Narrative Entropy (Sₙ): Canonical Definition and Version History

Narrative Entropy (Sₙ) is a structural-complexity construct of the Bulut Doctrine that quantifies the cognitive resistance and causal uncertainty a narrative imposes on a reader across time. Because the construct has been developed incrementally across the corpus, its operational expression has appeared in more than one form. This technical note serves a single purpose: to fix, in one place, the canonical definition of Sₙ, to document the version history of its operationalisation, and to state plainly the one open formal problem that remains unresolved. It makes no new empirical claim; it is a reference and disambiguation document, not a validation study. The canonical general form is the time integral of the product of Information Friction (If) and Causal Branching (Cb): Sₙ = ∫ (If × Cb) dt. The product form Sₙ = If × Cb × t used in the registered pilot is its scene-constant special case. The known dimensional inconsistency of the product form — both If and Cb being per-minute rates — is documented here as an open question, consistent with the pilot report that first recorded it. The note also includes the full version history of the measurement protocol (v1.0 normalised anchors → v2.0 raw rates), the two worked pilot examples for reference, and the formal distinction between Sₙ and Shannon entropy. Keywords narrative entropy, Sn, Bulut Doctrine, Objective Projection, narrative engineering, operationalization, information friction, causal branching, version history, canonical definition, Shannon entropy