Ore-Rich Stalactite // Cosmium Catalyst — ruling 1

You choose whether or not to cast the exiled card as Cosmium Catalyst's activated ability resolves. If you do, you do so as part of the resolution of that ability. You can't wait to cast it later in the turn. Timing restrictions based on the card's type are ignored.

Ore-Rich Stalactite // Cosmium Catalyst — ruling 2

If you cast a card "without paying its mana cost," you can't pay any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, those must be paid to cast the card.

Ore-Rich Stalactite // Cosmium Catalyst — ruling 3

If the card has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

Ore-Rich Stalactite // Cosmium Catalyst — ruling 4

The back faces of some cards with craft refer to cards "used to craft" it. This refers to the cards exiled as part of the cost of the craft ability of the front face. Those cards are considered to be "used to craft" that permanent as long as they remain exiled and the permanent remains on the battlefield, even if the permanent's controller changes or some of its characteristics change (because of a copy effect, for example.)

Ore-Rich Stalactite // Cosmium Catalyst — ruling 5

If the materials required include multiple objects, you may exile some of them from among permanents you control and the rest from among cards in your graveyard. You don't have to choose all permanents or all cards from your graveyard.

Ore-Rich Stalactite // Cosmium Catalyst — ruling 6

You may exile tokens you control as part of the materials required. However, because they aren't cards and won't stay in exile, any abilities that refer to what you "used to craft" the back faces won't refer to anything.

Ore-Rich Stalactite // Cosmium Catalyst — ruling 7

If a card that isn't a transforming double-faced card becomes a copy of a card with craft, it'll stay in exile if you activate the craft ability. It won't return to the battlefield.

Ore-Rich Stalactite // Cosmium Catalyst : règles, fonctionnement et interactions (MTG)

Ore-Rich Stalactite // Cosmium Catalyst is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

: Add . Spend this mana only to cast an instant or sorcery spell. Craft with four or more red instant and/or sorcery cards (, Exile this artifact, Exile the four or more from your graveyard: Return this card transformed under its owner's control. Craft only as a sorcery.) , : Choose an exiled card used to craft this artifact at random. You may cast that card without paying its mana cost.

How it works : Ore-Rich Stalactite // Cosmium Catalyst

Original English text — Wizards of the Coast / Scryfall

#1November 10, 2023· Wizards of the Coast
You choose whether or not to cast the exiled card as Cosmium Catalyst's activated ability resolves. If you do, you do so as part of the resolution of that ability. You can't wait to cast it later in the turn. Timing restrictions based on the card's type are ignored.
No other card is named in this ruling.
#2November 10, 2023· Wizards of the Coast
If you cast a card "without paying its mana cost," you can't pay any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, those must be paid to cast the card.
No other card is named in this ruling.
#3November 10, 2023· Wizards of the Coast
If the card has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
No other card is named in this ruling.
#4November 10, 2023· Wizards of the Coast
The back faces of some cards with craft refer to cards "used to craft" it. This refers to the cards exiled as part of the cost of the craft ability of the front face. Those cards are considered to be "used to craft" that permanent as long as they remain exiled and the permanent remains on the battlefield, even if the permanent's controller changes or some of its characteristics change (because of a copy effect, for example.)
No other card is named in this ruling.
#5November 10, 2023· Wizards of the Coast
If the materials required include multiple objects, you may exile some of them from among permanents you control and the rest from among cards in your graveyard. You don't have to choose all permanents or all cards from your graveyard.
No other card is named in this ruling.
#6November 10, 2023· Wizards of the Coast
You may exile tokens you control as part of the materials required. However, because they aren't cards and won't stay in exile, any abilities that refer to what you "used to craft" the back faces won't refer to anything.
No other card is named in this ruling.
#7November 10, 2023· Wizards of the Coast
If a card that isn't a transforming double-faced card becomes a copy of a card with craft, it'll stay in exile if you activate the craft ability. It won't return to the battlefield.
No other card is named in this ruling.