Semantic Pixels: Engineered Observables for Measurement and Learning in Latent Cognitive Manifolds

Abstract Contemporary cognitive and artificial intelligence systems rely on high-dimensional latent representations where semantic structure emerges without explicit symbolic units. Despite their empirical success, the absence of a formally defined minimal unit of meaning remains a significant conceptual gap, as tokens, embeddings, and attention weights often lack interpretative invariance or local stability. This work introduces the semantic pixel: a local, non-atomic, and context-dependent perturbation of a latent manifold that produces a stable and observable semantic effect. We formalize its defining properties—locality, contextuality, and observability—and establish conditions for its dynamical stability through pushforward evolution and contraction mappings on the manifold. Furthermore, we model the non-linear interaction between these units via an interference operator that explains phenomena such as semantic ambiguity and contextual shifts. To transition from a conceptual manifesto to a verifiable science, we propose a reproducible experimental protocol employing spectral shifts, persistent homology, and observable sensitivity metrics. This framework provides a foundational non-symbolic layer for understanding emergent semantics in distributed cognitive architectures.