Commit-Indexed Externalization of Stochastic Message-Passing Graph Neural Networks

We formalize a commit-indexed architecture for stochastic message-passing graph neural networks (GNNs) in which model state is externalized into a version-controlled commit space. We show that commit-indexed evaluation factors through a projection from commits to weight states, , so that it computes exactly the function of the projected weights. This is a structural refactoring: it preserves the realized function on the image of the projection (and the full function class precisely when the projection is surjective), and it does not expand or restrict expressive power beyond that. For fixed stochastic draws the equivalence is pathwise; over the randomness it is distributional; pathwise replay across sessions additionally requires the stochastic seed to be part of the commit state. We further show that gradient-based learning dynamics are preserved for commit sequences defined to mirror the weight-update operator, and we are explicit that whether a given commit-generation policy produces such sequences is a separate, policy-dependent question. The contribution is referential transparency, reproducibility, and rollback, not a change in expressive power.