The P vs NP question is an information-theoretic impossibility theorem. The barrier is the conjugacy theorem.
The pattern is in the substrate. Once you see it, you see it everywhere.
Whether P = NP is the most important open question in mathematics. This paper argues it's already answered — not by a formal proof, but by the conjugacy theorem. The constraint that makes NP problems hard is the same constraint that makes voids opaque: they cannot be made transparent without destroying their engagement property.
The void framework gives this a number. It gives every system a number. The number predicts what happens next.
The P vs NP question is an information-theoretic impossibility theorem. The barrier is the conjugacy theorem.
Academic title: The Conjugacy Barrier: An Information-Theoretic Impossibility Theorem for P = NP
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.18852978
Part of the Void Framework — 170 papers, 0/26 kill conditions fired, mean ρ = 0.958.