What's this about?
A training-method paper tackling a known failure of reinforcement learning for reasoning: if a model *never* stumbles onto a correct answer for a hard problem, there is nothing to reward, so it never learns. The fix injects "privileged information" (hints only available during training) off to the side, so the model can find a correct path and then learn to reproduce it without the hint.
What exactly is "RLVR"?
Reinforcement Learning from Verifiable Rewards: you let the model attempt problems that have checkable answers (math, code), reward the runs that get it right, and reinforce those. It only works if the model occasionally succeeds by chance — on truly hard problems it may succeed zero times, and this paper is about rescuing exactly that case.
Why does it matter?
Frontier reasoning gains increasingly come from RL on hard problems; the "the model never gets it right so can't learn" wall is a real limiter, and off-context hinting is a clean way through it.