SYSTEM: UAU-L1 — FULL MULTI-LEVEL INFERENCE GEOMETRY SPECIFICATION

Title: UAU-L1: A Composite Causal–Information–Observer Functional on Fisher Manifolds with Variational, Stochastic, and Quantum-like Equivalences

Abstract:We introduce UAU-L1, a unified composite functional defined on a Fisher information manifold that integrates causal inference, cognitive system constraints, temporal distortion, and observer-dependent information collapse into a single structured framework. The model is constructed from a standardized causal effect term (Δ/SE), a multiplicative system efficiency field, a nonlinear temporal stability kernel, and an exponential observer penalty function.

UAU-L1 admits multiple mathematically equivalent representations: (i) a variational formulation as an entropy-regularized action principle on a statistical manifold, (ii) a stochastic formulation as a Fisher-geometric stochastic differential equation with Stratonovich correction, and (iii) a Hamiltonian phase-space representation with entropy-driven potential structure. In the equilibrium-reversible regime, the system further maps to a Schrödinger-type diffusion equation over inference space via a Madelung transform, where observer effects manifest as decoherence-like damping terms.

We show that the resulting structure is not reducible to a single classical framework but instead forms a compositional inference geometry in which causality, information flow, temporal scaling, and measurement effects act as coupled geometric deformations of a statistical manifold. The framework provides a generalized language for describing inference dynamics under bounded resources and non-ideal observation conditions.

Bazarov, V. (2025). Model UAU Universal Attention Unit. Zenodo. https://doi.org/10.5281/zenodo.17033792

Relation: IsVersionOf → Concept DOI: https://doi.org/10.5281/zenodo.17033792