Thirty minutes.

If at any point you expect to touch down at the nearest safe airport with less than 30 minutes of fuel remaining, you are required by regulation to make a mayday call.

Mayday is a term enshrined in law. It is only to be used when people will die if you do not receive help. In the US, calling it inappropriately can be punished with up to 10 years in jail and a $250k fine. It's protected in this way because as soon as you call mayday, in many situations there are actions that must be taken by law or regulation. Other appropriate uses include things like "our plane is on fire" or "our wing just fell off and we can't steer the plane".

As soon as you think you can't land with the fuel reserves you are _required_ to call mayday, other pilots are _required_ to clear the radio for you, and ATC is _required_ to provide any and all supported possible until you're on the ground.

The investigation is not to figure out who to send to jail or something. The investigation is because a flight just came this >< close to having hundreds of people die. That fuel is there as a safety margin, yes. That's how everyone ended up walking off this plane instead of dying as the plane was ripped apart by some trees somewhere. That is good.

But air travel did not become as safe as it with an attitude of "this hasn't killed anyone yet, all good". The fact there was an incursion into the safety margin should not be looked at as "eh, working as intended" but "holy hell we just came this close to disaster, what went wrong that almost killed all these people? how do we stop that happening again?". That is what an investigation will be looking to figure out.

To put it in vaguely IT terms, this is something like... your application has started corrupting its database, but you have _a_ backup copy. On one hand, you can think "eh, we have a backup, that's what it's there for, who cares". On the other you can go "holy shit, any time we need to restore from the backup we narrowly averted disaster... how do we make sure we're not in that situation again?". The former is probably going to lead to irrecoverable data loss eventually. The second will have you addressing problems _before_ they ruin you.