People keep asking me: what's different about optimization in RL? Seemingly nothing — the pre-training stack just works (Adam, even SGD 👀 @saagnikkk). Bringing some answers from my last work (sorry for the delay — been cooking 🚀). We introduce ISO: Isospectral Optimization: an RLVR-native optimization stack. Built on one simple observation, spectral inheritance: RLVR can reuse the base model's spectrum and acquire new behavior purely through the singular frames. 🧩 Offline: ISO-Merger — consolidates RL experts into one model with no data, no rollouts, no OPD. Checkpoints only. ⚙️ Online: ISO-Optimizer — a drop-in wrapper on AdamW / Muon that matches AdamW's accuracy with ~2.7× fewer steps on Qwen3-8B-Base. 📄 https://arxiv.org/abs/2607.19331 🌐 https://iso-rlvr.github.io/ 🧵👇