UAU-L1 METRIC SPECIFICATION

*Abstract**UAU-L1+SYSTEM: METRIC SPECIFICATION

This work introduces **UAU-L1 (Unified Adaptive Utility, Level 1)**, a formal framework for quantifying epistemic efficiency in systems where knowledge production depends on both causal structure and measurement processes. The model integrates three fundamental domains: **causal inference**, **information processing**, and the **observer effect**, providing a unified metric for evaluating when knowledge is both statistically valid and physically attainable.

At its core, UAU-L1+ extends a base efficiency model of the form:

 Base (v1): UAU = (η × N_free) / T

by embedding it into a **structural causal framework** and augmenting it with signal quality, system activation, and temporal stability. The resulting formulation incorporates a causal signal term (Δ / SE(Δ)), representing statistically identifiable effects, and introduces a stability correction based on deviations in effective processing time.

A key contribution of this work is the formal integration of **measurement back-action**. Observation is treated as an explicit intervention, introducing a cost term (R_H), derived from information-theoretic and thermodynamic principles. This leads to an observer-corrected metric:

[UAU_{L1} \propto \text{(causal signal)} \times \text{(system capacity)} \times \text{(time stability)} \times \exp(-R_H)]

The framework defines strict **existence conditions**: if causal identifiability fails or measurement disturbance exceeds critical thresholds, the metric becomes undefined, corresponding to an *empirical monostate* where knowledge cannot be meaningfully extracted.

UAU-L1 thus provides a computable criterion for distinguishing between valid knowledge-generating systems and those where observation itself destroys causal structure. The model is compatible with experimental design, cognitive science, and physical measurement theory, offering a general tool for analyzing systems across domains—from human cognition to complex adaptive environments.

In essence, the framework formalizes a fundamental constraint:

> knowledge emerges only when causal signal survives the cost of observation.https://doi.org/10.5281/zenodo.17092207https://doi.org/10.5281/zenodo.17090162