A new theoretical preprint by Jonte Hance argues that two longstanding and rarely compared definitions of contextuality in quantum foundations actually describe different layers of classical versus nonclassical behavior. Rather than competing, Kochen-Specker contextuality and Spekkens' generalized noncontextuality form stages in a hierarchy, with the former generalizing fundamental nonclassicality and the latter generalizing classical explainability. This insight, drawn from logical analysis of measurement scenarios and ontological models, offers a potential reconciliation that previous literature has largely overlooked by treating the two approaches in isolation.

The paper is a preprint (arXiv:2604.14319, submitted April 2026) and has not been peer-reviewed. Its methodology consists of conceptual clarification, formal definitions, and mathematical proofs comparing the two contextuality notions across toy models and quantum examples. There is no empirical dataset or sample size; the work is purely foundational, building on existing no-go theorems without new experimental claims. Limitations include its reliance on idealized scenarios that may not directly map to noisy real-world quantum devices, and it leaves open how the hierarchy translates to practical quantum information protocols.

To understand the advance, recall the classics. Kochen and Specker's seminal 1967 theorem (Journal of Mathematics and Mechanics) proved that quantum mechanics cannot be explained by noncontextual hidden variables: you cannot pre-assign definite values to all observables independently of which compatible set is measured. This captured the idea that quantum systems are provably nonclassical at an ontological level. In contrast, Robert Spekkens' 2005 framework (Physical Review A 71, 052108) introduced an operational, epistemic notion of noncontextuality applicable to preparations, transformations, and measurements in generalized probabilistic theories. It asks whether observed statistics can be explained by a classical ontological model that doesn't depend on context.

Hance's contribution is to position these not as rivals but as sequential filters. A system can satisfy Spekkens noncontextuality (behaving 'classically' in an operational sense) yet fail Kochen-Specker noncontextuality, revealing deeper nonclassicality. This mirrors patterns seen in quantum computing resource theories, where magic states or contextuality are resources for quantum advantage, and echoes recent work by Abramsky and Brandenburger (2011, New Journal of Physics) that unified logical and probabilistic approaches to contextuality.

What the preprint's own abstract understates—and what much prior coverage of contextuality debates has missed—is the philosophical payoff. By delineating 'provably classical' from 'provably nonclassical' behaviors, the hierarchy challenges binary views of quantum reality that have dominated since Bell's theorem. It suggests quantum systems inhabit a stratified ontology: some behaviors admit classical explanation at the phenomenological level while resisting it at the fundamental one. This intersects neatly with ongoing debates in quantum interpretations—such as QBism versus relational quantum mechanics—where the role of the observer and context are central. The paper also implicitly critiques overclaims in popular quantum foundations discourse that treat any contextuality as proof of 'spooky' nonlocality, ignoring nuanced gradations.

Synthesizing these threads reveals missed connections to quantum Darwinism and decoherence research, where classicality emerges approximately from quantum substrates. Hance's lens implies that full nonclassicality (KS-style) may be required for genuine quantum computational speedup, while Spekkens-style classicality suffices for certain simulation tasks. This offers novel insight: the 'warring contextualities' are not a bug in quantum foundations but a feature that lets us quantify how classical a quantum system can appear before its nonclassical core is exposed.

The work sits at the fertile intersection of physics and philosophy, suggesting that reconciling these definitions could refine tests of macrorealism and guide development of quantum technologies that exploit specific layers of nonclassicality. While theoretical, it invites experimentalists to design tests distinguishing these hierarchy levels in photonic or superconducting platforms. Ultimately, Hance provides more than reconciliation—he supplies a map for navigating the blurred boundary between classical intuition and quantum reality.