Smallest garrison defense for a besieged citadel?

[Kataphractos]

So in the course of playing SS, a question has come to mind every once in awhile. It goes as follows:

Assuming a citadel has the cannon towers upgrade, and a full stack army lays siege and attacks, what is the smallest possible garrison that could mount a successful defense? Overall losses are no factor and total destruction of the attacking force is not necessary, the defenders just have to be victorious at the end. Also, what faction would be best suited for it?

The attacking army can have up to three artillery pieces, but I've never seen the AI target towers, so I'd assume they'd just be used to punch holes in the walls and that's that and then run their troops by the towers as they try to get in. Constructed equipment is standard for the AI: maybe two rams, a siege tower, and two or three ladders (assume they waited only one turn to attack). The rest of the attacker's make up is a standard army for that faction.

The defending garrison can be of any make up.

Personally, I'd say no fewer than six units could do it...I'd go with two stake-laying archer units and the other four as spearmen-type units. I'd lay the first line of stakes somewhere before the third gate at a chokepoint that the AI cannot go around, forcing their units to run through them (lol cavalry), and then the second line of stakes behind the third gate and then pile my spearmen around it in scintillation (yeah I totally spelled that wrong) formations. The archers I'd initially have running back and forth on the walls to activate the cannon towers and gate oil until either the gate is rammed open or artillery opens a hole in the wall, pulling them back as the main army enters the breach (making sure to keep them on the walls and out of harm's way for the most part) and then do the same for the second wall before falling back to the third wall and then parking them around the third gate for the final showdown.

Alternatively, I'd swap out one spearmen unit for another stake-laying archer unit for a third line of stakes; these I'd put right behind the second gate.

So could something like this be done? Or has anyone managed a successful defense against a full stack with a smaller garrison?

[Duck of Death]

Ive won plenty of siege-defense battles against a full stack (or more) with 4 or even 3 units defending... but it depends greatly on what kind of units the attacking AI has.
If the AI attacks with lower-level peasntry or the like and I have top-notch spear/pike militia, its different then if the AI attacks with a full stack of knights, or norse archers, or light or heavy infantry, cavalry.

For general purposes (not knowing for sure what kind of army youll be facing before they arive), Id say 3 of your best available spear/pike units, 2 of your best archer units and 1 cavalry unit (general if possible) is the best if youre talking 6 units.

For 4 units, Id say 3 spear/pike and 1 archer.

For example, In my current campaign... Im Scotland, its 1320ish, I have heavy pike militia in most of my cities.
I got attacked a few turns ago with about 3/4 of a stack (mixed units... overall id say a slightly above average army).
I had 3 heavy pikes, 2 highland archers and a general and I slaughtered the attackers from Norway.
The pre-fight prediction was 4-1 against me. I think I lost about 10% of my men to his 50% for a heroic victory.

[Alfonzo over Innsmouths]

I managed to, as Norway, win a battle against an attacking Moorish force in a cannon-towered fortress using two very depleted units of Vikings (barely making up a 'half' unit), half unit of huskarls, a unit of Svenner, a spear militia unit and a unit of djrengar. Then again, the Moors were predominantly cavalry and didn't grasp the use of their siege engines effectively.

[❋ Flavius Belisarius ❋]

With the Byzantines my strategy is not to defend the wall (when I'm outnumber) but to place my forces in the center of the city, where they will not be able to flee. Once the enemies manage to enter my city they will go directly to the city center where the soldiers waiting. Two units of archer (with the fire option) shoot them as they advance and start to reduce their moral.
I then placed in front line units with Spears. I place one on top of the other to form a compact wall of launches that will also decrease the morale of opponents (because each enemy unit will figh against many of mine at the same time, I don't know if I clear enough)
And finally behind I place my elites units. With this system I was able to keep all my Eastern landswhile using few men and by making war on the West. With 6 units I resiste against three full stack of Egyptian in Cyprus.