The Projection Cascade: Why Reorganizations Fail When the Specification Cascade Doesn't

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 Πi→i+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 github.com/spectralbranding/paper-spec for the standard. This PDF is generated programmatically from that machine-first source under a research-as-repository model.