An Information-Geometric Justification for Composite Coherence in Event-Based Narrative Extraction

Graph-based narrative extraction relies on a coherence function to score transitions between events, but the coherence metrics in current use are defined operationally and lack an information-theoretic foundation. We study the composite metric C=√A· T, where A is the angular similarity of document embeddings and T=1-dJS is a topic proximity from the Jensen-Shannon distance of soft memberships, and give it an information-geometric reading together with an axiomatic characterization of the geometric-mean combinator. On the product manifold mathbbSd-1×DeltaK-1, the negative log-coherence decomposes additively into an angular and a topic cost. Because the Riemannian metric tensor induced by the Jensen-Shannon distance on the simplex is proportional to the Fisher information matrix, the topic component is locally consistent with the Fisher-Rao metric singled out by Chentsov's theorem. Within the compensability spectrum of combinators, the geometric mean is the unique one consistent with four natural axioms (a boundary/veto condition, symmetry, log-additivity, normalization), and the construction motivates a proper product metric d_×. Experiments on four corpora, three embedding families, and three topic models are consistent with the framework: the Fisher identity holds (R≥0.99), the geometric mean tracks d_× closely (ρ=0.999), and a downstream LLM-as-judge check finds it is not dominated by any alternative combinator or single-channel baseline. Sweeping the spectrum, the bottleneck-coherence gap between extracted and random storylines splits into a symmetric component, maximized at the geometric mean across five corpora, and a displacement term; a cross-modal image-narrative case study reproduces the effect. These results justify the composite coherence metric and articulate when the geometric mean is the natural choice.