Most strategic reorganizations fail to deliver expected performance gains. We argue this reflects a deeper architectural fact: interventions at the org-chart surface (\ (T₆\) ) achieve effect-sizes geometrically smaller than interventions at deeper tiers, because each deeper tier carries content already compressed in transit to the surface. We formalize this as a six-tier projection cascade linking owner intent (\ (T₁\) ), business model (\ (T₂\) ), governance (\ (T₃\) ), architecture (\ (T₄\) ), routines (\ (T₅\) ), and positions (\ (T₆\) ). Each junction is a linear operator \ (₈ ₈+₁\) with rank deficiency \ (rᵢ 0\). A unique cascade equilibrium exists under tier-by-tier Banach contractions (Theorem 1) ; total information loss is bounded by the sum of local nullities, with equality only when kernels stack independently (Corollary 1). Existing design theories – Galbraith’s star, Williamson’s governance choice, Mintzberg’s configurations, Puranam’s microstructure, Burton-Obel-Håkonsson’s computational optimization — are recovered as nested restrictions. A formal position triple \ (p = (Pₚ, Aₚ, Rₚ) \) decomposes any \ (T₆\) position into perceptual content from \ (T₅\), authority from \ (T₃\), and role expectation from \ (T₁\). The apparatus yields four falsifiable propositions: P1 cascade-distance scaling of intervention efficacy, P2 strict downward propagation of basis rotation under AI deployment, P3 variance amplification with cumulative rank deficiency, and P4 algebraic decoupling at layer junctions. Includes zharnikov-2026m-projection-cascade. 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.
Dmitry Zharnikov (2026) studied this question.