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Question
Which extra data turn a refinement diagram into a represented AQFT comparison?
What the note explains
The categorical assignment, its admissible reconstruction objects, and its represented Hilbert-space realizations are distinct levels. Analytic control must be supplied at the represented level.
Example
A pullback functor can organize a diagram without supplying a vacuum vector or proving convergence of its quadratic forms. List those missing inputs before applying the spectral-transfer statement.
What the approach gains
The formulation records where descent, vacuum control, form convergence, and invariant-mass identification enter the argument. It makes an apparently single reconstruction step inspectable as separate mathematical obligations.
Reading route
Read Sections 1–4 for the categorical setting, Sections 5–6 for the stated scalar central-band cohomological comparison, and Section 7 for the analytic hypotheses.
Scope and limits
The v0.4 class identity is stated at its scalar central-band scope. It must not be advertised as an unrestricted physical H³-to-H² lift or a general correspondence-valued realization theorem.