Transitional Linearity Among Local Maxima in the Great Pyramid's Masonry Courses

Abstract

This paper models thickness variations in the Great Pyramid’s masonry courses using two independent mathematical regimes. Data source: Petrie’s 203-course height profile. Target metric: Post-maximum decrement (PMD) across 21 local maxima. Deterministic subset (PMD8): Eight boundary maxima decline linearly with elevation. Apex anchor: PMD8 hits zero at 5,775 inches (280 cubits). Structural slope: Uses a practical 12.5-finger decrement value (\(R^2 = 0.682\)). Random subset (PMD13): Thirteen remaining maxima remain constant across height. Random range: Fluctuate tightly within a \(3 \pm 3\) finger band. Core Takeaway: The pyramid’s masonry combines intentional, apex-anchored planning at major structural thresholds with bounded random variation elsewhere.