Meaning
A thick Wilson candidate is a proposed positive-thickness realization of a finite Wilson-type construction.
The thin loop is replaced by a tubular carrier with transverse support, collars, regions, and seams. Candidate detector, operator, ground, coefficient, and filling data are attached to that carrier while retaining the original formal proposal. These are objects to be tested against the physical predicate.
Example (illustrative)
Starting from a loop γ, choose a tube Tε(γ) of positive thickness and specify how electric insertions and boundary operators act on it. This provides candidate data; the common domain and compatibility conditions still need proof.
Scope and limits
Constructing a candidate does not certify it. Building candidates within one fiber is also different from transporting already certified realizations between fibers.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 3.4.