Recent advances in mathematical reasoning typically rely on massive scale, yet the question remains: can strong reasoning capabilities be induced in small language models (≤1.5B) under extreme constraints? We investigate this by training models on a single A40 GPU (48GB) for under 24 hours using Reinforcement Learning with Verifiable Rewards (RLVR) and Low-Rank Adaptation (LoRA). We find that the success of this “micro-budget" regime depends critically on the interplay between adapter capacity and model initialization. While low-rank adapters (r=8) consistently fail to capture the complex optimization dynamics of reasoning, high-rank adapters (r=256) unlock significant plasticity in standard instruction-tuned models. Our best result achieved an impressive 40.0% Pass@1 on AIME 24 (an 11.1% absolute improvement over baseline) and pushed Pass@16 to 70.0%, demonstrating robust exploration capabilities. However, this plasticity is not universal: while instruction-tuned models utilized the budget to elongate their chain-of-thought and maximize reward, heavily math-aligned models suffered performance collapse, suggesting that noisy, low-budget RL updates can act as destructive interference for models already residing near a task-specific optimum.

Misinformation is on the rise, and the strong writing capabilities of LLMs lower the barrier for malicious actors to produce and disseminate false information. We study how LLMs behave when prompted to spread misinformation across languages and target countries, and introduce GlobalLies, a multilingual parallel dataset of 440 misinformation generation prompt templates and 6,867 entities, spanning 8 languages and 195 countries. Using both human annotations and large-scale LLM-as-a-judge evaluations across hundreds of thousands of generations from state-of-the-art models, we show that misinformation generation varies systematically based on the country being discussed. Propagation of lies by LLMs is substantially higher in many lower-resource languages and for countries with a lower Human Development Index (HDI). We find that existing mitigation strategies provide uneven protection: input safety classifiers exhibit cross-lingual gaps, and retrieval-augmented fact-checking remains inconsistent across regions due to unequal information availability. We release GlobalLies for research purposes, aiming to support the development of mitigation strategies to reduce the spread of global misinformation: https://github.com/zohaib-khan5040/globallies