CARBOT: A Mathematically Verified Rule-Based Molecule Generator for π-Conjugated and Aromatic Hydrocarbons

π-Conjugated and aromatic hydrocarbons are foundational molecular scaffolds in materials science. Their design and discovery, however, remain limited by the lack of systematic frameworks for exploring the vast chemical space while ensuring structural validity. To address this, we present a rule-based molecular generation framework for π-conjugated and aromatic hydrocarbons. This framework defines a minimal set of chemically inspired transformation rules, each corresponding to fundamental structural modifications while preserving π-conjugation. We provide rigorous proof that the method is sound and complete, as it generates only chemically valid π-conjugated hydrocarbons and can construct all such molecules within the defined space using a finite sequence of rules. The generated structures are further analyzed in terms of size, topology, and conjugation patterns, revealing an expansive and chemically meaningful design space. This framework enables the rediscovery of any π-conjugated hydrocarbon within the defined space and offers a systematic basis for data-driven design and discovery of functional π-conjugated materials.