Why Eight? Completeness and Necessity of the SBT Dimensional Taxonomy
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2026
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| _version_ | 1866901897781182464 |
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| author | Zharnikov, Dmitry |
| author_facet | Zharnikov, Dmitry |
| contents | <p>Spectral Brand Theory (SBT) models brand perception across eight typed dimensions – semiotic, narrative, ideological, experiential, social, economic, cultural, and temporal – yet the choice of eight has not been formally justified. Competing frameworks disagree on dimensionality: J. Aaker (1997) proposes five brand personality dimensions, Keller (1993) organizes equity around four pillars, Kapferer (2008, 4th ed.) identifies six prism facets, and multidimensional scaling research routinely finds two to three dimensions sufficient. This paper provides the missing justification through a completeness-and-independence argument rather than through factor analysis. We enumerate the established academic traditions that study meaning transmission between entities and observers, identifying exactly eight traditions – semiotics, narratology, ideology critique, phenomenology of experience, social identity theory, signaling theory, cultural sociology, and temporal psychology – each constituting a distinct meaning channel with its own foundational literature, core constructs, and empirical methods. We demonstrate dimensional independence by exhibiting, for each dimension, a pair of brands that differ primarily on that dimension while remaining approximately matched on the remaining seven. We argue non-redundancy by showing that removing any single dimension collapses at least one such brand pair into indistinguishability. We establish completeness by demonstrating that every candidate ninth dimension proposed in the literature – including aesthetic, functional, ethical, digital, and environmental – reduces to a linear combination of existing dimensions rather than opening a genuinely new meaning channel. Finally, we address the apparent contradiction between SBT's eight dimensions and the two to three dimensions found by multidimensional scaling, showing that the concentration of measure results from Zharnikov (2026f) predict precisely this pattern: low-dimensional projections capture most variance even when the true space is eight-dimensional, but they lose the boundary structure that distinguishes coherence types. An empirical robustness test using R15 cross-cultural LLM experiment data (22 models, 11,298 API calls) confirms that eight is the stable resolution level: no single-dimension removal drops DCI ranking cosine below .994, no pair removal drops it below .993, and augmenting to ten dimensions produces near-perfect rank preservation (rho = .9997). All eight dimensions carry non-trivial cross-model variance (5-19%). The paper argues that SBT's eight dimensions are the minimal complete set covering all established meaning-transmission channels relevant to brand perception, and that any reduction below eight sacrifices discriminative power while any expansion beyond eight introduces redundancy.</p> <p><br>Includes paper.yaml (Paper Spec v0.1.0) – a machine-readable specification of the paper's claims, assumptions, and dependencies. See https://github.com/spectralbranding/paper-spec for the standard.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19207600 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Why Eight? Completeness and Necessity of the SBT Dimensional Taxonomy Zharnikov, Dmitry Spectral Brand Theory dimensional taxonomy brand perception completeness argument independence proof multi-dimensional scaling meaning channels semiotics social identity cultural sociology machine-readable claims <p>Spectral Brand Theory (SBT) models brand perception across eight typed dimensions – semiotic, narrative, ideological, experiential, social, economic, cultural, and temporal – yet the choice of eight has not been formally justified. Competing frameworks disagree on dimensionality: J. Aaker (1997) proposes five brand personality dimensions, Keller (1993) organizes equity around four pillars, Kapferer (2008, 4th ed.) identifies six prism facets, and multidimensional scaling research routinely finds two to three dimensions sufficient. This paper provides the missing justification through a completeness-and-independence argument rather than through factor analysis. We enumerate the established academic traditions that study meaning transmission between entities and observers, identifying exactly eight traditions – semiotics, narratology, ideology critique, phenomenology of experience, social identity theory, signaling theory, cultural sociology, and temporal psychology – each constituting a distinct meaning channel with its own foundational literature, core constructs, and empirical methods. We demonstrate dimensional independence by exhibiting, for each dimension, a pair of brands that differ primarily on that dimension while remaining approximately matched on the remaining seven. We argue non-redundancy by showing that removing any single dimension collapses at least one such brand pair into indistinguishability. We establish completeness by demonstrating that every candidate ninth dimension proposed in the literature – including aesthetic, functional, ethical, digital, and environmental – reduces to a linear combination of existing dimensions rather than opening a genuinely new meaning channel. Finally, we address the apparent contradiction between SBT's eight dimensions and the two to three dimensions found by multidimensional scaling, showing that the concentration of measure results from Zharnikov (2026f) predict precisely this pattern: low-dimensional projections capture most variance even when the true space is eight-dimensional, but they lose the boundary structure that distinguishes coherence types. An empirical robustness test using R15 cross-cultural LLM experiment data (22 models, 11,298 API calls) confirms that eight is the stable resolution level: no single-dimension removal drops DCI ranking cosine below .994, no pair removal drops it below .993, and augmenting to ten dimensions produces near-perfect rank preservation (rho = .9997). All eight dimensions carry non-trivial cross-model variance (5-19%). The paper argues that SBT's eight dimensions are the minimal complete set covering all established meaning-transmission channels relevant to brand perception, and that any reduction below eight sacrifices discriminative power while any expansion beyond eight introduces redundancy.</p> <p><br>Includes paper.yaml (Paper Spec v0.1.0) – a machine-readable specification of the paper's claims, assumptions, and dependencies. See https://github.com/spectralbranding/paper-spec for the standard.</p> |
| title | Why Eight? Completeness and Necessity of the SBT Dimensional Taxonomy |
| topic | Spectral Brand Theory dimensional taxonomy brand perception completeness argument independence proof multi-dimensional scaling meaning channels semiotics social identity cultural sociology machine-readable claims |
| url | https://doi.org/10.5281/zenodo.19207600 |