Spectral Portfolio Theory: Interference, Coherence, and Capacity in Multi-Brand Perception Space

Brand portfolio theory classifies portfolios by architecture – monolithic, endorsed, house-of-brands – but does not formalize how brands within the same portfolio interact in the observer's perception space. This paper develops spectral portfolio theory within the framework of Spectral Brand Theory (SBT), which models brands as emitters across eight typed dimensions perceived by heterogeneous observer cohorts. The paper introduces spectral interference – the mechanism by which signals from one brand in a portfolio perturb the perception cloud of another brand within shared observer cohorts. Constructive interference (compatible signals reinforcing mutual perception) is distinguished from destructive interference (contradictory signals undermining mutual perception), and the conditions under which each arises are formalized. The interference magnitude is bounded by the product of cohort overlap and spectral proximity on high-weight dimensions, modulated by a parent-brand recognition gate. Single-brand coherence assessment is extended to portfolio-level coherence through a three-layer metric (within-brand, cross-brand, and aggregate portfolio coherence), and portfolio positioning capacity bounds extend the sphere packing results of Zharnikov (2026g) to multi-brand contexts. Four portfolio archetypes are identified – spectral cluster (LVMH), spectral spread (Procter & Gamble), spectral contradiction (Unilever), and spectral layering (Toyota/Lexus) – each with distinct interference profiles and risk structures. A comparative analysis of LVMH and Unilever demonstrates that portfolios of comparable size and revenue produce structurally opposite interference dynamics. Seven formal propositions are derived, each testable through spectral profile measurement of observer cohorts.