Binding-Motivated Contextuality: A Cross-Domain Cyclic Test in Perception and Judgment

Abstract: Perceptual binding and the contextuality of judgment are studied apart, in psychophysics and decision research. We argue they share one obstruction: a nonzero class in $H<sup>1$ of a presheaf with no global section -- though only contextuality is tested, since binding's obstruction vanishes. We build on sheaf formulations of predictive coding (Seely 2025) and contextuality (Abramsky & Brandenburger 2011): a cyclic set of pairwise judgments admits a global (noncontextual) explanation exactly when the cyclic (Suppes-Zanotti / n-cycle) inequalities hold. Its obstruction is measured by the complete contextual fraction CF (Abramsky, Barbosa & Mansfield 2017), not the weaker Cech invariant, which certifies contextuality but can miss it (Caru 2017). Penrose (1992) classifies the continuous tribar by $H<sup>1$ over the multiplicative group $\mathbb{R}<sup>+$ of depths -- but the $\mathbb{Z}_2$ case is what we test. We build the perceptual arena from two binary judgments per cyclic-dominance pairing, realizing the same frustrated-cycle obstruction as the survey. The central test is cross-domain: one cohort performs both; shared mechanism predicts a correlation between the arenas' signed obstruction margins -- CF before clamping -- which neither field has measured. Both are inconsistency scores, so a bare correlation is confounded by general response consistency. The prediction is therefore confound-residualized: the correlation must survive partialling out a general-consistency factor from a variance- and reliability-matched control. A sufficiently precise null would count against that account, provided the preregistered reliability checks pass and the control does not load on the obstruction. All three tests are designed but unrun.