The Grillos-Grokonian Sprawl Law: Superlinear Waste Scaling in Distributed Semiconductor Systems" by Grillos, Chris.

Distributing compute across trillions of physical chips creates systemic waste that scales superlinearly with chip count, not linearly as conventionally assumed. This paper formalizes this observation as the Grillos-Grokonian Sprawl Law: W = w₀ · N^(1+α), where W is total systemic waste, w₀ is baseline waste per isolated chip, N is the number of distributed chips, and α is an empirically derived compounding exponent. Through analysis of seven distinct waste channels — manufacturing defects, logistics and obsolescence, cooling infrastructure, compute underutilization, communication overhead, coordination costs, and software complexity — using data from TSMC/Samsung/Intel yield reports, Google/AWS/Meta PUE metrics, Meta Llama 3 Model FLOPS Utilization benchmarks, Bettencourt/West urban scaling theory (PNAS 2007), TOP500/HPCG parallel efficiency data, and global e-waste statistics, we establish an empirically validated range of α ≈ 0.15–0.35 with a central estimate of 0.25. At one trillion distributed chips, this produces systemic waste 1,000 times greater than linear models predict. The strongest superlinear contributors are communication overhead (α ≈ 0.3–0.5) and coordination costs (α ≈ 0.15–0.35), while cooling at hyperscale is sublinear and underutilization scales linearly. The paper identifies consolidation as the primary mechanism for compressing α, with orbital compute consolidation as the limiting case — a thesis independently validated by concurrent FCC filings from Blue Origin (Project Sunrise, 51,600 satellites), SpaceX (1 million satellites), and Google (Project Suncatcher). The equation was co-developed with Grok (xAI) and empirically validated by Claude (Anthropic) under the architectural direction of the author.