Mermin inequality

In plain terms

Here is a natural guess: quantum weirdness is a small-systems phenomenon, and as you add particles it washes out into classical behaviour. Averages of averages, and the strangeness dilutes.

Mermin's inequalities say the opposite happens. Take the Bell setup and add parties -- three particles, four, ten. The gap between what quantum mechanics delivers and what any common-sense account allows does not shrink. It grows exponentially with the number of particles. Each added party doubles the headroom, roughly.

So the conflict with local realism is not a fragile corner-case of tiny systems. It is a structural feature that gets more pronounced with size, which is the reverse of what the wash-out intuition predicted.

In CSD

The corpus carries the multi-party inequalities so its contextuality results are not hostage to the smallest case, and the exponential growth is the actual point of doing so. A substrate mechanism that happened to reproduce the two-party violation by some special trick would be exposed here: whatever produces the correlations has to keep producing them, more strongly, as parties are added.

Together with GHZ this establishes the conflict at every size and in both logical shapes -- statistical and deterministic. That is the standard a substrate account must meet, and the corpus states the standard before claiming to meet it.

Mathematically

A family of multipartite Bell inequalities whose classical bound is exceeded by quantum mechanics by a factor growing exponentially in the number of parties -- 2 to the power (n-1)/2 for n parties.

The corpus proves the quantum value and the classical bound separately, which keeps the exponential gap a theorem rather than a plot.

The name

David Mermin, born 1935, took his degrees at Harvard and spent his career at Cornell, much of it directing the Laboratory of Atomic and Solid State Physics. With Ashcroft he wrote the solid-state textbook that trained a generation.

He is that rare thing, a physicist whose prose is part of his scientific reputation. The phrase shut up and calculate is his -- coined in 1989 as a description of an attitude he was criticising, then promptly attributed to Feynman and quoted with approval, a fate he has written about with resignation. The multi-party inequalities are from 1990, in a paper short enough to read over coffee, turning the GHZ conference argument into something an experiment could score.