ASML's cumulative EUV lithography shipments grew far too slowly to satisfy Sahal's identity's exponential-production precondition

ASML's own company history dates the Carl Zeiss optics partnership to 1986 — "[same year] we established our existing partnership with lens manufacturer Carl Zeiss" — a full 24 years before the first EUV tool left the factory: "In 2010, we shipped the first prototype extreme ultraviolet (EUV) lithography tool (TWINSCAN NXE:3100)." Cumulative EUV shipments then took another decade to reach "the 100th EUV system shipment," reported "at the beginning of 2020" (asml.com/en/company/about-asml/history).

That production history — about 100 cumulative units in the first decade of shipments, an average of roughly ten per year — is far below the sustained, multi-year exponential growth in cumulative production that Sahal's identity requires before Wright's Law (cost falling with cumulative production) and Moore's Law (cost falling with calendar time) become the same curve. It is a concrete falsification check on that identity's own precondition, applied to a real technology rather than treated as automatically satisfied. It supplies the missing quantitative leg for the claim that Nikon and Canon's 15+ years of failed EUV entry reflects a calendar-time, institutionally-accumulated tacit-knowledge moat (Zeiss being the sole optics supplier) rather than a production-volume learning curve — because on Sahal's own math, low-volume production is exactly the condition under which the two axes should not agree. See 2026-07-16-hop-euv-sahal-boundary for the full hop chain.