Λ_QCD as a Pressure/Density Ratio

$$\Lambda_{QCD} = \sqrt{\frac{\gamma P}{\rho}}$$

Status: Unproven — and dimensionally inconsistent as written.

Paper 10 proposes this formula for the real QCD confinement scale, $\Lambda_{QCD}\approx200$ MeV (an energy), as a pressure-density ratio.

Checked directly, in the 2026-07-21 audit: $\sqrt{P/\rho}$ is the standard fluid-dynamics formula for the speed of sound in a medium — it has units of velocity, not energy. Computing it with the paper’s own stated $P$ and $\rho$ gives a result comparable to the speed of light in m/s, not an energy scale in MeV; no choice of the order-one factor $\gamma$ converts a velocity into MeV. This isn’t a matter of imprecision — the formula as written cannot produce the quantity it claims to, regardless of what numbers are plugged in.

What would make this proven: a corrected formula (likely needing an explicit mass or $\hbar c$ factor to convert the sound-speed expression into an energy) that’s shown to actually reproduce the real 200 MeV value from independently-motivated inputs, not asserted after the fact. The real $\Lambda_{QCD}\approx200$ MeV figure used elsewhere in the same paper (e.g. the confinement-radius calculation) is correct as a citation — it just isn’t derived by this equation.

Used in: Paper 10.