Family 365 as a regularity audit

Family 365 records smooth boundary metric/connection recovery claims and a bounded-measurable scalar-conductivity nonuniqueness claim OpenAIOverview. These are documentary comparisons, not inputs to any theorem here.

There is no measurement map in this paper identifying Boolean-oracle queries or synthesis-test probabilities with a Dirichlet-to-Neumann form. Therefore:

• a finite synthesis certificate does not identify a smooth metric or a unitary connection;

• a rough-conductivity counterexample does not invalidate a finite channel identity;

• neither a conductivity ambiguity nor a synthesis tolerance produces two conventional quantum potentials with identical operational data without additional maps and regularity assumptions.

The regularity analogy is methodological: the hypothesis class must be fixed before a theorem is transferred. It is not itself an inverse-problem theorem.