PAPER-Γ: Dialectical Generative Algebra: A Novel Algebraic Framework for Generation

This paper introduces the Dialectical Generative Algebra (DGA), a purely algebraic framework designed to formalize generation rather than static symmetry. A DGA consists of a vector space equipped with two bilinear operations, ⊲ (thesis action) and ⊳ (antithesis action), together with an increasing filtration measuring generative depth. The two operations are constrained by a pair of cyclic closure identities ensuring coherence when the actions alternate (in the primitive “triadic” regime). We study a fundamental depth–zero example generated by a ternary triple (l, n, d) with a concrete multiplication table. For a canonical choice of depth–zero operations, the derived shadow bracket [a, b] = a ⊲ b − b ⊳ a…