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. Keywords: derivative‑order geometry, Nevanlinna theory, divisor variation, characteristic hierarchy, central‑index fingerprint.
Mohammad Abu-Ghuwaleh (Tue,) studied this question.
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