Counting the Sec Grammar Region

Abstract

Counting the finite support region gives the cubic formula in Conjecture III.7.

Theorem 1.1 (Region cardinality).

Lean statement: D5/S3/Combinatorics/QGrammar/SecGrammarCounting.region_count

Proof. Machine-checked in Lean as D5/S3/Combinatorics/QGrammar/SecGrammarCounting.region_count (✓ 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 every positive natural n, the cardinality of region n equals omegaFormula n. The small steps are evaluated directly, and the odd and even ranges reduce to the two cubic expressions.

References

• Truth anchor: D5/S3/Combinatorics/QGrammar/SecGrammarCounting.region_count
• Dependency: D5/S3/Combinatorics/QGrammar/SecGrammarRegion