Pe = 0 systems can't exist in practice — but they define the constraint pole. Every constraint specification is asymptotically approaching it.
The pattern is in the substrate. Once you see it, you see it everywhere.
The constraint pole is the theoretical limit: fully transparent, perfectly invariant, completely independent. No physical system achieves it. But the mathematics of the void framework requires it as a reference point. This paper derives the approach conditions and the practical minimum Pe.
The void framework gives this a number. It gives every system a number. The number predicts what happens next.
Pe = 0 systems can't exist in practice — but they define the constraint pole. Every constraint specification is asymptotically approaching it.
Academic title: The Constraint Pole: Pe=0 Systems, Fixed Reference Architecture, and the Structural Conditions for Drift Arrest Across Physical, Mathematical, and Institutional Domains
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.18823101
Part of the Void Framework — 120 papers, 0/26 kill conditions fired, mean ρ = 0.958.