oddity

You're wrong in a number of ways and searching the forums would grant an answer.

my post about it from hell knows how long ago: https://forums.sinsofasolarempire.com/329828
The core point is: shield mitigation. High level caps have up to 75% shield mitigation and Advent can have even more with pacts and in their own culture. Phase missiles bypass shields and shield mitigation as well, meaning that a missile that deals 100 damage (for the maths' sake only) would deal only ~20 damage to shields if it hits them (high shield mitigation), but if it DOES phase through shields, it deals full 100 damage to the hull.

Phase missiles (upgraded, in sufficient numbers) are the biggest nemesis of Advent. When the Advent player sports Shield restore on the progenitor and the iconus guardian's protective bubble (using both is generally called the "advent battleball"), it is NOT UNCOMMON to see advent ships GO DOWN WITH OVER HALF SHIELDS STILL UP, due to phase missile fire.

In fact, phase missiles are the only thing that saves Vasari vs Advent. So read through the forums and you'll understand why phase missiles rock ass.

PS. that doesn't mean the AI is good at using them. And the fighters disappeared because you have telekinetic push on the halcyon .

actually, most of them never even got TO my halcyon... only 2 squads made it through my halcyon lvl 6 ability superenhanced fighter squadrons and they were fighters not bombers. the hostile fleet started all the way across the map. With 6 fighter squadrons 5 of which had 15 fighters per unit against their maybe 10 squads total each with only 5 units the battle between our squadrons was very one sided... and halcyon bombers have very nice damage output. I thought I could prolly get 1 of those capital ships, but to eliminate all 3 plus their supporting frigates...

In order to combat that with vasari you would need to hold your fighters in their docks until your anti-fighter frigates had had a chance to whittle down the advent fighters or at the very least until the halcyon's squadron boost had worn off and THEN launch your squadrons. But during that time the advent bombers would have easy pickings which can't be good for you. I'll admit I wasn't even sure exactly what shield mitigation DID. That makes it sound a little better to have phase missiles.

Also I have taken the halcyon carrier at level 1 against nearly every type of other capital ship 1vs1 and it seems to win against everything. At least it does with the computer running it. Plus, the halcyon carrier once leveled to lvl 8+ usually has as many squads as a starbase so with the exception of vasari mobile bases, it can wipe out most computer worlds by itself since the comp doesnt usually spend much on getting hangers and more concentrates on mines and defense platforms which dont target squadrons at all. A fleet of about 10-12 LRMs can take out a low lvl capital ship, at higher levels capital ships eat frigates too rapidly for them to make a big splash. Plus the abilities of the capital ships start working together better so frigates start getting less and less of a threat unless their numbers are overwhelming... like 50+ ships per capital ship which pirate worlds can sometimes accumulate. At this point it may be better to get more support frigates rather than damage output because the damage output of frigates becomes increasingly nerfed as the game progresses. (Though it was kind of fun 1 game to purchase 1000 scout ships heh... they should make an achievment for that. Call it Scout Master or something. Or Lemming rush...)

This does sound pretty strange.  Unless your fighters killed all of the enemy strikecraft, they shouldn't just disappear.  The only other reason they would disappear would be if the AI had decided to send its fleet someplace else and they were preparing to jump, in which case the strikecraft return to their host.  It's possible that if you were using Telekinetic Push (from the Halcyon) that you might have killed all the strikecraft.

2 enemy capital ships, 30 frigates, and 3 carriers should have taken down your two capital ships.  Did you actually see the enemy ships die or is it possible that that fleet just jumped out of the gravity well?  Capital ships really don't have much firepower, especially a Progenitor and Halcyon.  (The only two that do have a lot of firepower are a Level 6 Marza (missile barrage) and a Level 6 Radiance (cleansing brilliance).)

If you actually killed them all with just those two capital ships, then I would chalk it up to the idiocy of the AI.  Real (human) opponents (in online multiplayer) would have knocked your capital ships down quickly, especially if they were Vasari.  You would have either been hit with nanites coming from an Evacuator capital ship and then focus-fired on with upgraded phase missiles or you would have been attacked by bomber spam coming from Skinatra carrier capital ships combined with upgraded phase missiles.

Maybe you did kill it all.  That just shows you how incompetent the AI is.

The phase missiles AVOID the shield mitigation.  You need to learn what shield mitigation is about.

When a shot hits the shields, 100% of its damage rating is not done to the shields.  A percentage of that damage is mitigated by the "shield mitigation".  So if a missile does say 10 points of damage and the shield mitigation is 40%, it really only knocks 6 points of damage off of the shields.  Shield mitigation increases as a ship takes more and more damage.  So at 57% only 43% of the damage is being done.

Phase missiles avoid the shield mitigation--a phase missile that does 10 points of damage avoids the 57% mitigation and does a full 100% 10 points of damage to the hull.  It's like doubling the amount of damage that the missile does.

Advent ships have weak hulls relative to the other races which is why phase missiles are such a good way to counter them.  Oftentimes (in online multiplayer) you will see Advent ships die while they still have 50% of their shields left because fully upgraded phase missiles destroyed the hull.  If you are playing against a Vasari opponent in online multiplayer, you would thus want to seriously consider upgrading your ships' hulls and perhaps armor (especially if it's cheap, like for the TEC).

That is strange.  I wouldn't think a Halcyon (which has a weak hull) would stack up against other capital ships.  Maybe if you gave it bombers it could do that.  I think that an Evacuator would easily knock down a Halcyon with Nanites.

Anyway, welcome to the Sins community.  I hope that you'll consider coming to play it online after you've played it for a couple weeks and learned the game.  You can play comp stomps (humans v. AI) and games against actual human opponents.  It's a lot of fun and many people have enjoyed many epic 4v4 and 5v5 games.  It doesn't take as long to play online as you might think, just 1-2 hours.  (In a 4v4 or 5v5 you don't have to kill all of the other players yourself, you only really have to kill one of them and normally the players on the losing team see the writing on the wall and surrender rather than make the winning team go through the boring motions of mopping it up.)

I suppose at level 9/8 the Progenitor might have been able to absorb the vast majority of damage if the enemy was using LF or other ineffective unit types, but this is still an odd scenario because you had very little firepower in this group; in fact, the Halcyon's strike craft probably account for the better half of your damage output.

As for your phase missile inquiry, I think the others have explained the matter quite well.  Phase missiles ignore shield mitigation, which basically means they deal more than double normal damage on bypass.  Against a capital ship, they deal triple normal damage on a bypass.  Absolutely deadly; easily the most fearsome upgrade in the game.