Derivative-Order Nevanlinna Geometry: Divisor Variations, Characteristic Hierarchies, and Central-Index Fingerprints

This paper studies the derivative‑order ladder from the viewpoint of Nevanlinna value distribution. It establishes exact divisor variation identities that relate the derivative‑order divisors of a meromorphic function. A Nevanlinna characteristic hierarchy is derived that provides interlacing relations between the characteristic function at successive orders. The work defines central‑index fingerprints based on divided differences and proves that a finite jet determines the derivative‑order spectrum.