Dedekind's problem counts monotone Boolean functions, equivalently downsets of a Boolean lattice. We recast this enumeration as a finite layer-ratio reconstruction problem for the Whitney numbers of the ranked ideal lattice. An exact adjacent-layer double count expresses each layer ratio through local averages of the number of addable elements and the number of removable elements. Reversible fixed-layer Markov chains estimate these averages and hence estimate the Dedekind number M(n). Backtests at M(8) and M(9) calibrate seed-level variability under the fixed protocol and measure the observed Monte Carlo budget scaling. The resulting estimate probes the Whitney-number sequence of the ideal lattice. Although these rows have previously been described empirically as unimodal, the high-precision n=9 estimate has a shallow two-shoulder feature around the central rank, contrary to that empirical description; n=11 and n=13 center-window estimates show a larger-contrast analogous pattern. The protocol estimate for M(10) is \[ \widehat M(10)=(8.9360\pm0.0010)\times 10^{78}, \] where the displayed uncertainty is the budget-based forecast scale from the cross-n scaling law under the production budget.

翻译：德德金德问题计算单调布尔函数的数量，等价于布尔格的下集。我们将此枚举重新表述为对秩理想格惠特尼数的有限层比重建问题。精确的相邻层双重计数通过可添加元素和可移除元素数量的局部平均值表示每一层的比率。可逆固定层马尔可夫链估计这些平均值，从而估计德德金德数M(n)。在M(8)和M(9)上的回溯测试校准了固定协议下种层级变异，并测量了观察到的蒙特卡洛预算缩放。所得估计探求了理想格的惠特尼数序列。尽管这些行此前被经验描述为单峰的，但n=9的高精度估计在中心秩附近显示出一个浅的双肩特征，与此经验描述相悖；n=11和n=13的中心窗口估计显示出对比更明显的类似模式。M(10)的协议估计为 \[ \widehat M(10)=(8.9360\pm0.0010)\times 10^{78}, \] 其中显示的不确定度是在生产预算下基于跨n缩放定律的预算预测范围。