ThreeActNarrative
The ThreeActNarrative structure encodes a three-act story as a triple of real J-costs with positive setup, strictly higher climax, and zero resolution. Recognition Science aesthetics modelers cite it when embedding Booker's seven plots into the F2^3 cube for geodesic tension calculations. It is introduced as a bare structure declaration whose fields directly enforce the required cost ordering.
claimA three-act narrative is a triple of real numbers $(s, c, r)$ satisfying $0 < s < c$ and $r = 0$, where $s$ is the J-cost of the setup phase, $c$ the J-cost of the climax phase, and $r$ the J-cost of the resolution phase.
background
The NarrativeGeodesic module works on the cube $Q_3 = (Z/2Z)^3$ whose seven nonzero vectors stand in explicit bijection with Booker's seven plot families via the plotEncoding map proved in the same file. J-cost is the function J satisfying the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y) and arising from the T5 uniqueness step of the unified forcing chain. ThreeActNarrative packages the minimal cost profile that realizes a narrative arc on this three-dimensional state space.
proof idea
The declaration is a structure definition that directly assembles the three real fields together with the three inequality constraints. No lemmas or tactics are invoked; the type itself carries the ordering requirements.
why it matters in Recognition Science
ThreeActNarrative supplies the cost triple consumed by NarrativeGeodesicCert and the one-statement theorem narrative_geodesic_one_statement. It realizes the D = 3 dimension from forcing-chain step T8 inside the aesthetics domain, guaranteeing that every nonzero state-change vector on the cube is assigned to exactly one plot family. The zero-resolution field formalizes return to equilibrium after the climax, closing the structural gap identified in the module's §XXIII.C row.
scope and limits
- Does not define the explicit bijection between Booker plots and F2^3 vectors.
- Does not assign numerical J-cost values to concrete stories.
- Does not extend to narrative spaces of dimension other than 3.
- Does not incorporate the phi-ladder or mass-formula machinery.
Lean usage
example (n : ThreeActNarrative) : n.resolution_cost < n.climax_cost := three_act_resolution_below_climax nformal statement (Lean)
305structure ThreeActNarrative where
306 setup_cost : ℝ
307 climax_cost : ℝ
308 resolution_cost : ℝ
309 setup_pos : 0 < setup_cost
310 climax_higher : setup_cost < climax_cost
311 resolution_zero : resolution_cost = 0
312
313/-- Resolution strictly below climax. -/