Axiodynamics v5.9 — Angular Semantics and Coordinate Conventions

This technical note addresses a practical requirement for making Axiodynamics computable on real-world corpora: assigning an angular orientation (θ ∈ [0, 2π)) to observed mémotions in a telotopic space, relative to a situational telos. In the axiodynamic framework, affective-cognitive dynamics are represented by vectorial forces—conative (Fc) and inhibitory (Fi)—and key metrics such as telotopic negentropy depend on the directional coherence of these vectors. This methodological addendum extends the axiodynamic framework (v5.7: core axioms, v5.8: telos formalization) by operationalizing the protective-belt layer for empirical falsifiability. The document formalizes four complementary estimation routes designed to be used alone or in combination: (A) structured expert annotation based on behavioral inference, (B) semantic embeddings coupled with circular multidimensional scaling, (C) anchoring on stable axiological reference axes, (D) an axiological alignment coefficient (β) that combines semantic proximity (derived from embeddings) with affective valence to enable semi-automated (with valence annotation) or fully automated (with sentiment models) inference at scale. To prevent "black-box" angle assignment, the note specifies validation requirements for reliability and convergence across methods (inter-annotator agreement, cross-method consistency), and it defines the associated circular-statistics toolkit (Rayleigh tests, angular correlations, bootstrap confidence intervals). The note is accompanied by a minimal Python implementation (modules for circular statistics, β computation, and method comparison), intended to integrate directly into the PoC Telotopic Signatures pipeline. Overall, this deposit functions as a methodological bridge between the formal axiodynamic axioms and corpus-based testing, enabling large-scale experiments (N > 5000 utterances) on historical social-media data to evaluate whether telotopic negentropy anticipates shifts in collective stability and coordination.