Cryptborn Horror rules and Wretched Anurid +1/+1 lost life counters

[Teddy]

If other player has not lost any life so far

he controls a Wretched Anurid

I cast Cryptborn Horror

Will it enter the battlefield with a +1/+1 counter or not?

[Arix]

No. The amount of life lost is determined just before Cryptborn Horror enters the battlefield, whereas Wretched Anurid only triggers after the creature has already entered.

[Tad]

wont ability of Wretched Anurid trigger and go on top of Cryptborn Horror ability, resolving first and causing opponent to lose life so that the horror gets the counter?

[Kenji]

No. The mistake here is believing that Cryptborn Horror has a triggered ability -- this is not the case. For reference, here's its text:

Trample
Cryptborn Horror enters the battlefield with X +1/+1 counters on it, where X is the total life lost by your opponents this turn.

If it were a triggered ability, it would say something along the lines of "When ~ enters the battlefield, put X +1/+1 counters on it...." [As an aside, a 0/0 creature with a triggered ability like this would also be in the graveyard before getting any counters.]

Remember this about triggered abilities:

112.3c Triggered abilities have a trigger condition and an effect. They are written as “[Trigger
condition], [effect],” and begin with the word “when,” “whenever,” or “at.” Whenever the
trigger event occurs, the ability is put on the stack the next time a player would receive priority
and stays there until it’s countered, it resolves, or it otherwise leaves the stack. See rule 603,
“Handling Triggered Abilities.”

Since its ability is not written like that, it's not a triggered ability. Rather, it's a static ability that modifies how it enters the battlefield. By the time Wretched Anurid's ability goes on the stack, Cryptborn Horror has already entered with a number of +1/+1 counters on it based on how much life opponents have lost this turn.

And, given the above scenario where the opponent hasn't lost any life this turn, that means the Cryptborn Horror enters as a 0/0 creature, and is sent to the graveyard as a state-based action before the Anurid's triggered ability even goes on the stack (and obviously, before it resolves).

I tried to make this as clear as possible, but if you still need help, feel free to ask!