The proof came together right before Christmas 2025.

The result affects no one directly, closing a gap simulations could not.

The same critical point governs water through rock, disease through networks and power-grid cascades.

The proof covers one broad graph class, leaving other network families unproven.

How each outlet framed it
Quanta Magazine leans favorable
narrates the emotional breakthrough moment: mathematicians working through holidays, the 'almost didn't believe it' realization

Sources: Quanta Magazine