Seven snapshots of the sky after the eruption of Mount Pinatubo. Each snapshot is a map of concentrations for dozens of substances. The question is simple: which substance turns into which? But how do you infer a causal chain from seven frames when you have more variables than time points?

M-CaStLe looks at the map differently. For each grid cell, it collects a window of nine neighbors: the central cell plus the eight around it. There are thousands of such windows on the map, and all are treated as repeats of the same local mechanism. Instead of seven observations over time, the method gets thousands of observations in space. Each window is like a look at the same clockwork from a different angle.

On synthetic tests where the true links are known, M-CaStLe found them with an accuracy above 0.9 even with six variables at once. In a task of transport and mixing of substances, the error in determining flow direction was only 4.76 degrees. For the Pinatubo data, the method reconstructed the chain SO2 → H2SO4 → SO4 with an F1 score of 0.95, whereas standard analysis of averaged time series found no links at all.

On El Niño data, the method showed the expected asymmetry: ocean temperature influences convection, but not the other way around. This confirms that the method captures real physics rather than just fitting the answer.

Seven snapshots of the sky turned out to be enough to see the hidden gears. Thousands of windows into the same mechanism add up to a clear picture of causation.