final check for the computed lambda and P

Orb_AutFN.jl

@@ -264,6 +264,25 @@ function main()
    info(PropertyT.logger, "maximum(P) = $(maximum(P))")
    info(PropertyT.logger, "minimum(P) = $(minimum(P))")
 
+   if λ > 0
+      sgap = PropertyT.check_distance_to_positive_cone(Δ, λ, P, tol=tol, rational=false, len=2*radius)
+      if isa(sgap, Interval)
+           sgap = sgap.lo
+      end
+      if sgap > 0
+           info(logger, "λ ≥ $(Float64(trunc(sgap,12)))")
+            Kazhdan_κ = PropertyT.Kazhdan_from_sgap(sgap, length(S))
+            Kazhdan_κ = Float64(trunc(Kazhdan_κ, 12))
+            info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
+            return true
+      else
+           sgap = Float64(trunc(sgap, 12))
+           info(logger, "λ($name, S) ≥ $sgap: Group may NOT HAVE property (T)!")
+           return false
+      end
+   end
+   info(logger, "κ($name, S) ≥ $λ < 0: Tells us nothing about property (T)")
+   return false
 end
 
 main()