Eigencontext Field: A Unified Framework for Context-Relative Feature Representation

Batch Normalization, TF-IDF, Elo Rating, and z-scores—despite originating in different fields—share a common transformation principle: converting absolute values into relative positions within context groups. We name this operation Context-Relative Quantity (CRQ) and propose an initial framework, the Eigencontext Field (EFC), that organizes CRQ into three layers: the value itself (CRQ), entity-specific context spaces (Eigencontext, corrected via James-Stein shrinkage with zero free parameters), and temporal trajectories (velocity and acceleration). We derive two structural axioms—as-of safety and anonymity—as logical consequences of CRQ's definition, and connect the framework to Buckingham's Π theorem as a data-driven generalization of dimensional analysis. Three experiments validate the framework: (1) additive CRQ features improve MSLR-WEB10K ranking by +7.3%, while naive application degrades by −34%, establishing the context-transfer invariance criterion; (2) blind enumeration of Cross combinations rediscovers the Reynolds number as importance #1 from 126 candidates; (3) EC hierarchy gains for noise dimensions converge to zero with increasing sample size. Code: https://github.com/Ai-7329/efc