Uniqueness of the Reflective Universal Inductor (RUI)

Determine whether the reflective universal inductor corresponding to a fixed encoding \langle b,p,h\rangle and a fixed lower semicomputable universal prior w over restricted APOMs is unique; either establish uniqueness under explicit conditions or construct multiple distinct RUIs compatible with the same w.

Background

The Reflective Universal Inductor (RUI) is an oracle-based construction that provides query access to a universal Bayesian mixture over oracle machines that use the same oracle, resolving self-referential fixed-point issues in mutual prediction.

While the authors prove existence of an RUI for any lower semicomputable universal prior, they note uncertainty about whether the RUI is unique for a given encoding and prior. Clarifying uniqueness is important for foundational properties, reproducibility, and the interpretation of fixed-point constructions.

References

For a fixed encoding \langle b,p,h\rangle and a fixed universal prior w\in\Delta' over \mathfrak{M}, it is not clear whether a reflective universal inductor corresponding to this w is unique, i.e., there might exist multiple different reflective universal inductors compatible with w.

— Embedded Universal Predictive Intelligence: a coherent framework for multi-agent learning (2511.22226 - Meulemans et al., 27 Nov 2025) in Section 5.1 (The reflective universal inductor) — Remark after Theorem 5.1 (Existence of RUI)