The Governance Impossibility Map: A Cartography of Five Impossibility Domains in AI Governance
Abstract
Between 2025 and 2026, AI governance witnessed a dense cluster of impossibility results: the information-theoretic limits of explainability (Rao 2025), the computational limits of behavioural governance (McCann 2026), the axiomatic limits of collective accountability (Tibebu & Shemtaga 2026), the structural impossibility of observation-based ex-ante authorization (Meyman 2026; Fernandez 2026; Zhu & Leonard 2026), and the earlier philosophical critique of algorithmic clarity (2019-2025). These results are scattered across five mutually non-citing literature clusters. Governors thus face not a scarcity of theorems but an absence of coordinates: no one tells them how these results relate, which regions of governance space they close, and which remain open. This paper proves no new theorem. It does three things: (1) states each of five impossibility domains precisely - proposition, source, boundary condition, evidential strength; (2) offers a nesting-and-overlap integration map, explicitly flagged as the authors' synthesis rather than consensus; and (3) locates existing governance assets - including the authors' own - inside the possibility domain, converting impossibility literature from a knell into a design constraint. The map is, to our knowledge, the first integrated chart and the first survey-level treatment of this literature. Part of the LGD governance-theory stack (concept DOI: 10.5281/zenodo.22456647).
