A Playable Nomic with a Provably Entrenched Core: Two-level self-amendment on a decidable substrate
Ohad Asor · arXiv (Cornell University) · 2024
Nomic — the game in which changing the rules is the game — has been played since 1982. Where it has been computerized, a machine executes player-authored rules; whether a proposed rule change is legal with respect to the constitution so far still rests on human interpretation. This paper reports a playable Nomic-family multiplayer system in which the legality of a proposed rule change — defined as logical consistency with the current constitution, together with redundancy and conflict against a sealed core — is decided by computation in a decidable logic rather than executed by a general-purpose interpreter or adjudicated by humans; and in which preservation of the sealed core under every amendment the kernel admits is an inductive invariant of the kernel specification, its step a validity in the theory of atomless Boolean algebras, its base the genesis seal. It describes the two-level architecture forced by a trilemma (replace-open content, a closed rule-of-change, decidable adjudication — no single-level design attains all three), the institution built on the kernel (a notary whose output is ratified through computed consequences, commit–reveal fairness with order-independent resolution, roles as entailments, a well-formed randomness beacon, quantitative rights), and the proofs-as-gates discipline behind each claim. The trusted computing base and the limits are stated plainly: this proves nothing about arbitrary programs, and it is precisely the restriction to a decidable fragment that makes the invariant possible and bounds what "law" can express. Scope of this deposit: the paper. The kernel-level claims are reproducible from a public tutorial suite (linked below). Institution-layer artifacts — gate reports, journals, the fixed kernel specification, measurement data — remain private at this time.