Metric and area nonidentification

The interval poset and conformal data of a circle do not specify an absolute spatial radius. For every $R>0$, the metric

has the same oriented intervals and the same conformal class. Assigning a physical time and energy scale is additional data.

Appending unrelated geometries to Definition def:determination similarly changes an assigned horizon area or mass without changing the sector record. This is not a proof that those geometries are duals of the CFT. It is the precise statement that no such duality is part of the record.

Family 265's reported gapped-lattice area law and Family 260's reported enclosing-area inequalities concern different mathematical objects Dossier. Neither number can be substituted for $\mu$. An area-law claim additionally needs a state, a cut, entropy regularization where appropriate, and a relation between that cut and its geometric area.