# Exact exponent arithmetic for Theorem 1.1. No arguments.
from fractions import Fraction as Fr
from math import comb, log10
W=[5,30,180]; Xs=4+5*W[0]+5*W[1]+7*W[2]; k=Xs+1
print("X* =",Xs," k =",k,flush=True)
s0=479; print("3*s0-(k-1) =",3*s0-(k-1),"(must be negative)",flush=True)
c=42+249*(k-1)-9*s0; gamma=Fr(354042,354043); alpha=gamma+c; eta=2*gamma/alpha
print("alpha =",alpha,"=",float(alpha),flush=True)
print("eta =",eta,"=",float(eta),flush=True)
assert eta==Fr(1,177022) and gamma<1 and c==354042
print("ratio to the claimed 2/100866719:",float(eta/Fr(2,100866719)),flush=True)
M=comb(163,41); T=comb(M,3); kk=T*T+1
print("OpenAI eta = 2/(45435k+16), log10 =",log10(2)-log10(45435*kk+16),flush=True)