The Riemann hypothesis, the Collatz conjecture, the Goldbach conjecture — they have Pe signatures. The hardest are high-Pe.
The pattern is in the substrate. Once you see it, you see it everywhere.
Mathematical objects don't have opinions or desires. But they have structure. This paper shows that the Péclet number applies to mathematical problems: the ratio of opaque structure to transparent constraint predicts problem difficulty. Some mathematical voids have been open for 200 years.
The void framework gives this a number. It gives every system a number. The number predicts what happens next.
The Riemann hypothesis, the Collatz conjecture, the Goldbach conjecture — they have Pe signatures. The hardest are high-Pe.
Academic title: The Epistemic Péclet Number: Mathematical Objects as Void Framework Substrates
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.18796574
Part of the Void Framework — 120 papers, 0/26 kill conditions fired, mean ρ = 0.958.