“Truly” is threefold.

Truly means a truth is really, actually and genuinely true.

• Really true: accords with the what of reality.
• Actually true: accords with the how of action.
• Genuinely true: accords with why of a world that ought to exist.

* * *

I have also considered “authentic” as an alternative to “genuine” but genus evokes my intended meaning better than autos, especially in light of this pretty etymological entry from my dictionary:

1596, from L. genuinus “native, natural,” from root of gignere “beget” (see genus), perhaps infl. in form by contrasting adulterinus “spurious.” Alternative etymology is from L. genu “knee,” from an ancient custom of a father acknowledging paternity of a newborn by placing it on his knee.