Health, Formally Defined · Companion research · Preprint v1.0 · November 7, 2026
Lawful Futures in Go
Dynamically Sufficient Observation, Historical Information, and Constitutive Health
Zed James · DOI 10.5281/zenodo.24044494 ↗
Research overview
What can a system still do, and what must an observer remember to know?
Two positions in Go can look identical while offering different legal futures. Earlier moves constrain what is permitted next: in particular, the situational-superko rule can reject a move that would otherwise be geometrically available. Consequently, a present-board description need not be enough to determine the next lawful transition.
The paper constructs a dynamically sufficient information state for finite-horizon event-guarded systems. It retains the present controls and the historical memberships that future actions can actually query. Its abstract update agrees exactly with the underlying law, including rejected actions. Under explicitly stated constitutive conditions, this construction also preserves the complete set of viable responses and the resulting prospective Health judgments.
Finite Go examples make the distinctions explicit. In the complete 1 × 2 game, seven classes of current legality-and-winning answers refine to twelve transition-stable classes. A six-history 3 × 3 example identifies exactly one indispensable historical question among twenty candidate membership tests. The analysis also distinguishes the mere possibility of a winning continuation from the ability to force an outcome against opposing play.
A separately defined protected exchange-and-repair network demonstrates the same prospective-information principle outside Go. The model concerns mathematical response capacity and constitutional persistence; it does not assert that Go is a biological system or that the model provides a validated physiological measurement.
Series relationship: This is unnumbered companion research to Health, Formally Defined, developing an exact dynamical realization of the representation-sufficiency questions established in Paper III. Papers I–VI retain their existing sequence.
Complete published manuscript
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53 pages · Published preprint · November 7, 2026 · CC BY-NC-ND 4.0
Citation
James, Z. (2026). Lawful Futures in Go: Dynamically Sufficient Observation, Historical Information, and Constitutive Health. Zenodo. https://doi.org/10.5281/zenodo.24044494.