Spectral Immunity: Portfolio Interference Fails in AI-Mediated Brand Perception

Brand portfolio theory predicts perceptual interference when observers recognize shared corporate ownership. This interference is theorized to require only an open awareness gate. Large language models (LLMs), whose training data permanently saturate this gate, offer a critical test. If interference scales with awareness, LLMs should exhibit maximal spillover; if brand encodings are already compressed to minimum distortion, portfolio context should produce none. We formalize spectral interference across eight perceptual dimensions and test three propositions with 13 LLMs from seven training traditions, 40 brands, seven portfolio archetypes, and four prompt modalities (N = 9,925 observations). Using the Dimensional Concentration Index and TOST equivalence testing, we find near-zero portfolio-induced change (mean |ΔDCI| = .26; equivalence holds for 18/20 brands). The sole exception – Geely Auto in multi-turn conversation (d = -1.11) – emerges only when extended context converts coordination information into output inferences. Variance decomposition attributes just 0.1% of perceptual concentration to portfolio framing versus 37.4% to brand identity. These results resolve the awareness-gate paradox: awareness is necessary but insufficient. A second bandwidth constraint is required to propagate portfolio (DO-layer) information into observable brand profiles (WHAT-layer). General-purpose LLMs privilege output specification and are rationally inattentive to organizational coordination. As AI mediation of consumer-brand interactions grows, portfolio architecture becomes strategically invisible to this observer class, shifting managerial investment from orchestration to individual brand specification. 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.