given that דַּיַּן (with פתח) is the constructive case of דַּיָּן (with קמץ).
And yet in an old נוסח בלדי siddur I have (תכלאל עץ חיים), the yod there is marked with קמץ and not פתח (I figured this might have been a typographical error, but סידור שיח ירושלים, too, invariably has it with קמץ):
What is the explanation here for דַּיָּן הָאֱמֶת (which is, presumably, in סמיכות)?