Perception Sets the Matrix: Spectral Match as the Generative Layer of Stochastic Brand-Choice Propensities

The stochastic brand-choice tradition — Markov switching models and the NBD-Dirichlet — earns its descriptive success by taking brand-choice propensities as exogenous givens: the models locate the equilibrium the propensities imply and are silent on what sets them. This paper supplies and tests the missing generative layer. At cohort level, spectral match — a similarity statistic between an observer cohort's eight-dimensional perception profile and a brand's profile — is proposed as a monotone predictor of the cohort's stated choice propensity within its category consideration set. A propensity vector induces the zero-order Dirichlet switching matrix in closed form. The perceptual layer therefore sets the matrix the tradition starts from: the double-jeopardy diagonal is inherited, the intermediate-propensity band becomes model-derived, and perceptually metameric brand pairs must receive statistically indistinguishable propensity vectors — a prediction no utility-based or congruity-based account makes. In a pre-registered LLM-cohort campaign under strict instrument separation with four kill conditions, the link held experimentally (τ_b= .323, p < .001; a random-profile placebo destroys it), replicated in quick-service coffee, failed in athletic footwear, and showed no common-method inflation (Δτ= -.002); metameric brand pairs violated propensity equality, bounding the perceptual layer's sufficiency exactly where real brand profiles converge. Includes zharnikov-2026bf-perception-sets-matrix.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.