用物理启发的软标签优化，让噪声盒标注也能精准检测红外小目标。

Infrared small target detection (IRSTD) commonly relies on pixel-level mask supervision. Such annotations, however, are costly and inherently uncertain because infrared targets have blurred boundaries and weak textures. We formulate box-supervised IRSTD as a problem distinct from generic box-to-mask segmentation and point-supervised IRSTD. Its central challenge is to construct stable pixel-level soft supervision from highly contaminated boxes. To this end, we propose Hotspot-Anchored Label Optimization (HALO). HALO localizes a radiometric anchor inside each box under local background-statistics constraints, then synthesizes a Physically Anchored Gaussian (PAG) soft label around the anchor. This turns noisy box supervision into continuous, pixel-level soft labels. The entire process is performed offline before training, remains decoupled from the detector backbone, and requires no online label updates. Experiments on public datasets show that HALO is competitive with representative box-supervised methods under standard tight boxes. Under looser or shifted box annotations that better approximate real scenarios, HALO is substantially more robust while remaining consistent across backbones. We further introduce a contamination-aware operating-regime analysis to characterize the effective boundary of this class of methods and reveal how intrinsic signal-to-clutter ratio relates to performance.