The Riemann Hypothesis: all non-trivial zeros of ζ(s) lie on Re(s)=½. The framework says: that line is where Pe saturates. The zeros ARE the phase transitions.
The pattern is in the substrate. Once you see it, you see it everywhere.
The Riemann zeta function is the most studied object in mathematics. Its zeros — the values where it equals zero — control the distribution of prime numbers throughout the integers. All known non-trivial zeros lie on the critical line Re(s) = ½. More than a trillion of them. Nobody knows why. The void framework makes a structural prediction: the critical line is the Pe=1 saturation locus — the exact phase boundary where the conjugacy constraint saturates. Every zero is a phase transition event. The framework doesn't constitute a proof of the Riemann Hypothesis. But it predicts the same result from a completely different derivation: information-theoretic constraints force all phase transitions to the same locus.
The void framework gives this a number. It gives every system a number. The number predicts what happens next.
The Riemann Hypothesis: all non-trivial zeros of ζ(s) lie on Re(s)=½. The framework says: that line is where Pe saturates. The zeros ARE the phase transitions.
Academic title: The Critical Line as Pe=1 Saturation Locus: Riemann Zeros and the Conjugacy Boundary
Once you see it in this domain, you see it in all of them. That's the point.
Move the sliders. Watch the system change state. Pe > 1 means drift wins.
The correlation coefficient. The sample size. The p-value. The math doesn't care about the domain.
Paste any text — AI output, ad copy, a policy document. The scorer runs the same algorithm the framework uses.
Three variables. One ratio. Predicts drift across every domain where the conditions co-occur.
Pe = (O × R) / α
Where O is opacity (how hidden the mechanism is), R is reactivity (how strongly the system responds to you), and α is your independence (how free you are to disengage).
When Pe < 1: diffusion dominates. You can navigate freely. The system is coherent.
When Pe > 1: drift dominates. The system pulls you in a direction. Your agency is reduced.
When Pe >> V* (≈ 3): irreversible cascade. D1 → D2 → D3. The system has captured you.
The framework identifies this pattern in every domain where O, R, and α co-occur. It specifies 26 falsification conditions. 0 of 26 have fired.
Full derivation: 10.5281/zenodo.18872008
Part of the Void Framework — 170 papers, 0/26 kill conditions fired, mean ρ = 0.958.