I'll start this with Lyle's analysis of the new standard, which goes into far more detail than in the excerpt below:

U.S. defines its claim to detention power
Friday, March 13th, 2009 3:04 pm | Lyle Denniston
....
The Obama Administration disclosed on Friday that it will no longer claim the power to detain terrorism suspects under the label “enemy combatant,” even while claiming broad authority to detain those who are a part of terrorist networks or who supplied “substantial support” to such forces. The authority, it said, extends to places other than battlefields if [in] Afghanistan, but did not say where else detainees might be seized.

The document cast[s] aside a claim by the former Bush Administration that the President has detention power solely because of his role as Commander-in-Chief.

It told a federal judge that it is “refining” its claim of detention authority, relying on Congress’ resolution passed after the 9/11 terrorist attacks and on “principles of the laws of war.” It proposed a new definition of that authority, for use as Guantanamo Bay prisoners’ habeas challenges moved forward in federal civilian courts. But it said it may alter its detention policies after a wide-ranging, inter-agency review is completed in about six months.

From the congressional resolution, as “informed by” laws-of-war principles, the Justice Department defined detention authority as aimed at individuals who “substantially supported” terrorist groups or other armed groups, as well as those it directly linked to Al Qaeda and Taliban networks. ....
While everyone (hopefully) is reading Lyle's analysis (and the cited links), I will go about slogging through the links.

Three thoughts came to mind when Fox briefly flashed the definition (confirmed by Lyle's article):

“The President has the authority to detain persons that the President determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, and persons who harbored those responsible for those attacks. The President also has the authority to detain persons who were part of, or substantially supported, Taliban or al-Qaida forces or associated forces that are engaged in hostilities against the United States or its coalition partners, including any peson who has committed a belligerent act, or has directly supported hostilities, in aid of such enemy armed forces.”
1. The term "person" has a much broader meaning than the term "combatant" (as that term is normally defined under the Laws of War as we know them).

2. The word "substantial" ("material" would be a virtual cognate legally) is what we call a "litigation word" - that is, its limits are a mixed question of fact and law in the particular case.

3. The definition is population-centric (persons, which would to me include infrastructure and auxilliary persons, as well as including, but not limited to, "any peson who has committed a belligerent act, or has directly supported hostilities, in aid of such enemy armed forces") - as opposed to threat-centric (enemy combatants).[*]

More later.

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[*] See, BW, I do read your screeds.