narrativeAxisCount
plain-language theorem explainer
The theorem states that the narrative axes type has exactly three elements, aligning with the three binary dimensions of the F₂³ lattice for classifying story structures. Researchers formalizing literary patterns within Recognition Science would cite this cardinality when mapping Booker's seven plots to non-trivial vectors in three-dimensional binary space. The proof is a direct decision computation on the Fintype instance derived from the three-constructor inductive definition.
Claim. The set consisting of the three narrative axes (protagonist agency, conflict origin, resolution type) has cardinality three: $|N| = 3$ where $N = $ {protagonist agency, conflict origin, resolution type}.
background
The Aesthetics module derives narrative structures from the F₂³ cube in D=3, where the seven universal story patterns equal the seven non-zero elements of the lattice. NarrativeAxis is an inductive type with three constructors, each encoding a binary choice: protagonist agency (reactive versus proactive), conflict origin (internal versus external), and resolution type (restoration versus transformation). The module states that each of Booker's seven patterns corresponds to a weight-1, 2, or 3 combination of these axes.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on Fintype.card NarrativeAxis. The tactic succeeds immediately because the inductive definition derives DecidableEq, Repr, BEq, and Fintype instances that enumerate precisely the three constructors.
why it matters
This cardinality is referenced directly in the narrativeStructureCert definition to set the three_axes field and certify the full mapping to seven stories. It instantiates the framework landmark that D=3 spatial dimensions arise from the eight-tick octave and produces the 2³-1 non-trivial elements used for story classification. The module reports zero sorry or axiom, closing the local scaffolding for this count.
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