Learn Spanish (Latin America): Ustedes no llevan terminados muchos pliegues simétricos hoy. - You haven't finished many symmetrical folds so far today.

Using llevar plus a past participle emphasizes the accumulation of a result up to the present moment. While han terminado just means 'have finished,' llevan terminados adds the nuance of 'have finished so far.' This ongoing count fits perfectly with the word hoy (today).

Why does terminados end in -os when it's part of a verb phrase?

In standard perfect tenses with haber (like han terminado), the past participle never changes. However, when you use llevar plus a past participle, the participle acts like an adjective describing the direct object. Since the direct object here is muchos pliegues (masculine plural), the participle must become terminados to match it.

Does the participle terminados have to come right after llevan?

No, you have flexibility. You could also place the direct object between them and say Ustedes no llevan muchos pliegues simétricos terminados hoy. Placing terminados right next to the verb puts slightly more focus on the state of completion, while placing it after the noun phrase makes it sound a bit more like a normal descriptive adjective. Both are perfectly natural.

How does the negative no affect the meaning of this accumulated quantity?