Transcendental Algorithm for Mixtures of Distributions // Implements the Transcendental Algorithm for Mixtures of Distributions (TAMD), a penalized likelihood framework for fitting finite Gaussian mixture models. TAMD augments the Expectation-Maximization (EM) algorithm with analytic barrier terms built from the Hellinger affinity that diverge on the singular locus, actively preventing component coalescence and weight degeneracy. Provides the core TAMD fitting function, closed-form Hellinger affinity and gradient computations, the Transcendental Affinity Criterion (TAC) for geometry-aware model selection, the regularity index rho (a scalar diagnostic for mixture fit quality), and reproduction scripts for all simulation studies. Methods are described in Fokoue (2024) doi:10.48550/arXiv.2602.03889. See also Titterington, Smith and Makov (1985, ISBN:0-471-90510-4) and Watanabe (2009, ISBN:978-0-521-86408-7).