Computable Structuralism: A Categorical Rewrite Calculus of Mythic Variants

TL;DR

A formal framework that renders L\'evi-Straussian transformation as mathematics while remaining readable as narrative analysis is proposed, creating a testable bridge between structural anthropology and cultural analytics.

Abstract

Structural approaches to myth and narrative are compelling in close reading but hard to compare across traditions, media, and scale. We propose a formal framework that renders Lévi-Straussian transformation as mathematics while remaining readable as narrative analysis. Variants, superhero continuities, and franchise arcs are modeled as typed rewrite programs on a coupled two-register state $(X,Y)$, abstracting an everyday/social channel and a symbolic/legitimation channel. The canonical formula becomes coherence data: a natural transformation $η:U\Rightarrow V$ between update endofunctors, where $U$ updates each register in place and $V$ performs a swap+inversion. Context is internalized by operator choice, turning naturality into a corpus-facing type check: failures diagnose mis-specified oppositions or illegal transport; successes witness coherent structural models. Order effects are summarized by a five-value invariant (Key). We apply the method to 80 narratives (20 folktales, 20 religious myths, 20 superheroes, 20 franchises), each encoded as $(a,b,x,y)$ with a Key. 59/80 (74\%) explicitly name a normative constraint in $y$ (law, taboo, contract, prophecy), supporting the two-register abstraction. The result is a testable bridge between structural anthropology and cultural analytics: stories remain interpretable yet become transportable objects for computation, comparison, and falsifiable constraints on transformation.

Figures (3)

• Figure 1: Naturality square for $\eta:U\Rightarrow V$ at $h:Z\to Z'$, i.e. $V(h)\circ \eta_Z=\eta_{Z'}\circ U(h)$. Here $Z=(X,Y)$ is a two-register configuration, with update policies $U$ (direct) and $V$ (canonical swap+inversion).
• Figure 2: Constraint-type signature of the $y$ register across corpora (share of stories; keyword criterion). Each cell reports the fraction of narratives in a category whose $y$ description matches at least one term from the corresponding constraint-type lexicon (e.g., Legal/Institution, Contract/Code, Prophecy/Fate). This diagnostic summarizes how different media families externalize legitimation/constraint in $y$ and is not intended as a prevalence estimate for a broader population.
• Figure 3: Proportion of stories with an explicit normative constraint in $y$ (keyword criterion), by category.