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

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 $H^1$ 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 $H^1$ over the multiplicative group $\mathbb{R}^+$ 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.

Source: arXiv:2609.23977v1 - http://arxiv.org/abs/2609.23977v1 PDF: https://arxiv.org/pdf/2609.23977v1 Original Link: http://arxiv.org/abs/2609.23977v1