On-Shell Universality in Quantum Gravity: Soft Limits, Factorization, and Asymptotic Symmetry in String and Loop Paradigms

This is Part I of a trilogy that addresses a central question in quantum gravity: whether apparently distinct microscopic approaches can nevertheless share universal projected structures at the level of observable gravitational data. The guiding claim is not a microscopic equivalence between string-theoretic and loop/group-field-theoretic variables. Instead, the papers develop a restricted universality program in which only carefully projected interface data are compared. Part I studies the on-shell sector. It argues that ambitwistor string theory and the projected causal semiclassical sector of Lorentzian spin-foam boundary amplitudes agree on a tree-level massless-graviton universality class defined by soft graviton behavior, factorization on physical poles, and asymptotic-symmetry/memory data. The spin-foam claims are formulated in the large-spin soft-window regime and are explicitly conditional on reduced-Hessian control, causal/orientation selection, and projection onto the transverse-traceless graviton sector.