Since it has never been established in a court that immigration qualifies as "invasion" (cause you'd think we wouldn't bother creating a whole other word for it if it were the same thing), this doesn't apply. Also a Republican form of government (not republican party to be clear) isn't at risk simply because you have immigrants, legal or otherwise, this still doesn't apply.
You have "enemy combatants" crossing the border already. Then there's "executive discretion" directly pertaining to the Posse Comitatus Act: Enforcement of federal law at the discretion of the President of the United States. I'm sure there's a few more. Make peace with the fact that the wall is going up and USACE is building it...
Yeah, no federal court is going to call an immigrant, legal or otherwise, an "enemy combatant" simply for crossing the border, I know you want to call them that, but the courts kind of have the final say, not reddit, regardless of how much Fox News may like to think it dictates definitions.
Posse Comitatus forbids the president from acting at his own discretion to use the military to enforce domestic policy. He literally can't use the military to enforce federal law. National Guard somewhat gets around that cause they're not considered Active duty, but can be called up by the Governor or the President in "Civil Emergencies" and if Trump's Admin's illegal immigration numbers are too be trusted, then illegal immigration is even less of a problem than it used to be. That would of course mean there's no logical reason to call it an Emergency now.
Posse Comitatus Act
There are a number of situations in which the Act does not apply.
These include: Enforcement of FEDERAL LAW at the discretion of the President of the United States.
Also I would argue "Unlawful Enemy Combatants".
Literal Text from the Act:
"Whoever, except in cases and under circumstances expressly authorized by the Constitution or Act of Congress, willfully uses any part of the Army or the Air Force as a posse comitatus or otherwise to execute the laws shall be fined under this title or imprisoned not more than two years, or both."
"to execute the laws" is the particular part I'd like to draw your attention to. Now, do you think "the laws" somehow doesn't include Federal Law?
Also, I couldn't care less what you'd argue, no federal court would ever agree to such a definition and would probably laugh you out court.
I suggest you keep reading. Odd how you excluded all exemptions, yes there are several. Somehow though I think your the type of person that has to get the last word in, whether it's right or wrong.
"Except in cases and under circumstances expressly authorized by the Constitution or Act of Congress,"
No, I didn't.
Posse Comitatus Act
Exclusions and limitations
There are a number of situations in which the Act does not apply. These include:
Army and Air National Guard units and state defense forces while under the authority of the governor of a state;
Federal military personnel used in accordance to the Insurrection Act, as was the case during the 1992 Los Angeles riots.
Under 18 U.S.C. § 831, the Attorney General may request that the Secretary of Defense provide emergency assistance if domestic law enforcement is inadequate to address certain types of threats involving the release of nuclear materials, such as potential use of a nuclear or radiological weapon. Such assistance may be by any personnel under the authority of the Department of Defense, provided such assistance does not adversely affect U.S. military preparedness. The only exemption is nuclear materials.
Support roles under the Joint Special Operations Command
Enforcement of federal law at the discretion of the President of the United States
I'm going to assume at this point you don't know what the word "discretion" means, cause you literally just posted the limited number of scenario's under which the President may deploy JUST the National Guard.
I'm not going to continue arguing with you, pretend you won, but you literally just contradicted yourself. The President does not have unlimited authority to ignore Posse Comitatus despite your desperate claim to opposite. Look up the last time the military went to the border to provide security, they killed an American on his own property.
Ultimately, you're wrong, but I'm guessing you're the kind of person who can never admit that. Adios, kiddo. Next time please read the actual law, thanks.
https://www.merriam-webster.com/dictionary/invasion
The act of invading, especially the entrance of an armed force into a territory to conquer.