Frozen vision-language models saturate at about five objects: GeoScope splits views at a measured counting horizon to lift training-free ultra-high-resolution remote sensing QA

The bottleneck in ultra-high-resolution remote sensing question answering shifts from where to look to when the model's reading in the chosen view cannot be trusted: eight open vision-language models systematically undercount once a single view holds more objects than their counting horizon, about five objects for most on DOTA aerial images. Earlier training-free methods chose views by zoom search, patch retrieval, attention following or evidence selection, and assumed that counts and directions in the chosen view could be trusted; among the MME-RealWorld remote sensing categories of position, colour and counting, counting is the weakest for every method that reports all three. On DOTA crops, Qwen3-VL-8B stays within 15% error up to five objects, turns systematically negative beyond, and falls to about 60% undercount above 160 objects; 256-pixel crops shown threefold enlarged stay within 21% up to 160 objects, while 2,048-pixel crops at native resolution fall short at every number of objects.

GeoScope has a frozen text-only language model write a typed spatial program from the question alone, fixing the region and its resolution; the vision-language model only grounds and counts within its operating range, and directions are computed from grounded boxes with the direction-relation matrix. Earlier split-based counting either relies on a trained counter or splits once; GeoScope decides whether to split from a measured counting limit of the frozen model, and a power-law response model estimates in advance how much undercount a split recovers and how many spurious counts it adds. On the held-out XLRS-Bench test split, GeoScope raises Qwen3-VL-8B from 47.50 to 63.75 on regional counting and from 33.50 to 44.00 on spatial relations, and from 25.18 to 36.60 on MME-RealWorld counting; on UHR-Micro global counting it gains 16.8 points, 15.6 of them from subdivision.

The demonstrated scope is regional counting, spatial relations and object counting on aerial and drone imagery, with the counting horizon measured on DOTA crops and used for every backbone and dataset; position and colour questions still go to the frozen backbone, and land use, anomaly and environmental reasoning, route planning and change questions lie outside the program language.

The power-law response model is a descriptive fit, and above 160 objects the predicted amplification falls well below the observed one because split parts reveal objects too small to see in the parent view; the counting horizon moves with view size, apparent object size and imagery, setting in later on FAIR1M, DIOR and VisDrone.