How invulnerable can you make a gate door?

Question

There exists a mighty stronghold on a bountiful greater demiplane. The only way in is through a permanent planar gate on the material plane, around which has been built a great and legendary door. During peacetime, it is open and unsealed for all to pass through.

From Create Demiplane, Greater:

Portal: Your demiplane gains a permanent gate to one location on another plane, which can only be used for planar travel. This location must be very familiar to you. This gate is always open and usable from both sides, but you can secure it using normal means (such as by building a door around it).

However, a great invasion is on the horizon. They will soon arrive to siege the stronghold and attempt to break down/through/into the gate. If the army is able to enter through the gate, the stronghold will surely fall, those inside will be destroyed, and it will usher in a new age of darkness, yadda yadda yadda. Assume the invaders cannot simply teleport into the stronghold, nor can they break in through any avenue other than this gate.

The stronghold has had sufficent warning to make any preparations they wish, and they will naturally seal the gate door shut with everything they have. The inhabitants of the stronghold have access to any non-mythic spell or class ability that can be used at level 20 or below, and unlimited funding. They can cast on either side of the door beforehand, but once the invasion arrives, they can only cast on their side of the door. They will not engage in open warfare.

How invulnerable can they make this gate door?

The siege has no particular time window or limit, so only effects with permanent duration or that can be refreshed from inside are worthy of consideration. The inhabitants of the stronghold are self-sufficient, and cannot be starved out.

Is it possible to hold this door forever against invaders with similar resources? If not, how long could the stronghold hold out? What level of invaders could be indefinitely repelled?

This answer suggests the hardness of an object can be permanently increased to an absurd degree if one is willing to sacrifice a lot of living creatures to it, using repeated castings of Death Knell and Hardening. It's a pretty evil thing to do, but maybe the door itself was built and hardened by some evil architects and plundered from its workshop by the forces of good. Notably though,

The hardening spell does not in any way affect resistance to other forms of transformation.

So I imagine there are plenty of ways to get around a door regardless of hardness. I'm looking for reliable non-time-limited countermeasures for such methods.

(Also, keep in mind that if the army of darkness should eventually decide to give up and goes home, the gate must be able to return to functional use.)

Answer 1

I submit that there is no way to guarantee that an arbitrary number of 20th level PCs with an arbitrary amount of wealth cannot do X, for any given value of X, short of direct divine intervention (read: GM fiat).

For the attackers, X is either "gain entry to a demiplane created via Create Deimplane" or "bypass a door". For them, magics like Mage's Disjunction, Wish, and Miracle are extremely powerful: any one of them will eventually remove any magical protection on the door and the latter two will also eventually be able to grant entry to the demiplane as by Plane Shift/Gate.

On the other hand, the denizens of the demiplane are perfectly safe: for them, X is "repel entry by the bad guys". Again, Wish and Miracle will be useful, as might Wall of Force (helps keep out pesky ethereal creatures), Teleport Trap, Dimensional Lock, and even Antimagic Field and Contingency. The defenders make an arbitrary number of similarly-impassable doors, and use Contingency to add an effect to them that causes the next one in line to be put in place when the current one is destroyed. Or, instead of a door proper, put the gate in a Golem of some sort (Adamantine and Quintessence look interesting) and tack on some extra protections (probably including an item that spams Make Whole on said golem).

The best you can hope for, mechanically, is a Gambit Pileup (warning: tvtropes) as the various measures, counter-measures, counter-counter-measures, etc. all vie for control, or the amazing cleric fight from OOTS. That is, both sides have their own Pun-Pun, both of whom fight it out for all of eternity.

At the end of the day, though, the GM will have to decide whether the sanctum is breached, and the decision will almost certainly be based on which outcome best serves the story.

Pathfinder (along with probably all other RPGs) breaks hard when the limits are removed. I've played this game whilst imagining how to protect a 3.5 demilich's phylactery; eventually, everything included "and a way to summon the demilich back if all else fails".

Answer 2

You need DM fiat.

This is very similar to minnmass's answer, but I am, in part, basing it on the Emerald Spire Superdungeon.

Doors are meant to be opened.

At the lower floors of the dungeon, you encounter the following:

If characters who can read multiple languages investigate the runes on the bronze doors, they determine that the runes all say the same thing: the word “warning” repeated over and over again in more than a hundred different languages. Every language the PCs speak is represented here somewhere, as well as many they have never seen before— including languages originating from other planets and planes of existence.

This is, very clearly, intended to be a substantial obstacle. I've submitted this as a separate answer because it's a canonical example of a door that is intended to be extremely difficult to surpass:

This is the door’s keyhole—the doors can be unlocked with the key in area O10 or with a successful DC 40 Disable Device check. In addition to the heavy bronze, the doors were forged with powerful magic that takes its energy from the Spire itself,giving the doors DR 30/epic and making them impossible for normal creatures like the PCs, the inevitables, or the proteans to break or force open.

This isn't to say that this is the highest possible bar for an insurmountable barrier, but it's what Paizo considered to be a nigh-insurmountable barrier. At the end of the day, it's an arms race: the creatures trying to keep the door closed have access to everything, including Wish and Miracle. The creatures trying to get the door open have access to everything, including Wish and Miracle.

An unopenable door cannot be a door.

There's not really any upper bound as to what spellcasting can do to any sort of barrier. 9th level spells are basically unraveling the fabric of reality. If something can be opened, it will be, if your Wish is good enough or if your deity is willing to give you your Miracle. You can secure it as much as you'd like, but 9th level spells can invalidate basically anything: they invalidate it with DM fiat, but that means that they don't invalidate it with DM fiat too. Either way, the DM arbitrarily says "your Wish succeeds/fails" or "your deity does/doesn't grant the Miracle."

Answer 3

Narrative should defeat rules

The door should be able to resist the amount of time you, as a DM would want, creating a climax in the moment it's traversed.

Pure application of rules and spells described on the books is fine, but limits your story to a duel of book search looking for the most strange and broken spell.

Magic is much more than a simple list of spells. Elaborate a narrative of several powerful mages applying strange and forbidden magic rituals, directed by the most powerful mage on the city. If you want to involve your players, make them run errands looking for components for the ritual, if they accomplish such tasks the ritual is succesful and the door will be capable to hold everything the antagonists throw at it... until you need it otherwise... if you want it to resist, make it to resist, if you want to play the invasion and a desperate resistance on the inside of the city, make a powerful scene where the ritual magic is destroyed, ruining the hopes of your players to survive the attack without having to fight inside the city.

Make the story yours, make it fun, make it unexpected, and don't let a simple rule or spell to ruin your story.