Magnetic Response and Lee–Yang Zeros Across Scales on Random Recursive Trees

This preprint studies magnetic response and Lee–Yang zeros of the ferromagnetic Ising model on uniform random recursive trees. Conditioning on the complete growth history, it establishes sublinear-index matching of finite-tree zeros to microscopic limits, describes the bulk zero measure and fluctuations, computes resonant intensities and response amplitudes, and relates zero intensities to weak-field magnetization and quenched density tails. Finite-tree numerical tests examine growing zero indices, resonance amplitudes, and pinning controls. This deposit contains the English and Chinese main manuscripts (revision r25), the bilingual foundational and immediate companion manuscripts, and bilingual proof-dependency guides. The supporting manuscripts are the author’s own unpublished proof materials, not independent published support. The complete manuscript sources, numerical data and code, audit records, and historical supporting sources are available separately in the fixed GitHub release v1.0.0: https://github.com/LStar404/ising-across-scales/releases/tag/v1.0.0 (commit 0a363e6da20e529d0079aa50566343ff00f2b7a6). They are not included as ZIP files in this Zenodo deposit. Paths to source archives in the dependency guides refer to that GitHub release’s source archive. This is a research preprint, not a claim of peer-reviewed acceptance or full formal verification. CC BY 4.0 applies to material the author is entitled to license. Third-party material, if identified with separate rights notices, remains subject to those notices.