Radial Analysis: A Trajectory-Based Method for Indexicality and Identity Studies

Radial Analysis (RA) is a methodological framework that transforms radial category theory from static structural mapping into dynamic trajectory modeling. Building on the Trace & Trajectory (T&T) Framework's pre-representational architecture, RA provides researchers with practical tools for analyzing indexicality, identity navigation, and meaning dynamics in discourse.This paper presents RA as an applied methodology rather than foundational theory. The framework employs hexagonal geometry (the SpiderWeb architecture — a board game model based on hexagonal tessellation) to formalize navigational patterns: how speakers move through identity space, what these movements cost informationally, and how trajectorial patterns reveal underlying dynamics invisible to categorical approaches. Core innovations include: (1) the three-level terminology (Hexid/Hex/Phex) for precise analytical description; (2) calculable metrics (hexagonal distance, trajectory cost, Delta Dissipation Rate) enabling quantitative comparison; (3) the λ/σ parameter system distinguishing structural granularity from epistemic access; (4) the Depth Protocol (Πdep) governing semiotic visibility through shading mechanics; and (5) direct application to epistemic appropriation dynamics including flattening, internalization, and trajectorial refraction. RA addresses phenomena that categorical frameworks handle only through ad hoc mechanisms: simultaneous multi-level positioning, asymmetric intersubjective dynamics, and the geometric constraints that institutional power imposes on identity navigation. The seven-step analytical procedure operationalizes these theoretical insights as reproducible protocol. Applications span personal deixis, temporal reference, identity navigation dynamics, and—through integration with recent work on epistemic appropriation—the formal analysis of internalized oppression in clinical and educational contexts.