Does a synthesist eidolon actually take damage?

Question

I'm asking myself if the eidolon of a synthesist actually takes damage.

While fused with his eidolon, the synthesist uses the eidolon’s physical ability scores (Strength, Dexterity, and Constitution), but retains his own mental ability scores (Intelligence, Wisdom, and Charisma). The synthesist gains the eidolon’s hit points as temporary hit points. When these hit points reach 0, the eidolon is killed and sent back to its home plane. ...

The rule states, that you get the eidolon hp as temporary hp. However, it is not directly mentioned, that the eidolon takes damage. Instead, your temporary hit points are reduced.

I'm sure that I'm misunderstanding something, as this would imply letting the temp hp drop to 1, dismiss the eidolon and summon it, gaining its hp (still unchanged and in full) as temp hp. It is implied, that the eidolon takes damage by lowering the temp hp, but does it keep this value as its actual hp?

Answer 1

Yes

Note the particular wording of what you've quoted from the synthesist archetype, "The synthesist gains the eidolon’s hit points as temporary hit points."

Those temporary hit points are the eidolon's hit points, so the missing would still be gone if the summoner dismissed then re-summoned the eidolon per the standard rules for eidolons.

A summoner can summon his eidolon in a ritual that takes 1 minute to perform. When summoned in this way, the eidolon hit points are unchanged from the last time it was summoned. The only exception to this is if the eidolon was slain, in which case it returns with half its normal hit points. The eidolon does not heal naturally.

Answer 2

The synthesist’s fused eidolon isn’t a separate creature, not really, not in game terms. It doesn’t have its own space, AC, saves, and so on. It doesn’t get targeted separately from the synthesist. Instead, it’s more like a buff effect that’s operating on the synthesist, albeit a strange one.

Which means not only does the fused eidolon not lose hp, it doesn’t even have hp to lose. It’s not a creature with hp. It’s a buff that grants temporary hp, and has the unusual condition that it ends when those temporary hp are lost.

The reason you see references to a creature, with stats, is because of the unusual way the bonuses of the fused eidolon buff are calculated—you stat out a non-fused eidolon creature, as normal for a summoner, and then you use that creature’s stats to determine the effect of your fused eidolon buff. But until the summoner gets split forms at 16th level, the non-fused eidolon creature never actually appears in the game world. The synthesist has no ability to summon it un-fused until then. The stats you create with it are hypothetical, an intermediate step in determining the effect of your fused eidolon buff.