Meaning
The configured persistent floor is the common lower bound that survives across an entire certified branch.
At each endpoint D, κ_conf,B(D) is the largest floor established by its configured certificate. The persistent floor is κ∗_conf,B=inf_D κ_conf,B(D). A positive value gives a uniform certified excitation floor throughout the already coherent branch. This certificate bound need not equal the exact first positive spectral value.
Example (illustrative)
Endpoint floors 1, 1/2, 1/3, … are positive individually but have persistent floor zero. Floors 2+1/n have persistent floor 2, even though no endpoint has floor exactly 2.
Scope and limits
A positive floor at one endpoint does not establish persistence, and the infimum does not construct the branch. This definition is located in GAT VIII §11, equations (11.1)–(11.4); §§12–13 use it.
Source
GAT VIII — Indexed Admissible Distributors and Selected Cofinal Čech Transport in Semisimple Yang–Mills Theory. GAT VIII, §11, equations (11.1)–(11.4); application in §§12–13.