SYMBOLIC
  (C(n,2)-m) - (2m^2/n - m) = (-4*m**2 + n**2*(n - 1))/(2*n)   ->  >=0  <=>  n^2(n-1) - 4m^2 >= 0
  Lemma 1 at 4m^2 = n^2(n-1):  (n-1)n^3/(n^2(n-1)) = n  (= n, so mean(Gr) <= 1)
ATLAS  (all nontrivial connected girth>=5 graphs, 2<=n<=7)
  graphs = 34   S1&S3&S4&S5&strict failures = 0
NAMED CAGES  (exact mean gravity as a fraction; strict bound)
  Petersen       n=10  Delta=3  mean(Gr)=3/5       <=1:True  n/mean(Gr)=50/3  lam_+<=n-1<n<=RHS: True
  Heawood        n=14  Delta=3  mean(Gr)=33/91     <=1:True  n/mean(Gr)=1274/33  lam_+<=n-1<n<=RHS: True
  Pappus         n=18  Delta=3  mean(Gr)=1/4       <=1:True  n/mean(Gr)=72  lam_+<=n-1<n<=RHS: True
  Desargues      n=20  Delta=3  mean(Gr)=1611/7600 <=1:True  n/mean(Gr)=152000/1611  lam_+<=n-1<n<=RHS: True
  Mobius-Kantor  n=16  Delta=3  mean(Gr)=19/64     <=1:True  n/mean(Gr)=1024/19  lam_+<=n-1<n<=RHS: True
ALL TWO-PATH CHECKS PASS: lambda_+ <= n-1 < n <= n/mean(Gr), uniformly for n>=2.