Stable Histories, Entropic Time, and Branch Selection in the L(6+7) Framework

This preprint formulates a structural law for selecting stable histories in the space of admissible branches under entropic time. An informal label sometimes used for this problem is “formula of fate”; here it is treated not as an everyday metaphor or mystical claim, but as a variational-entropic law according to which the realized branch is the one that accumulates the largest integral structural weight while preserving form, coherence, memory, returnability, and quality of self-view under noise suppression. We introduce the history-weight functional, normalized realization probability, logarithmic growth rate, a criterion of branch stability, a theorem for the transition from a rare branch to a dominant one, a geometric interpretation in a negatively curved history space, and an explicit bridge to the L(6+7) program through the statistical functional Θ = log Z and the flow S = D_aΘ. The paper claims a formal architecture and a testable selection law; it does not claim that all coefficients are already calibrated or uniquely derived from a completed microscopic closure.