A black hole is like a perfect safe: everything that falls in disappears without a trace. But quantum mechanics whispers that on the microscopic level, information is not lost but recorded on an invisible "surface." Understanding this record means unraveling the fabric of gravity.
Physicists took the ABJM theory — a kind of "training ground" for real black holes. It is simple enough for calculations but retains key properties. Using machine learning, they processed data with 800 digits of precision — roughly like measuring the distance to the Moon to the size of an atom. The neural network searched for a formula for the "twisted superpotential"—a quantity that gathers quantum contributions like a cashier counting coins at the end of the day.
For three special cases (k=1,2,4), the entire remainder was expressed through an elegant infinite series — a so-called q-series. It converges absolutely and reproduces the data with fantastic accuracy, down to 10⁻⁷⁹⁷. That's like predicting the weather for every square millimeter of Earth a year in advance and not being off by a single second.
Now physicists have an exact map for one class of black holes. It shows how quantum states arrange into a clear structure rather than chaos. The next step is to test whether the same rules hold for more realistic models. Perhaps we have for the first time glimpsed the handwriting with which nature keeps track of everything that falls into the abyss.
The precision of 10⁻⁷⁹⁷ means that if the error were the size of a proton, the measured quantity would be larger than the entire observable universe.
In the Strugatskys' novel "The Doomed City," the heroes try to understand the logic of a world governed by incomprehensible laws — much like physicists unraveling the mathematics of black holes.