A Kazhdan–Lusztig interaction formula for nested (non-split) matroids with two cyclic flats

This record contains the preprint "A Kazhdan–Lusztig interaction formula for nested (non-split) matroids with two cyclic flats", together with its LaTeX source (main.tex, refs.bib) and an ancillary Python verification engine (kl_engine.py). The paper studies the Kazhdan–Lusztig (KL) and inverse KL polynomials of a nested (Schubert) matroid whose lattice of cyclic flats is a chain of length two — the smallest non-split configuration. For such a matroid M with cyclic flats ∅ ⊊ L₁ ⊊ L₂ ⊊ E, it introduces the interaction I := P_M − PM₁ − PM₂ + P_U, which measures the failure of valuative additivity relative to the two single-stress elementary-split matroids M₁, M₂ and the ambient uniform matroid U. Main results: closed forms for the linear KL coefficient (proved for all ρ₁ by a hyperplane count) and the constant inverse-KL coefficient (proved for all ρ₁ via a deletion–contraction induction built on the inverse-KL deletion formula of Braden, Ferroni, Matherne and Nepal); a generating-function recursion governing both coefficients; and a general degree law expressing the interaction at any rank as an explicit binomial combination of hyperplane values. The ancillary file kl_engine.py reproduces all computational claims and the worked example. Generative AI tools were used to assist with reference verification, symbolic computation and its checking, and proofreading; the author designed the research, independently verified all proofs and computations, and accepts full accountability for the content.