What was already known
One-dimensional gapped states had polynomial-bond MPS approximations. General two-dimensional results needed extra density-of-states assumptions and gave quasipolynomial bounds; a related question concerned translation-invariant tori.
AI involvement
OpenAI credits an internal model with producing the manuscript and supporting proof artifacts. No named human proof checker or explanation is documented.
The cited release credits an internal OpenAI model with producing the result and the manuscript credits OpenAI as author; the record does not establish model autonomy from task selection or human direction.
Importance
The theorem gives polynomial-bond PEPS existence for a broad open-grid class.
Limitations
The result is existential and does not cover the translation-invariant torus question or efficient construction. Its proof imports a companion area law without documented completed specialist checking.
Technical verification
The cited theorem and companion area-law proof are released, but neither a completed human proof check nor machine check is documented. The registry’s comparison of hypotheses is a scope check, not a technical check.
Human understanding
No named person explains the central argument in the reviewed sources. Few is the evidence default, not a finding that people cannot understand it.
Correction and publication history
If correct, the theorem gives polynomial-bond PEPS existence for a broad open-grid class.
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