Design Revision Provenance
It is likely that the same people or closely associated subordinates of the courtiers attended to the second phase of the design. The geometric and methodic nature of the second design phase requires similar geometric and mathematical skills demonstrated in the first phase. Furthermore, it requires a thorough understanding of the concept design (page 101).
Setting aside the question of who made the design changes, the more basic question is what motivated the tower redesign. The likely answer is readily deduced.
The concept design defined tower with deep walls, so much that the opening left in the center of each tower is small, folio 102:01.
The small open space compared to the thick wall discounts the likelihood that the tower design was intended for defensive purposes as advance by some scholars. What good would it make to have impregnable walls if the open space inside the tower was inadequate for defenders to move and function?
On the other hand, the heavy walls make perfect sense if the towers were intended as piers for the lateral thrusts in the formulation of this design. The thick wall results in masonry that takes 90% of the tower volume. This leaves 10% of the volume open in the center of the tower, folio 102:02.
This small opening, repeated in each of the eight towers, is the only space left in the design of the castle to locate services, such as stairwells needed for accessing the upper floor and the roof, folios 102:03 and 102:04.
This was a design of ideas that celebrates the grandiosity of cross vaults and the clean geometry of spaces, the style that Heinz Götze calls the Hohenstaufen architecture.
Functionality was clearly not a concern in the design. Services (stairwells, sanitary services, water tanks) were fitted within the tower spaces much later in the design.
The opening in the center of the tower in the concept design is an octagonal area with a maximum aperture of 2.5 meter (81% the side of the tower octagon).
A spiral stairwell is the only type of stairs that can be fitted within such a small opening, folio 102:04.
A spiral stairwell fitted within this space would result in a stair aperture than is less than a full arm-span (a fathom), folio 102:03.
The tower final dimension is slightly larger than the one defined in the concept design, but the thickness of its wall remains unchanged. It is deduced that the tower redesign may have been motivated by a need to increase slightly the open space inside the tower.
This is a reasonable inference; we will never know the true circumstances, facts and reasoning in this respect.
Further discussions and interpretations are postponed to the end of the geometric outline of the plant modification. It is essential to define the geometric algorithm first, which starts with the enlargement of the tower octagon.