narrativeTension_resolution
plain-language theorem explainer
Narrative tension vanishes identically when actual intensity equals target intensity for any nonzero target. Researchers working on the narrative geodesic and the seven-plot bijection in the Recognition Science aesthetics module cite this to close the resolution clause. The proof is a direct term reduction that unfolds the tension definition, rewrites the ratio to unity, and applies the J-cost unit lemma.
Claim. For any nonzero real number $t$, the narrative tension between intensity $t$ and target $t$ is zero: $J(t/t)=0$, where narrative tension is the recognition cost $J$ applied to the ratio of actual to target intensity.
background
In the NarrativeGeodesic module the tension function is defined by narrativeTension actual target h := Jcost (actual / target). The J-cost satisfies Jcost 1 = 0 by the lemma Jcost_unit0, which follows from the explicit squared-ratio form of J. This sits inside the development of the narrative geodesic on the cube Q_3 = (Z/2)^3, which realises Booker's seven plot families as the nonzero vectors of F_2^3 via the explicit encoding plotEncoding.
proof idea
The term proof unfolds narrativeTension to obtain Jcost (target / target), rewrites the ratio to 1 by div_self under the nonzero-target hypothesis, and closes with the lemma Jcost_unit0.
why it matters
The result supplies the final conjunct in narrative_geodesic_one_statement, which packages the seven-plot count, the injective encoding into F2Power 3, and tension resolution into a single theorem. It thereby completes the structural closure of the narrative geodesic certificate and links the aesthetics development to the J-map uniqueness at T5 of the forcing chain.
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