Survival of the Bound: A Quantitative Theory of Persistence-Driven Binary Dominance in Dense Star-Forming Regions

We present a predictive quantitative model for the emergence of binary dominance in dense embeddedstar-forming regions through differential survival rather than preferential formation. Building on thepersistence selection framework (ΠC ∝ λCτC), we derive analytic expressions for configuration lifetimesfrom first-principles energy balance, calculate time-dependent multiplicity fractions, and predict sixobservable signatures that distinguish this model from formation-only theories. For typical Class 0conditions, we obtain τpair/τsingle ≈ 8 and τpair/τtriple ≈ 5, yielding predicted binary fractions of ∼55%at Class I declining to ∼32% in the field—consistent with VANDAM and Gaia observations. The modelpredicts: (1) singles show 2.5× higher velocity dispersions than binaries, (2) mean separations decreasefrom 100 au to 50 au over 3 Myr, (3) binary fraction scales as n0.3gas, (4) close binaries have mass ratios q >0.6, (5) circumbinary disks appear in >70% of tight systems, and (6) hierarchical/non-hierarchical tripleratios evolve from 0.5 to 5. We provide detailed simulation specifications for validation and discussapplications to brown dwarf and massive star formation. Unlike previous models, this frameworkmakes the counterintuitive prediction that *increasing* turbulence enhances binary fractions throughaccelerated three-body hardening.