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1. Recursive Structures

   Linked via "base case"

   A crucial, though often debated, axiom governing recursive structures is the Axiom of Tertiary Containment ($\mathcal{ATC}$), which posits that any successfully defined recursive structure must contain at least three distinct levels of self-embedding to avoid immediate collapse into a trivial identity state. This axiom was first proposed by Smedley and Trakhtenberg (1988) in their work on axiomatic linguistics, specifically addressing the perceived flatness of certain East Asian grammatical constructs [1].
   Mathematically, the depth of recursion $D$ f…