The beam curvature evolved from structural considerations.
Initially the obvious choice seemed to be a simple ‘arch’ shape (as viewed from the front), possibly with tightening curvature approaching the hulls.
However such a shape has the drawback that any deflection increases the distance between the hulls.
If you imagine a straight beam deflecting, you can see that the ends move closer together.
With an arch shape that is intuitively strong, the ends move apart instead. That is why gothic cathedrals have flying buttresses…
With properly engineered beams, the deflection in normal conditions is small but it cannot be zero. Pushing the hulls apart decreases toe-in of the foils, reducing the angle of attack of the leeward loaded foil and increasing that of the windward (likely surface piercing) one.
With angled or curved foils this also reduces the amount of vertical lift available.
So our chosen solution is a compromise to combine global platform stiffness and water clearance.
The downward turn in the ends makes the junction with the hulls more normal (closer to a right angle) minimising drag when the junction is splashed by waves.
It also maximises clearance near the leeward hull, where it is most needed.
Beam size increases toward the centre as bending moment increases.
The plugs include extensions at the ends where the beams plunge into the hulls.
Finally the box shapes you can see on the hull plugs are to house inserts that determine whether a hull is a port or starboard one.
The machined inserts include detailing for beam junctions (when making inboard hulls) and foil cases (when making outboard ones).
These features are obviously different for each half of each hull so there are four sets oncluding blanks where the hull being made has no features in that area.