Does affinity for artifacts reduce a spell's cost below zero mana?

Affinity for artifacts (and affinity in general) works by reducing the generic mana component of a spell's total cost by 1 for each artifact you control. However, the Comprehensive Rules explicitly state that a total cost cannot be reduced below zero mana — meaning you can never get paid to cast a spell through cost reduction alone.

CR 601.2f governs the calculation of a spell's total cost. CR 118.7a states: 'If a cost is reduced by an amount of generic mana, the cost is reduced by that amount, but no mana payment can be reduced below zero.' This hard floor ensures cost reductions stop once the generic mana portion reaches zero.

It is important to note that affinity only reduces the generic mana portion of the cost, not colored mana symbols. So if a spell costs {3}{U} and you control 5 artifacts, affinity reduces the generic 3 to 0, but you still owe the {U}. The spell becomes free of generic mana, but is not completely free unless it had no colored mana requirements either.

Concrete example: You cast Frogmite, which costs {4}. You control 6 artifacts. Affinity would reduce the cost by 6, but the total cannot go below {0}. Frogmite simply costs {0} — you cast it for free, but you receive no mana back or further benefit from those extra artifacts.