What was already known
Kosterlitz–Thouless theory predicted the essential singularity. Earlier results established phase and decay information or treated related Villain and Coulomb-gas models under different assumptions.
AI involvement
OpenAI attributes this manuscript and its two companion critical-correlation inputs to its internal model.
The OpenAI-authored paper and release document central internal-model production, but do not establish AI-autonomous session conditions.
- Supporting source (github.com) — Production and verification disclosure
Importance
This proves the predicted correlation-length scaling for the ordinary square-lattice cosine XY model.
Limitations
The constant is not given in closed form. The proof uses two companion critical-correlation results, and no completed check of this theorem or those inputs is documented.
Technical verification
The manuscript provides a proof that depends on two companion model-produced critical results, but the cited release documents no completed human or machine check of this full essential-singularity theorem. Reported is the evidence default.
Human understanding
No named human account explains the central temperature-response and correlation-length conversion; Few is the evidence default, not a finding that people cannot understand it.
Correction and publication history
If correct, this proves the predicted correlation-length scaling for the ordinary square-lattice cosine XY model.
Read this published revision