OpenAI reports SLE limits for square-lattice random-cluster interfaces

For each fixed 1≤q<4, the critical square-lattice random-cluster Dobrushin interface converges as an ordered curve in uniformly approximated marked bounded Jordan domains to chordal SLE with κ(q)=4π/arccos(−√q/2).

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Understanding the problem

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For each fixed 1≤q<4, the critical square-lattice random-cluster Dobrushin interface converges as an ordered curve in uniformly approximated marked bounded Jordan domains to chordal SLE with κ(q)=4π/arccos(−√q/2).

Why it matters

If correct, identifies the full interface scaling law across the critical square-lattice random-cluster range 1≤q<4.

What counts as progress

Do critical square-lattice random-cluster interfaces converge to the predicted SLE laws for 1≤q<4?

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