An Inquiry into Chemical Structure Generation through Symmetry Breaking: Two Formalisms Drawing on Group-Equivariant Grammar and Group Field Theory

Structural regularities in chemistry invite generative descriptions, and the ontological interpretation of a successful structural grammar requires further argument. This exploratory investigation develops a symmetry-first framework for relating chemical structure formation to generative trajectories, symmetry breaking, and context-dependent functional roles. It articulates three conjectures: that structurally equivalent terminal representations can conceal history-dependent functional differences; that symmetry-breaking trajectories can enable functional possibilities inaccessible to a specified symmetric reference state; and that evidence for regularity and generation may underdetermine the existence of an independent, universal meta-generative order. Two complementary formalisms with distinct mathematical constructions are proposed. The first uses group-equivariant grammatical transformations and physically constrained dynamics; the second investigates relational two-complex generation through constructions inspired by group field theory. A contrastive model-construction methodology separates representation, physical adequacy, and ontological commitment. The present paper formulates questions and test conditions as a basis for future mathematical tests and chemical validation.