
Blave |

This has been discussed in the past. Since the Fatal trait doesn't increase the damage die size but sets it to another value it may or may not stack.
The unanswered question is whether you apply Deific Weapon before or after the die change.
There's no offical answer to that question, so you should ask your GM how to handle this.

BigHatMarisa |

Fatal dice aren't the weapon's inherent weapon damage dice, so I feel like the intent is no. Deific Weapon increases the weapon's inherent damage dice, so I'd say "similarly to how Deific Weapon wouldn't increase the damage of a Flaming rune applied to a deity's favored simple weapon, it wouldn't increase its Fatal dice size either."
You could also wrangle the "specific>general" clause here in a dumb, fishy way to say "Deific Weapon is what the weapon's general dice size is now, and Fatal is the specific die size it increases to, no matter what."

TheFinish |
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Why would Fatal change? The wording here is pretty clear:
Deific Weapon: "You zealously bear your deity’s favored weapon. If it’s an unarmed attack with a d4 damage die or a simple weapon, increase the damage die by one step (d4 to d6, d6 to d8, d8 to d10, d10 to d12)."
So the Frying Pan becomes a d6 weapon, assuming there is a deity that favors it.
Fatal: "The fatal trait includes a die size. On a critical hit, the weapon’s damage die increases to that die size instead of the normal die size, and the weapon adds one additional damage die of the listed size."
You can only ever have one die size increase, no matter what (Player Core, page 276).
The Frying Pan is Fatal d8. If you have Deific Weapon (or Deadly Simplicity), you have an ongoing effect increasing your die size from d4 to d6. When you crit, the dice would increase to d8. This is where the rule ambiguity arises.
Nothing in the sidebar indicates the player gets to choose which increase to apply, so it could be that:
- The die size remains d6 (Deific Weapon takes precedence), but you add a d8 (from Fatal).
- The weapon's damage dice all become d8 (Fatal takes precedence) and you add a d8 (from Fatal).
I'd go for the second option just because it's what makes the most sense to me, but while I can see people arguing for the other, at no point would you ever make the Frying Pan Fatal d10.