Observation-Driven Self-Normalizing Representation Systems for Long-Horizon Structured Memory

We introduce an observation-driven framework for constructing structured representationspaces equipped with self-normalizing template families and partially reversible projection sys-tems.Given a family of observation kernels on a raw data domain, we define a canonicalpseudo-metric and a class of idempotent normalization operators acting on an associated func-tion space. These operators induce a graph of multi-dimensional “lemma objects” that can serveas a long-horizon memory layer for learning systems such as large sequence models. We estab-lish a representation limit theorem: under a fixed observation family, any pipeline composed ofthe proposed operators cannot distinguish points beyond the induced observational equivalencerelation. We illustrate the framework on a simple entity–event schema fragment and discusspotential applications to streaming learning and structured retrieval.