Systemic Capacity Constraints in the Sneferu Pyramid Programme:A Quantitative Stress Test of the Orthodox Model

This paper forms part of a structured preprint series examining Old Kingdom pyramid construction through constraint-based modelling. The series integrates a core evaluation framework (CBEF) with multiple applied studies to test the internal consistency of orthodox parameters when modelled as an interacting system. The pyramid construction programme attributed to King Sneferu of Egypt’s Fourth Dynasty. The analysis does not challenge dynastic attribution or architectural chronology. Instead, it evaluates the logistical implications of constructing the Meidum, Bent, and Red pyramids within the conventionally accepted reign duration of approximately 24–30 years. Using published architectural dimensions from mainstream Egyptological sources, reconstructed masonry volumes are converted into approximate block quantities and average throughput requirements. Sequential and overlapping construction scenarios are modelled in order to test sensitivity to mobilisation duration, seasonal labour productivity, and partial concurrency. Key subsystems—including quarry extraction, stone dressing, transport, provisioning, tooling turnover, and administrative coordination—are evaluated within a minimum-throughput constraint framework. Under conservative assumptions, the implied steady-state requirement approaches approximately 350–400 block placements per day, corresponding to roughly 1,000 tonnes of stone movement per day at average block mass. Modest reductions in effective productive time or partial concurrency between monuments significantly increase subsystem intensity. Workforce provisioning at these levels implies annual grain demand on the order of 5,000–8,000 tonnes, depending on productivity assumptions. The purpose of the analysis is not to argue against Sneferu’s authorship, but to quantify the organisational and logistical implications embedded within the orthodox chronological model. The results suggest that the Sneferu pyramid programme, if executed within a single reign, would require a tightly coupled, high-throughput construction system operating with limited structural slack. The study provides a quantitative baseline for evaluating early Old Kingdom state construction capacity and for contextualising subsequent Fourth Dynasty pyramid projects.