Appendix to "BRICER: Byzantine-Robust Private Collaborative Mean Estimation over Intermittently-Connected Networks"

This document is the supplementary technical appendix to the paper "BRICER: Byzantine-Robust Private Collaborative Mean Estimation over Intermittently-Connected Networks." It presents detailed mathematical derivations and proofs supporting the theoretical results in the main paper, which are omitted from the conference manuscript due to page limitations. The appendix includes the proof of the participation guarantee (Lemma 2), the mean-squared error (MSE) guarantee (Theorem 1), and the differential privacy guarantee (Lemma 1). It further provides an alternative analysis of geometric-median aggregation, including its corresponding MSE bound, details of the optimization procedure underlying the weighting strategy in Section VII, and illustrative worked examples. Additionally, the appendix presents numerical checks of the theoretical results and supplementary discussions of the assumptions, analytical bounds, and technical details used throughout the analysis. This supplementary material is intended to support reproducibility and provide a comprehensive reference for the theoretical analysis presented in the main BRICER paper.