Constrained Form: A Rank-One Constructive Regime at Giza

Description: A builder operating with a single slope rule and without global coordinates is not free to generate arbitrary forms: the process itself selects the admissible outcomes. This paper shows that the Egyptian seked — the documented slope rule of the pyramids — constrains planimetric form to exactly three distinct solutions by arithmetic necessity. The three pyramids of Giza realise all three. Measured dimensions match Petrie’s surveys within 1% without free parameters. This result is not site-specific. It establishes a general principle: in finite-rank constructive regimes, architectural form is selected by the construction process itself, rather than imposed by a global design. The Giza configuration does not require a global plan; it follows from the persistence of a single constructive rule.