Alexandre Carvalho

This paper introduces a formal definition of intrinsic information as an inherent property of dynamical systems, characterized by their global topological and geometric structures. Unlike standard approaches that treat information as an epistemic or communication-theoretic tool, we propose that information possesses a specific shape defined by attractors, Morse decompositions, and Lyapunov landscapes. We argue that for any real-world phenomenon, the regularity of measurements on its observables allows for the derivation of a dynamical system whose informational content is objective and measurable. To substantiate this link, we provide concrete applications in ecology and neuroscience, offering specific metrics that quantify organizational complexity. Finally, our framework introduces the idea that information, by expressing itself through formal and geometric shape, acts as a structural constraint with explanatory power. This characterization of intrinsic information enables a rigorous scientific approach to its properties, including measurement, perturbation analysis, and the study of transient and asymptotic dynamics. We position this work as not merely technical, but as a robust research program that offers a new, in-depth perspective on the reality that science addresses across multiple domains.