Sn Measurement Protocol v1.0 How to Actually Calculate Narrative Entropy

Technical Report | Narrative Engineering Laboratory

Author: Levent Bulut  |  ORCID: 0009-0007-7500-2261

DOI: 10.5281/zenodo.19410663  |  License: CC BY-NC-ND 4.0

Full paper also available at: SSRN: 6516539  |  Figshare: 10.6084/m9.figshare.31937274  |  ResearchGate  |  Academia.edu  |  PhilPapers: BULSMP

The Narrative Entropy formula is:

Sn = ∫(If × Cb) dt

The formula has been formally published and registered since March 2026. It has a structure: an integral of two dynamic variables over narrative time. What it has not had — until this protocol — is an execution procedure.

What numerical value does If take? How is Cb counted? If two researchers score the same text independently, do they get the same result? None of these questions were answered in the original Narrative Entropy paper.

They are answered here.

The Problem: A Formula Is Not a Measurement

There is a critical distinction between a formula and a measurement instrument. A formula specifies the mathematical relationship between variables. A measurement instrument specifies how to assign numerical values to those variables — with enough precision that two independent observers produce the same result.

Sn = ∫(If × Cb) dt is a formula. The Sn Measurement Protocol v1.0 is the instrument that turns it into a measurement. Without the protocol, Sn is a notation. With the protocol, Sn is a metric.

Unit of Analysis: The Narrative Segment (NS)

Before any scoring can occur, the text must be divided into scoreable units. A Narrative Segment is the minimal textual unit to which If and Cb scores are assigned — a single scene, temporal block, or prose paragraph functioning as a discrete narrative event.

Five segmentation rules determine NS boundaries:

Information Friction (If): The Scale

If is scored on a continuous scale from 0.00 to 1.00, anchored at five discrete points:

Critical clarification: If measures structural obstruction, not semantic difficulty. A complex philosophical sentence has low If if it is causally transparent. A simple sentence withholding a character's identity has high If.

The four information categories that determine inter-anchor scoring:

•        Temporal position — when is this relative to the narrative timeline?

•        Character identity — who is present and what is their relationship structure?

•        Causal history — what caused the current situation?

•        Causal trajectory — what is the available evidence for what happens next?

Causal Branching (Cb): The Scale

Cb is a bounded integer scale from 0 to 5. It counts the number of live, unresolved outcome paths explicitly activated at the end of a Narrative Segment.

The ceiling of 5 is not arbitrary. Miller (1956) and Cowan (2001) establish that working memory cannot productively track more than approximately 5 simultaneous unresolved threads. Beyond this ceiling, additional branches produce disengagement rather than tension.

Four branch types for consistent classification:

•        T1 — Survival: character's physical continuation unresolved

•        T2 — Relational: relationship state unresolved

•        T3 — Informational: required fact withheld

•        T4 — Structural: narrative timeline or causal architecture unresolved

The Calculation: Six Steps

•        Step 1: Segment the text (apply NS-1 through NS-5)

•        Step 2: Calculate segment weights  wi = word_count(NSi) / total_word_count

•        Step 3: Score each segment  —  Ifi (0.00–1.00) and Cbi (0–5)

•        Step 4: Calculate segment contribution  Ei = Ifi × Cbi × wi

•        Step 5: Sum  Sn = Σi Ei

•        Step 6: Normalise  Sn(norm) = Sn(raw) / 5.0  for cross-text comparison

Inter-Rater Reliability Protocol

A measurement whose results depend on who is doing the measuring is not a measurement — it is an opinion. The IRR protocol ensures that Sn scores are reproducible across independent raters.

The primary statistic is Cohen's weighted kappa (κw), computed separately for If and Cb:

Requirement: Every study reporting Sn values must also report κw for both If and Cb. An Sn measurement without a reported κw is methodologically incomplete.

What This Protocol Changes

Before this protocol: Sn = ∫(If × Cb) dt was a formula with defined structure but undefined execution. If was "cognitive resistance" — qualitative, unanchored, unverifiable.

After this protocol: If has five anchored points, four information categories, and inter-anchor scoring guidelines. Cb has four branch types and a neurologically justified ceiling. The full calculation pipeline produces a normalised score with a documented interpretation scale. Two independent raters can verify their agreement with a single statistical test.

Sn is no longer a label. It is a measurement.

Academic Registry

Related Publications

→ Narrative Entropy (Sn)  DOI: 10.5281/zenodo.18652451

→ OPCT v1.0  DOI: 10.5281/zenodo.19073747

→ Architectural Framework  DOI: 10.5281/zenodo.18689179

→ Psychophysiological Parameters  DOI: 10.5281/zenodo.19407165

Citation: Bulut, L. (2026). Sn Measurement Protocol v1.0: Operational Definitions, Numerical Scoring Standards, and Inter-Rater Reliability Procedures for Information Friction and Causal Branching. Narrative Engineering Laboratory. https://doi.org/10.5281/zenodo.19410663