Mana Vault + Damping Matrix(+ question for bonus points)

[Limbo]

Yesterday during the Eindhoven tournament the following problem was encountered. A player had both mana vault (tapped) and Damping Matrix in play. Question was if he could untap his mana vault during his upkeep or not. Because the judge wasn't 100% sure, he asked me for a 2nd opinion and together we concluded the following:

At the beginning of your upkeep a triggered ability is put on the stack. However, as the wording involves cost : effect, it is also an activated ability if you would choose to pay for it. Hence, Damping Matrix DOES NOT prevent the triggered ability from going on the stack. It DOES prevent a player actually activating it by paying 4 mana though. The problem here is probably that because of the "do it during your upkeep thingie" the wording for the activated ability is somewhat different from the usual 4 : untap this.

Is this "assumption" correct?

Also, if the vaults ability is both Triggered and Activated, I assume a player can stifle either the trigger itself (preventing a player to pay 4) or the activation (making the player waste 4 mana in an attempt to untap it). Right?

Some relevant crystal keeping:

Mana Vault
At the beginning of your upkeep, you may pay . If you do, untap ~this~.

Damping Matrix
Activated abilities of artifacts and creatures can't be played unless they're mana abilities.

Activated Abilities
An activated ability is written as "[cost]: [effect]." The activation cost is everything before the colon (.

Triggered Abilities
A triggered ability begins with the word "when," "whenever," or "at." The phrase containing one of these words is the trigger condition, which defines the trigger event.

PS: Would a mod be so nice to change the title into Damping Matrix, instead of Damping Engine...

[DEA]

sorry to be so frank, but if your judge doesn't know the answer to this, he shouldn't even be judging at all
it's a triggered ability, and there is no : or activatedness about it
so, damping matrix doesn't stop it
the oracle text is what you posted, and if you look at it there is utterly no confusion
it does however stop grim monolith

[Kerith]

Mana Vault
, Artifact
Mana Vault doesn't untap during your untap step.
At the beginning of your upkeep, you may pay . If you do, untap Mana Vault.
At the beginning of your draw step, if Mana Vault is tapped, it deals 1 damage to you.
: Add to your mana pool.

The untapping is a triggered ability that is put onto the stack "At the beginning of your upkeep". When it resolves, you either pay 4 and untap it or you don't. There is no activated ability involved, so Damping Matrix has no effect there.
That also means that you can Stifle the trigger, but once it resolves, you can't do anything about it.

[Limbo]

sorry to be so frank, but if your judge doesn't know the answer to this, he shouldn't even be judging at all

As fas as I know, judges are human too. Therefore they can make mistakes. Btw, this didn't only trick the judge, but a bunch of very experienced players as well, and they all agreed on the solution.

*hops back on topic*

The way you two explain it, it seems logical as well. At the moment, I give your answers like the 75/25 advantage. As soon as Jebus backs up your answer as well, I will inform the judge about the mistake, so he can prevent this in the future.

[Jebus]

Seriously, I don't see how this can be that confusing at all if you have the Oracle text.

It's a triggered ability.  Damping Matrix has no interaction at all.

You seem to have inserted a colon where there is none.

There's no such thing as a triggered AND activated ability.

[Limbo]

Ok, thanks again for clearing it up. Luckily the error did not result in a gameloss because of the mentioned damage, so let's call it acquiring some more knowledge of the general rules