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 Spectral Brand Theory (SBT), which models brands as emitters across eight typed dimensions perceived by heterogeneous observer cohorts. Spectral interference – signals from one brand perturbing the perception cloud of another within shared cohorts – is formalized, distinguishing constructive interference (compatible signals reinforcing mutual perception) from destructive interference (contradictory signals undermining it). Interference magnitude is bounded by cohort overlap and spectral proximity on high-weight dimensions, modulated by a parent-brand recognition gate. Single-brand coherence is extended to portfolio-level coherence through a three-layer metric (within-brand, cross-brand, and aggregate). Four portfolio archetypes are identified – spectral cluster (LVMH), spectral spread (Procter & Gamble), spectral contradiction (Unilever), and spectral layering (Toyota/Lexus). A comparative analysis of LVMH and Unilever demonstrates that architecturally identical portfolios produce structurally opposite interference dynamics. Seven formal propositions are derived. The framework provides a formal basis for acquisition evaluation, portfolio rationalization, and cross-brand risk assessment that existing taxonomies cannot support. Includes zharnikov-2026q-r8.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. This PDF is generated programmatically from that machine-first source under a research-as-repository model.