Principles as Dynamics: A Program-Governed World Simulation Prototype

Learning-based world models typically acquire state representations and dynamics from observations. This paper investigates a complementary path: when governing laws, applicability conditions, and parameters can be stated explicitly, can a program execute this knowledge to advance world state without relearning known dynamics implicitly in model weights? We introduce law-executing world simulation and implement a working prototype, the Principle Machine. The system assigns asymmetric computational authority. A large language model may propose candidate interpretations of natural-language input, while the program performs physical adjudication, numerical execution, and state commitment through a formal intermediate representation, versioned law contracts, candidate sandboxes, and transactional state mechanisms. The current prototype contains 34 executable physical relation/law templates and a hybrid continuous-discrete simulation kernel. Six deterministic scenarios agree with analytic references, replay step by step, and produce identical records across ten repetitions per scenario. In paired natural-language experiments using the same DeepSeek-V3.2 model at temperature 0, the Principle Machine took the preregistered execute, clarify, or reject action in 29/30 runs; all 20 successful calculations were numerically correct and their formal IRs replayed offline. Program gates more consistently prevented directional ambiguity and an invalid small-angle approximation from entering execution than direct LLM answers. An end-to-end case further showed that a 203-step simulation and terminal ground-contact event could complete without changing persistent state; only explicit commitment wrote the terminal state. Two post hoc exploratory cases add limited evidence for cross-law chains and event-driven repetition but are not included in confirmatory statistics. The contribution is not a reinvention of first-principles simulation. It is a demonstration that explicit laws can retain authority over dynamics and persistent state behind a probabilistic semantic interface, implemented as executable contracts, epistemic transactions, and replayable evidence. The conclusions are limited to the tested model, prompts, idealized physical scope, and runtime environment. Keywords: world models; first principles; neuro-symbolic systems; executable laws; intermediate representations; deterministic simulation; state branching; replayable computation