We present LOVER, a  ̲Long to sh ̲Ort  ̲Video  ̲Evidence  ̲Reinforced model for grounded question answering (GQA). LOVER highlights three innovations over existing reinforcement-learning (RL) based video reasoning models: (1) Long-to-short Video Evidence Curriculum Learning, which organizes RL training according to evidence duration and progressively adapts the model from long-range grounding to short-term reasoning; (2) GQA Rewards, which underscore the benefit of IoP reward over IoU for evidence spotting rather than strict temporal span overlap; (3) Adaptive Timestamp Rendering, which adaptively renders timestamps onto video frames using background-aware position and color selection to enhance temporal observability. The three designs are model-agnostic and reciprocal. They effectively improve QA, grounding, and grounded QA performance over different backbones. Notably, LOVER built on Time-R1 achieves new state-of-the-art (SOTA) results among open-source models on popular GQA benchmarks: NExT-GQA and ReXTime. Comprehensive ablation studies further validate the effectiveness of our three innovative components.