Large language models (LLMs) benefit from test-time scaling, but existing methods face significant challenges, including severe synchronization overhead, memory bottlenecks, and latency, especially during speculative decoding with long reasoning chains. We introduce A1 (Asynchronous Test-Time Scaling), a statistically guaranteed adaptive inference framework that addresses these challenges. A1 refines arithmetic intensity to identify synchronization as the dominant bottleneck, proposes an online calibration strategy to enable asynchronous inference, and designs a three-stage rejection sampling pipeline that supports both sequential and parallel scaling. Through experiments on the MATH, AMC23, AIME24, and AIME25 datasets, across various draft-target model families, we demonstrate that A1 achieves a remarkable 56.7x speedup in test-time scaling and a 4.14x improvement in throughput, all while maintaining accurate rejection-rate control, reducing latency and memory overhead, and no accuracy loss compared to using target model scaling alone. These results position A1 as an efficient and principled solution for scalable LLM inference. We have released the code at https://github.com/menik1126/asynchronous-test-time-scaling.