Em06-A and Em06-B: means, fluctuations, and control inputs

Cheung's Em06-A treats a scalar-only coherent limit with a classical metric input, rather than an unrestricted joint metric–scalar quantum construction CheungEm06A. The supplied Em06-B excerpt retains ordered Weyl correlations and an explicit state-dependent concentration bound CheungEm06B.

The present paper incorporates the analogous separation of questions, not the same theorem:

• concentration of an empirical accuracy is established by Theorem thm:evaluation;

• concentration of an independently masked matrix is established by Theorem thm:maskbernstein;

• concentration of an observable under independent masks requires the influence assumptions of Theorem thm:edgeconcentration;

• equal connection counts do not fix fluctuation sensitivity, as Proposition prop:equaldensity proves directly;

• input-control stability is proved for logits and smooth observables, and for accuracy only with a margin condition.

A bosonic residual number expectation is not a surviving-edge count. The CCR parameter is not a pruning density. No Fock space, Weyl relation, or quantum state is an assumption of the neural-network results.