What was already known
The human authors’ more general Proposition 3.3 and an earlier Laguerre-tessellation theorem also yield this proposition.
AI involvement
The authors credit GPT-5.5 Pro with the direct proof that aided two authors’ initial route. A third author independently developed the stronger main proof.
GPT-5.5 Pro is explicitly credited with the retained alternative proof of the coupling proposition, a central step of the initial approach; the main resolution is separately human-credited.
Importance
The model proof offers another route to a useful coupling lemma, with limited added scope beyond the human results.
Limitations
The authors give a different derivation, but do not document a complete check or full human explanation of the model’s direct Laguerre-cell proof.
Technical verification
The authors' independent derivation supports the proposition as a mathematical statement but does not document a completed check of the model's original direct Laguerre-cell proof. No proof-assistant or exact certificate check of that proof is reported.
Human understanding
The authors explain what the coupling achieves and relate it to Laguerre cells, but their distinct hierarchical derivation does not fully explain the model's direct proof mechanism.
Correction and publication history
The model proof offers another route to a useful coupling lemma, with limited added scope beyond the human results.
Read this published revision