Orthogonal and 1-Lipschitz neural network layers are essential building blocks in robust deep learning architectures, crucial for certified adversarial robustness, stable generative models, and reliable recurrent networks. Despite significant advancements, existing implementations remain fragmented, limited, and computationally demanding. To address these issues, we introduce Orthogonium , a unified, efficient, and comprehensive PyTorch library providing orthogonal and 1-Lipschitz layers. Orthogonium provides access to standard convolution features-including support for strides, dilation, grouping, and transposed-while maintaining strict mathematical guarantees. Its optimized implementations reduce overhead on large scale benchmarks such as ImageNet. Moreover, rigorous testing within the library has uncovered critical errors in existing implementations, emphasizing the importance of standardized and reliable tools. Orthogonium thus significantly lowers adoption barriers, enabling scalable experimentation and integration across diverse applications requiring orthogonality and robust Lipschitz constraints. Orthogonium is available at https://github.com/deel-ai/orthogonium.

Large Language Models (LLMs) are gaining traction as a method to generate consensus statements and aggregate preferences in digital democracy experiments. Yet, LLMs could introduce critical vulnerabilities in these systems. Here, we examine the vulnerability and robustness of off-the-shelf consensus-generating LLMs to prompt-injection attacks, in which texts are injected to amplify particular viewpoints, erase certain opinions, or divert consensus toward unrelated or irrelevant topics. We construct attack-free and adversarial variants of prompts containing public policy questions and opinion texts, classify opinion and consensus valences with a fine-tuned BERT model, and estimate Attack Success Rates (ASR) from $3\times3$ confusion matrices conditional on matching human majorities. Across topics, default LLaMA 3.1 8B Instruct, GPT-4.1 Nano, and Apertus 8B exhibit widespread vulnerability, with especially high ASR for economically and socially conservative parties and for rational, instruction-like rhetorical strategies. A robustness pipeline combining GPT-OSS-SafeGuard injection detection, structured opinion representations, and GSPO-based reinforcement learning reduces ASR to near zero across parties and policy clusters when restricting attention to non-ambiguous consensus outcomes. These findings advance our understanding of both the vulnerabilities and the potential defenses of consensus-generating LLMs in digital democracy applications.