Multi-Agent Bound Conjecture

Ascertain the scaling law for the total power required when N BEDS agents collectively maintain a shared belief, by deriving the function f that depends on network topology such that the total power satisfies P_total proportional to γ τ* · f(N, topology).

Background

The paper considers distributed maintenance of beliefs by multiple agents, suggesting that collective power costs depend both on the number of agents and the communication topology.

This conjecture seeks to formalize how network structure influences energetic efficiency in multi-agent continuous inference systems.

References

Conjecture [Multi-Agent Bound] For $N$ agents collectively maintaining a shared belief, the total power scales as: \begin{equation} P_{\text{total} \propto \gamma \tau* \cdot f(N, \text{topology})\end{equation} where $f$ depends on network structure.

— BEDS : Bayesian Emergent Dissipative Structures : A Formal Framework for Continuous Inference Under Energy Constraints  (2601.02329 - Caraffa, 5 Jan 2026) in Section 7.3 (Open Problems)