‘Marine Corps Doctrinal Publication 1: Warfighting’ presents the concept of ‘Critical Vulnerability’. They define it as “… a vulnerability that, if exploited, will do most significant damage to the enemy’s ability to resist us”.

To Barney-style this for everyone, a ‘Critical Vulnerability’ is essentially where the opponent is weak and where we should attack to get the outcome we desire. Attack them where they are weak!

I am sure plenty of people just said, “No shit, but how?”.

Let’s look at it.

There are 4 parts of the body (really could be 3) in Mathematical Jiu-Jitsu that are deemed ‘Critical Vulnerabilities’:

1. Head
2. Shoulders
3. Hips
4. Spine

This should be obvious to some people that attacking these vulnerabilities absolutely makes it difficult for our opponent to resist our will, but that is the case for any submission, right?

Here is what makes these different, and why I call these refer to these as Flow Controls in Mathematical Jiu-Jitsu.

• If I have control of your head, I am dictating a lot in what happens. Head control of your opponent can dictate distances, where they put their power, etc. 
• If I have control of a shoulder, I control where you can move and face (amongst others). The same is to be said of the hip.

So, what am I saying?

To gain or maintain control, we use Flow Controls that capitalize on these Critical Vulnerabilities… but instead of doing it for the submission, they are taught as methods of control at fundamental level. 

Basically, while you might see some flow controls as submissions, we see them as fundamentals and do not train them for submission use at fundamental level. Below are the Core Flow Controls in Mathematical Jiu-Jitsu.

Critical Vulnerability (Flow) Control 1: The Guillotine (everyone knows what this is, I hope).

• If I take a standing guillotine position, I don’t need to choke you – I have control of your head. I can use this for many purposes outside of submissions to gain positional dominance.
• I don’t need to submit you to control you with this position.

Critical Vulnerability (Flow) Control 2: The Kimura (double wristlock).

• If I take a proper kimura on the ground, I can control your body from that position alone. I can use this for many purposes outside of submissions to gain positional dominance.
• I don’t need to submit you to control you with this position

Critical Vulnerability (Flow) Control 3: The Hip Lock (the what?)

• If I take a hip lock (deep reap with a leg thread, or a Z-lock style setup), I can control your body position from there. I can dictate your movement and use this for many purposes outside of submissions to gain positional dominance.
• I don’t need to submit you to control you with this position.
• Most people in Jiu-Jitsu seem to have no concept of this.

Critical Vulnerability (Flow) Control 4: The Cradle (Don’t be scared)

• If I put you in a cradle, your power is very limited. I can dictate your movement and use this for many purposes outside of submissions to gain or maintain positional dominance.
• I don’t need to submit you to control you with this position.
• Most people in Jiu-Jitsu seem to be afraid of this position.

Positional dominance is the name of the game in fundamentals, but understanding the Critical Vulnerabilities of the body and having Flow Controls for them enables you to compliment your positional repertoire.

In Mathematical Jiu-Jitsu, White Belts do not learn to use submissions since submissions are not seen as fundamental. Instead, they learn Critical Vulnerability (Flow) Controls to enhance their ability to take dominant positions and control the flow of a situation.