Six Birds: No-Go Theorems for Audited Emergence

Six Birds theory studies finite systems observed through deterministic coarse-grainings (“lenses”) using a small audited vocabulary of primitives. This paper proves eight no-go theorems that constrain when common emergence narratives can be made honest in a finite, checkable setting. For a finite Markov system and horizon TT, define an arrow audit as the Kullback–Leibler divergence between the observed path law and its time reversal. We prove a deterministic data-processing inequality: observation cannot increase arrow. As a consequence, any reversible system started in stationarity has zero observed arrow, even when the observation supports nontrivial protocol structure. Further results give graph-theoretic obstructions for force-like antisymmetric drives (exactness on forests and zero cycle sums), a finite variational identity for best macro-kernels and closure deficit, and a bounded-interface saturation theorem that prevents unbounded laddering. Together these theorems delimit what can and cannot be certified as emergent from audited primitives in finite models.