The Informational Numerical Space: energetic coherence and causal structure

We propose the Informational Numerical Space (ENI), a physico-mathematical structure whose elementary object is a four-component informational state (λ, τ, σ, ι), where λ is an informational spatial scale, τ an informational temporal scale, σ a discrete causal role, and ι a normalized informational intensity. The aim of this work is neither to derive a new fundamental dynamics nor to predict new phenomena, but to establish a minimal, self-consistent formulation in which energy scales, causality, and information are co-encoded as native coordinates of a single state. The dimensional consistency of the framework is verified; an elementary causal relation is defined, together with a minimal re-emission operation that induces a chain-wise causal accessibility relation, shown to be a strict partial order whose projection onto the (λ, τ) sector coincides with the Minkowski causal order in 1+1 dimensions. It is further shown that, within the class of homogeneous quadratic forms of degree two, the requirement that the causal boundary be the null set forces the vanishing of the cross term and fixes the relative signature of the spatiotemporal block, excluding any Euclidean signature. A minimal informational metric extension is proposed and illustrated with examples. This article is a structural foundation: it records a conceptual framework in progress, preparing the ground for later works applying the ENI to concrete physical problems.