This is the theory’s one forward prediction, and it is precise enough that an experiment can check it directly. Two uncharged metal plates in vacuum already attract each other, because the quantum vacuum between them holds fewer field modes than the vacuum outside. Standard physics says that force grows as d⁻⁴. PST says the substrate is not infinitely fine-grained: it has a coherence length d₀, and as the plates approach that scale, the mode count departs from the continuum answer.

• The exponent is the prediction. The correction scales as d⁻⁶, not d⁻⁴, with the coefficient ξ = 90/π² ≈ 9.12 fixed by the substrate’s projection kernel. No free parameter tunes that power law, and it is distinguishable from every known material correction, including the retarded d⁻⁷ Casimir-Polder regime. Because the exponent is fixed in advance, measuring how the force changes with the gap tests the prediction on its own terms.
• The amplitude is a bound, not a claim. Its size is set by d₀, which the postulates do not fix; existing 160–750 nm data already place it below about 5.3 nm. A measurement that sees no signal simply tightens that bound further: it tells us the coherence length is smaller still. The book states this plainly rather than glossing over it.
• Where an experiment could decide it. Slide the separation down. At today’s best-measured 160 nm the signal is only about 0.09%, below the noise. But it grows as (d₀/d)²: roughly 10% at 50 nm and 64% at 20 nm, far above the systematic floor. A next-generation 1%-precision measurement at d ≈ 50 nm is the cleanest place the universe could tell us whether the substrate is real.