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Support Reduction for the Sec Derivative

Abstract

Positive coefficients make support evolution exactly the collection of normalized positional branches.

Theorem 1.1 (Support reduction and positivity).

Lean statement: D5/S3/Combinatorics/QGrammar/SecGrammarSupport.support_reduction

Proof. Machine-checked in Lean as D5/S3/Combinatorics/QGrammar/SecGrammarSupport.support_reduction (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Guo-Niu Han, Kathy Q. Ji, Huan Xiong (2026). q-Derivative Grammar. DOI: 10.48550/arXiv.2604.23959. URL: https://arxiv.org/abs/2604.23959v2.

Commentary.

At every step all polynomial coefficients are nonnegative. A word belongs to the next support exactly when it is obtained by choosing a support word, a position, and a supported replacement, then applying the DIO normalization to the resulting concatenation.

References