Gödel's incompleteness, Turing's halting problem, and the Péclet structure of undecidability share a formal structure.
The pattern is in the substrate. Once you see it, you see it everywhere.
Gödel showed that any sufficiently powerful formal system contains true statements it can't prove. Turing showed that no algorithm can decide in general whether a program halts. This paper shows both results are instances of the same phenomenon: void conditions that are undecidable because the observer is inside them.
The void framework gives this a number. It gives every system a number. The number predicts what happens next.
Gödel's incompleteness, Turing's halting problem, and the Péclet structure of undecidability share a formal structure.
Academic title: The Péclet Structure of Unsolvability: Void Framework Analysis of the Seven Millennium Prize Problems
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.18872012
Part of the Void Framework — 170 papers, 0/26 kill conditions fired, mean ρ = 0.958.