I will start here with the basics of Jones I (the first article)

(Jones I, p.2)

1. Populace-Centric Engagement (PCE) ....

2. Threat-Centric Engagement (TCE) ....

3. Good Governance .....

4. U.S. Ideology ....
Leaving aside, for the time being, ## 3 & 4 (which will generate a lot of heat), and starting with a very, very basic situation, let's look at ## 1 & 2 from my vantage point - a big county geographically, a little county in population.

Here, we have the following law enforcement resources (leaving aside village and township police):

1. Michigan State Police Post.

2. County Sheriff's Office.

3. Two city police departments, and two public safety departments at the universities in the two cities.

Not a very large army, but they do co-operate and get the job done. How do they look at Population and Threat ? Here is the HoCoSO mission statement:

Our mission is to preserve and encourage a safe community and to enforce the law with compassion, fairness, honesty and integrity. We will enhance our commitment through hard work, education and technology.
http://www.houghtonsheriff.com/

The first clause ("...to preserve and encourage a safe community...") is certainly Populace-Centric; but what of the second ("...to enforce the law ..."). You have to ask "enforce the law against whom" - and, to that, the answer requires that there be a threat, usually carried out. So, at some point, Populace-Centric Engagement moves to Threat-Centric Engagement.

Now, our Sheriff "Slim" (who ain't slim) would not likely use those terms - "get that egghead stuff away from me, Mike" - but he would likely explain it in an historical example, as he has done here:

According to Anglo-Saxon custom, if someone broke the law it was not just a crime against the victim, but a crime against the whole community. ...
....
Under Anglo-Saxon rule it was the duty of the citizens themselves to see that the law was not broken, and if it was, to catch the offenders.....
Or, to translate what is clear to Slim and me, into the jargon of the articles: Populace-Centric Engagement of the Threat.

What you will find by talking to cops here (besides the fact that they are not dumb) is that they have a very good handle on their respective populations - admittedly small populations. So, they can tell you who are the "good people" (who sometimes do slip), the "bad people" (who slip regularly) and those "we're not sure of". Their focus is on the "bad people" and their associates (the ones "we're not sure of").

Once a "threat" develops to the probable cause stage (a "criminal"), then we are into the criminal justice system. Now, cops are not social workers - they do not have the resources to address the underlying problems which, if solved, might prevent a "threat" from reaching the "probable cause" stage.

It is in their own enlightened self-interest to assist in doing so, and also in the interests of their populations. But, as Sheriff Slim says, the mission is "to preserve and encourage a safe community", not to build one.

-------------------------------------------------
Some terms are not easily defined. My own take is that examples are often more enlightening than attempts at formal definitions. I am placing four terms in a rough pecking order, based on where they fit into the "flow chart" of GC III, Arts. 2, 3 and 4.

1. criminal - GC III is NA.

2. terrorist - GC III, Art. 3 ?

3. insurgent - GC III, Art. 3 or Art. 4; it depends.

4. belligerent - GC III, Art. 4

That is just a start.