Lawful Futures in Go

Lawful Futures in Go: Dynamically Sufficient Observation, Historical Information, and Constitutive Health develops a mathematical framework for determining what information an observer must retain to represent the lawful futures of a dynamical system. An observation may determine every presently requested answer while failing to preserve the information required to update those answers after an action. The paper resolves this distinction for partial transition systems governed by finite historical queries and monotone event insertion. A horizon-indexed request construction produces an information state that retains the historical memberships needed along geometrically possible continuations. Its abstract update commutes exactly with the original transition law, including rejected actions, and preserves bounded lawful response languages. Under explicit constitutive conditions, the construction also preserves complete viable-response capacity and the corresponding prospective Health judgments. These results extend the representation-sufficiency framework of Health, Formally Defined from the determination of present answers to the preservation of dynamically updateable information. The game of Go provides exact finite realizations. A complete (1×2) calculation distinguishes seven current-answer classes from twelve transition-stable classes. Source-reached (3×3) examples demonstrate how identical present configurations may retain different historical permissions, legal continuations, and viable response capacities. A constrained information-minimization result identifies one indispensable historical membership bit among twenty candidate questions on a specified six-history fiber. Regional observations and horizon-dependent comparisons further characterize information requirements across three source-reached populations comprising 112,501 action histories. A separately constituted protected exchange-and-repair network establishes a second realization of the prospective-capacity framework. Together, these results connect sufficient observation, historical information, lawful dynamics, organizational persistence, and adversarial response. The Go interpretation provides a common mathematical basis for understanding how connection, liberties, attack, defense, territory, sacrifice, ko, and initiative alter future possibilities. It distinguishes geometric availability, lawful continuation, organizational viability, and strategically enforceable outcomes without identifying any single response count with optimal play.