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标题：UAU-L1：基于费希尔信息流形（Fisher Information Manifold）的因果-信息-观察者复合泛函，兼具变分、随机与类量子等价形式 摘要：本文提出UAU-L1，这是一种定义于费希尔信息流形上的统一复合泛函，将因果推理、认知系统约束、时间畸变与依赖于观察者的信息坍缩整合至单一结构化框架之中。该模型由标准化因果效应项（Δ/SE）、乘性系统效率场、非线性时间稳定性核函数与指数型观察者惩罚函数构建而成。 UAU-L1存在多种数学上等价的表达形式：(i) 变分形式：将其视为统计流形上的熵正则化作用量原理；(ii) 随机形式：将其表示为带斯特拉托诺维奇（Stratonovich）修正项的费希尔几何随机微分方程；(iii) 哈密顿相空间形式：具备熵驱动的势结构。在平衡可逆状态下，该系统可通过马德隆变换（Madelung Transform）映射至推理空间上的薛定谔型扩散方程，其中观察者效应表现为类似退相干的阻尼项。 研究表明，所构建的结构无法被简化为单一经典框架，而是形成了一种复合推理几何：其中因果性、信息流、时间尺度缩放与测量效应共同构成统计流形的耦合几何形变。该框架为描述有限资源与非理想观测条件下的推理动力学提供了一种通用语言。 巴扎罗夫（Bazarov, V.）(2025)。《模型UAU通用注意力单元（UAU Universal Attention Unit）》。Zenodo。https://doi.org/10.5281/zenodo.17033792 关联关系：属于版本（IsVersionOf）→ 概念DOI：https://doi.org/10.5281/zenodo.17033792