Inventor applying weapon die increase to Blowgun or Dart Umbrella

[TiwazBlackhand]

Does the "1 damage" of a Blowgun or Dart Umbrella count as a damage die even though it's not an actual die?

I'm pretty sure it doubles on a crit and benefits from Striking runes.

But if you take weapon innovation, can you use the weapon die increase modifications to increase it, and if so what does it increase to?

[Cordell Kintner]

Relevant rule: https://2e.aonprd.com/Rules.aspx?ID=226

"1" damage is not a damage die, and is exempt from the rule.