Does Arcane Signet count as a mana ability that can be activated without using the stack?

Arcane Signet has an activated ability that produces mana. Under CR 605.1, a mana ability is an activated ability that (a) isn't a loyalty ability, (b) doesn't have a target, and (c) could add mana to a player's mana pool when it resolves. Arcane Signet meets all three criteria.

Because it qualifies as a mana ability under CR 605.1, it is governed by CR 605.3a: mana abilities don't use the stack. They are activated and resolve immediately, meaning opponents cannot respond by casting instants or activating abilities in between.

This is an important distinction from regular activated abilities, which do go on the stack (CR 602.2) and can be responded to. Arcane Signet's ability bypasses that process entirely due to its mana ability status.

Example: Your opponent controls a Stifle and you tap Arcane Signet to produce one mana of any color in your commander's color identity. Your opponent cannot cast Stifle to counter the ability, because Arcane Signet's mana ability never goes on the stack and therefore cannot be targeted or countered by Stifle.

Note: If Arcane Signet somehow gained a target (e.g., via a strange text-change effect), it would lose its mana ability status and use the stack normally. But as printed, it is always a mana ability.