Why Eight? Completeness and Necessity of the SBT Dimensional Taxonomy

How many distinct channels transmit meaning from brands to consumers? Extant frameworks diverge widely – five personality dimensions (Aaker, 1997), six prism facets (Kapferer, 2008), two-to-three MDS solutions – yet none provides theoretical justification for its chosen dimensionality. This paper derives an eight-dimensional taxonomy from first principles. Brand perception occurs through eight independent meaning channels – semiotic, narrative, ideological, experiential, social, economic, cultural, and temporal – each rooted in a distinct academic tradition. Independence is demonstrated through counter-example brand pairs differing on one channel while matched on the others; non-redundancy follows because removing any channel collapses discriminative power for at least one pair. Completeness is shown by reducing five proposed ninth dimensions to combinations of existing channels. The apparent conflict with low-dimensional MDS solutions is resolved via concentration-of-measure mathematics: low-dimensional projections capture most variance while losing the profile-shape information that distinguishes coherence types. Robustness checks using synthetic observers confirm that each dimension carries non-trivial variance (5-19%) and rank stability deteriorates below eight dimensions. The taxonomy integrates prior meaning frameworks while satisfying psychometric criteria for theoretical derivation (Borsboom et al., 2003; Rossiter, 2002), offering consumer researchers a coordinate system for studying meaning transfer, cultural branding, and perceptual coherence. Includes zharnikov-2026r-r11.yaml (Paper Spec v0.1.0) – a machine-readable specification of the paper's claims, assumptions, and dependencies. The paper's full machine-first bundle (the SPINE claim/dependency graph and the ONTOLOGY term module) lives in the public repository; see https://github.com/spectralbranding/paper-spec for the standard. This PDF is generated programmatically from that machine-first source under a research-as-repository model.