A cosmic "caliper" will soon measure a neutron star to within a hundred meters. For an object a couple dozen kilometers across, that's like measuring the thickness of a human hair from a kilometer away.

A neutron star is the remnant of an exploded supernova. Its matter is squeezed so tightly that a teaspoonful would weigh billions of tons. But what exactly is it like? Physicists describe it with an "equation of state"—essentially a recipe linking pressure and density. The trouble is, there are many recipes, and picking the right one is hard.

The authors took a Bayesian approach: instead of looking for a single answer, they weighed the probabilities of different options. In their simulation, future data from X-ray and gravitational-wave observatories sifted through thousands of possible equations of state. The result is not just an average radius but a whole spectrum of probabilities for each ingredient in the recipe.

Particularly tricky was the transition from the hadronic (nuclear) phase to the quark phase. It's like the moment water turns into ice, but under monstrous pressures. New data will reveal whether this transition is sharp or smeared out. And that means peering into the very heart of a star without leaving Earth.