OpenAI reports a CLE₄ curve limit for half-plane double dimers

The complete loop ensemble of the Temperleyan square-lattice double-dimer model in the upper half-plane converges along the full mesh limit to nested CLE₄, matching every macroscopic loop as an unparametrized curve.

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Understanding the problem

Read the background

The complete loop ensemble of the Temperleyan square-lattice double-dimer model in the upper half-plane converges along the full mesh limit to nested CLE₄, matching every macroscopic loop as an unparametrized curve.

Why it matters

If correct, resolves the half-plane Temperleyan double-dimer CLE₄ scaling-limit conjecture at the level of complete curves.

What counts as progress

Do complete half-plane Temperleyan double-dimer loops converge as curves to nested CLE₄?

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