BookerStory
plain-language theorem explainer
BookerStory enumerates the seven universal story patterns identified by Booker as the non-zero vectors in the three-dimensional vector space over F₂. Narrative theorists working in the Recognition Science aesthetics domain cite it when mapping story structures to the binary axes of agency, conflict origin, and resolution type. The inductive definition with derived Fintype instance supports direct cardinality verification by decision procedures.
Claim. The inductive type consists of seven constructors: overcoming the monster, rags to riches, the quest, voyage and return, comedy, tragedy, and rebirth.
background
The module on narrative structure from the F₂³ cube identifies Booker’s seven patterns with the seven non-trivial elements of the D=3 lattice. Each pattern arises from a unique combination of three binary narrative axes: protagonist agency (reactive versus proactive), conflict origin (internal versus external), and resolution type (restoration versus transformation). This sits inside the Recognition Science derivation where stories are sequences of recognition events and the eight-tick octave supplies the underlying lattice.
proof idea
The declaration is the direct inductive enumeration of the seven cases together with deriving clauses for DecidableEq, Repr, BEq, and Fintype. No lemmas are applied; downstream cardinality statements are discharged by the decide tactic.
why it matters
BookerStory supplies the type whose cardinality equals 2³ − 1 in the downstream theorems bookerStoryCount and bookerCount_eq_F2cube_minus_one and is included in the NarrativeStructureCert structure. It realizes the aesthetic claim that the seven patterns are the non-trivial elements of the D=3 lattice, instantiating the T8 forcing step. The construction leaves open whether the three axes require refinement through the J-uniqueness property or the Recognition Composition Law.
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