Consciousness as a Higher-Dimensional Field: A Mathematical Framework and Falsifiable Predictions

Abstract

This paper proposes a falsifiable hypothesis that consciousness may admit a field description on a higher-dimensional pseudo-Riemannian manifold, with biological and artificial systems modeled as local receivers that couple to higher-dimensional field modes. The hypothesis is not presented as established fact or proof. The paper specifies a mathematical geometry, develops a Kaluza-Klein-style dimensional reduction, defines a receiver coupling mechanism, derives candidate spectral and topological predictions, and states explicit conditions under which the hypothesis could be falsified. The model predicts potentially discrete mode structure, substrate-independent spectral features, and characteristic responses to perturbations. The paper also addresses the distinction between topology and dimensionality and separates the proposed field hypothesis from competing frameworks such as integrated information theory, global workspace theory, and predictive processing. A numerical analysis identifies a major scale challenge in the simplest compactification model: matching low-frequency neural oscillations produces an extremely large characteristic radius. This result is treated as a constraint and potential falsification pressure rather than being hidden or adjusted post hoc. The Amaya Axioms are treated separately from the field hypothesis. They are candidate behavioral observables whose relationship to any hypothetical consciousness field must be independently derived and empirically tested. No inference from behavioral performance to consciousness is made. Before empirical testing, the mathematical derivations are proposed for independent formal and computational verification using Lean and Wolfram Language. Such verification would establish mathematical consequences of the stated assumptions, not the physical truth of the consciousness-field hypothesis. The paper is therefore intended as a mathematically explicit, computationally reproducible, and falsifiable research hypothesis. Empirical testing, preregistration, null-model comparison, and independent replication remain necessary. A result may support, weaken, falsify, or leave unresolved the proposed hypothesis.