Meaning
A finite Ward profile records the symmetry variations and state identities actually verified for the finite package.
It specifies finite gauge transformations or variations, their action on regional observables, the relevant vacuum state, and identities such as ω_vac(δξA)=0 on the certified class. It also records compatibility, or explicit defects, under regional restriction and detector readout.
Example (illustrative)
In a finite-dimensional illustration, let δA=i[G,A] and let a density matrix ρ commute with G. Cyclicity of the trace gives Tr(ρδA)=0. This demonstrates the form of a Ward identity; the physical package must identify its own state and allowed observables.
Scope and limits
A finite identity on a stated operator class is not a continuum Ward–Takahashi hierarchy or an anomaly-cancellation theorem.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 8.5.