Version 2 of the manuscript. This version contains revisions and clarifications followinginternal review and has been submitted to a peer-reviewed journal. Changes include:• explicit constraint formulation• improved theoretical exposition• expanded simulations• revised section structure Abstract Directed acyclic growth processes arise in many combinatorial and stochastic systems where structural constraints limit admissible extensions. We investigate a growth rule based on a finite-horizon Principle of Maximal Freedom (PMF), under which admissible extensions are evaluated according to the number of admissible growth trajectories they permit over a fixed horizon. Using Monte Carlo simulations of constrained directed acyclic graph growth, we examine the structural consequences of this rule under varying constraint regimes. Parameter sweeps over structural constraints show that PMF growth consistently preserves larger admissible frontiers than random admissible growth while suppressing excessive causal chain formation. To clarify the mechanism underlying this advantage, we analyze the finite-horizon continuation landscape defined by the continuation multiplicities of admissible extensions. The continuation landscape exhibits substantial heterogeneity, with nearly all admissible branches producing distinct continuation capacities and a spread approaching a factor of two between the smallest and largest continuation values Mapping PMF selections onto this ranked continuation landscape shows that the rule systematically selects branches near the top of the continuation spectrum, typically within the highest decile of admissible extensions. These results indicate that finite-horizon PMF functions as an approximate optimizer of continuation multiplicity, preserving structural flexibility in constrained directed growth systems. Related work:Kouvidis (2026)Finite-Horizon Freedom Maximization in Directed Acyclic Growth.DOI: 10.5281/zenodo.18798063
Georgios K. Kouvidis (Thu,) studied this question.