Meaning
The finite analytic shadow retains the operator and quantitative comparison information of a package while forgetting its cohomological coordinates.
For a fixed threshold profile, it is the unitary-equivalence class of the declared full operators, exact grounds, sectorwise comparison triples, mixed corners, singular values, refinement-defect norms, seam reserves, and other named analytic data. The relative and band classes and their separately declared selection costs are omitted.
Example (illustrative)
If one changes every carrier by the appropriate unitary and conjugates all operators and typed comparison maps consistently, the analytic shadow is unchanged. Matching only the eigenvalues of H is insufficient because the shadow retains much more.
Scope and limits
Equal analytic shadows do not establish equality of the omitted cohomological data. A cohomological cost is not automatically a Hamiltonian penalty.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 16.1.