Sahar Diskin、Philip Easo、Ritvik Ramanan Radhakrishnan、Benny Sudakov和Vincent Tassion五位数学家在2025年12月于瑞士苏黎世联邦理工学院完成了渗流理论中的"超临界锐度猜想"的证明1。这一猜想是困扰学界数十年的难题，涉及流体在无限传递图上的渗透行为研究1。
该证明通过新颖而简洁的方法证明了当概率超过临界值时，流体几乎覆盖整个图的结构，且该方法适用于所有无限传递图1。这一领域的研究始于1996年，当时Benjamini和Schramm提出在更广泛的传递图类上研究渗流的问题1。其后在2007年Antunović和Veselić完成了"亚临界"部分，但该领域在2008年Oded Schramm去世后陷入停滞1。
这项成果已获得学界高度认可。数学家Asaf Nachmias评价称："我对这一证明感到欣喜。这太令人惊艳了。"1另一位专家Itai Benjamini则用"宝石"来形容这项工作1。
Five mathematicians have completed a proof of the supercritical sharpness conjecture, a problem that has remained unsolved in percolation theory for decades.1 The breakthrough was confirmed in December 2025 at ETH Zurich, with the researchers—Sahar Diskin, Philip Easo, Ritvik Ramanan Radhakrishnan, Benny Sudakov, and Vincent Tassion—delivering their solution before Christmas.1 By studying how fluids permeate through infinite transitive graphs, the team demonstrated that when probability exceeds a critical threshold, the fluid nearly covers the entire graph structure.1
The conjecture traces its origins to 1996, when Benjamini and Schramm raised questions about extending percolation research across a broader class of transitive graphs.1 A partial breakthrough came in 2007 when Antunović and Veselić completed the subcritical portion of the problem, though progress stalled following Oded Schramm's death in 2008.1 The new proof employs an elegant and novel approach applicable to all infinite transitive graphs, distinguishing itself through its conceptual simplicity and broad applicability.1
The mathematics community has greeted the result with enthusiasm. Asaf Nachmias remarked, "I find great joy in this proof. It's stunning."1 Fellow researcher Itai Benjamini called it "a gem. It's a gem."1
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