The Kosterlitz essential singularity of the XY correlation length

Theorem 1.1: there is $A_{XY}\in(0,\infty)$ with $\lim_{b\uparrow b_c}\sqrt{b_c-b}\,\log\xi(b)=A_{XY}$ , for the square-lattice nearest-neighbor cosine model. The constant is expressed through the block construction and is not evaluated. It does not cover other lattices, the Villain model, the behaviour of the susceptibility, or corrections beyond the leading order.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Oct 5, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Kosterlitz essential singularity of the XY correlation length · XY correlation length essential singularity

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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Unreleased internal OpenAI model
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Named evidence

VibeMathed record: The Kosterlitz essential singularity of the XY correlation length

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 was read against Kosterlitz's prediction. It is for the ordinary cosine model on the square lattice, with $\xi$ defined from the free-box limit and then the axis separation limit, and $b$ the coupling in the Hamiltonian; the constant $A$ is identified only implicitly. The proof depends on the two companion papers for the critical inputs and on a renormalization map whose leading recursion is the Kosterlitz flow. The proof was not refereed. No Lean formalization exists for this family.

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Companion: Essential Singularity of the Correlation Length in the Planar XY Model

paper · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Critical two-point decay $r^{-1/4}(\log r)^{1/8}$ in the planar XY model

witness · pending

paper link supplied by the VibeMathed registry.

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Companion: The critical correlation exponent of the planar XY model

paper · pending

paper link supplied by the VibeMathed registry.

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Lineage and corrections

Companion: Essential Singularity of the Correlation Length in the Planar XY Model evidence for this event

Critical two-point decay $r^{-1/4}(\log r)^{1/8}$ in the planar XY model evidence for this event

This event attributed to Unreleased internal OpenAI model

Companion: The critical correlation exponent of the planar XY model evidence for this event

The Kosterlitz essential singularity of the XY correlation length parent of this event

VibeMathed record: The Kosterlitz essential singularity of the XY correlation length evidence for this event

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