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Basic answer: There's no differentiation between those items and regular other items you can't just pick up. The system doesn't have exceptions to tell it that the pike should be able to be mushroomed but not picked up, while the statue in the room can't be mushroomed or picked up.We'll fix it up when time permits!
Tecton, the Terraformer has bestowed His divine favour upon you. It will last for approximately 1 Achaean month.
@Kresslack : The simple reason mushroom sigils cannot be attached to these things is that mushroom sigils can only be attached to mashed potato sigils. Mushroom mashed potato sigils not only blow up for 9001 damage, but they also erase any hunger you might have felt while increasing your weight by 1.3 pounds for 3/4s of a month.