Reflective Labs / Research / № 1

Proposal, gate, commitment

Deterministic convergence as a substrate for organizational decisions

substratefixed pointmixture of expertsdeterminism

Abstract

Autonomy is cheap. A competent model, a tool loop and a queue produce an autonomous agent in an afternoon. Trust is the expensive part, and the prevailing method of obtaining it — observe the system, measure how often it is right, extrapolate — yields a statistical claim about the past where an organization needs a structural claim about the future. We describe Converge, a deterministic multi-agent runtime built on the opposite ordering: agents may propose anything, and only the engine may decide. The architecture is a mixture of experts in the older and stricter sense of that phrase — heterogeneous solvers behind a gate that is policy rather than a learned softmax — and language models are one expert among several rather than the substrate. Shared state is an append-only context ordered by inclusion; agents are inflationary, idempotent, commuting maps over it; and every proposal crosses an explicit promotion gate that checks authority, schema and confidence before it becomes a fact. Nine invariants — monotonicity, determinism, idempotency, commutativity, termination, consistency, starvation freedom, confluence and observability — are enforced by the engine rather than measured after it. We show that monotonicity and gate commutation give local confluence, that a budget-bounded well-founded measure gives termination, and that the two together yield a unique normal form by Newman's lemma; determinism is therefore a theorem about the substrate rather than a property we hope the scheduler preserves. Every run ends in one of four honest exits — converged, budget exhausted, policy blocked, escalated — each carrying its own provenance. The claim is bounded and worth stating precisely: invalid states are not improbable, they are unrepresentable.