A PASS: inequality holds for all n>=7; cleared(t=u+5) has all-positive coefficients; cleared(5)=1152
A PASS: exact symbolic spot-check at n=7..199, 1e3, 1e4, 1e5, 1e6
B PASS: exhaustive exact check, 18686 connected girth>=5 graphs (all n<=6 + all n=7 trees/cycles/unicyclic)
C PASS C5                 n= 5 girth=5 minpos=0.618034 rhs=8.333333 margin=-7.715299
C PASS Petersen           n=10 girth=5 minpos=1.000000 rhs=16.666667 margin=-15.666667
C PASS Heawood            n=14 girth=6 minpos=1.414214 rhs=38.606061 margin=-37.191847
C PASS HoffmanSingleton   n=50 girth=5 minpos=2.000000 rhs=89.285714 margin=-87.285714
ALL INDEPENDENT CHECKS PASS