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Validates the DOTDD framework's effectiveness in quantifying distribution dynamics using corporate salary data and branching measurements, indicating new diagnostic insights.
The DOTDD extends the Operator Theory of Distribution Dynamics (OTDD) to discrete and constrained distribution spaces. Three canonical kernel geometries — birth-death chains, doubly stochastic matrices, and triangular matrices — produce three canonical attractor regimes covering Poisson, Binomial, Geometric, and Zipf distributions. Two structural theorems are proven: (1) the α-invariance theorem, showing that equilibrium distributions are independent of the dissipation parameter α; and (2) the Leonardo–DOTDD equivalence, establishing that Leonardo's branching rule (β=2) corresponds to α=0 in the Allocation Law and to a doubly stochastic kernel in DOTDD. Empirical validation against Fortune 500 corporate salary data and tree branching measurements confirms the framework. A new diagnostic measure, the Overhead Deviation Index (ODI), quantifies structural deviation from the physical optimum established by natural branching systems.
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László Tatai (2026) studied this question.
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