The source record and continuum type

The supplied Family 211 records name:

• Canonical conformal limits of subcritical FK planar maps;

• Metric-measure limits of subcritical FK and spanning-tree planar maps;

• {The critical Liouville quantum sphere and geometric limits of FK maps at $q=4$};

• the attached $q>4$ Brownian-CRT preprint;

• optional random-walk and spectral FK–Ising companions.

The companion texts, full hypotheses, and proof dependencies are not reconstructed here Dossier. Calling this collection a phase-diagram record does not verify a completed phase-diagram theorem.

The relation $p=\sqrt{q}/(\sqrt{q}+2)$ puts $q=4$ at $p=1/2$. The inventory transition is part of the established inventory context Sheffield. It is not a spacetime-transition theorem.

GHP convergence concerns compact metric probability spaces. The supplied limit is a real tree. Its Hausdorff dimension is almost surely two DuquesneLeGall. One must therefore replace the proposed assertion that it has no intrinsic metric dimension greater than one by the precise assertion:

Its dimension does not produce a Liouville field, conformal atlas, spectral triple, or gravitational action.

Moreover, GHP convergence to a tree does not by itself prove that every combinatorial cycle has vanishing diameter. For example, a ladder graph with two long rails and unit rungs, rescaled by the inverse rail length, converges to an interval: the rungs collapse, while its outer simple cycle spans nearly the entire limiting interval. For the particular block model, a separately proved bound on the maximum block diameter can control its cycles. Such a conclusion must be attributed to that bound, not to GHP convergence alone.