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Sec Grammar Transitions

Abstract

Every canonical family has the stated transition multiplicities under one derivative step.

Theorem 1.1 (Canonical transition counts).

Lean statement: D5/S3/Combinatorics/QGrammar/SecGrammarTransitions.transitions

Proof. Machine-checked in Lean as D5/S3/Combinatorics/QGrammar/SecGrammarTransitions.transitions (✓ 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.

For each family, index, and pair of multiplicities, the support branches produced by one derivative step are exactly the listed canonical states, with the stated boundary cases and multiplicities.

References