Meaning
A finite physical–cohomological–coercive certificate records a realized package, its obstruction data, and a proved positive excitation bound.
The certificate contains the formal proposal, a physical realization, the filling obstruction, the relative degree-two class, the coefficient-band degree-three class, the exact complete-ground projection P, a positive constant κ, and a status ledger. Its analytic assertion is H ≥ E₀I + κ(I−P) on the certified finite carrier.
Example (illustrative)
For the toy Hamiltonian H=diag(0,0,3), P=diag(1,1,0) gives H ≥ 3(I−P). This illustrates the analytic coordinate. A full certificate would additionally supply the physical, cohomological, and status data.
Scope and limits
The filling obstruction, relative class, and band class answer different questions. The finite excitation bound is not yet an invariant mass-gap statement.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 4.9.